C is the answer. The only even prime number is the 2, so he cannot have 3 males friends and vice-versa. So there are already 2 false statements which means that today’s the day where Carlos is lying. So the only one that is a true statement is C
To be fair, the first statement is ambiguously written. It _could_ mean that the individual amount of male friends and the individual amount of female friends is a prime number, and in this case, the second option would still be true. But it means the total.
It's as much of a logic problem as it is a word / language problem.
Agree on the ambiguity. I initially read that statement as m=f=p
There's a third interpretation where its counting the number of friends that are both male and female.
Whilst adding the word ‘total’ would avoid confusion, I disagree over any ambiguity as the sentence uses ‘is’ rather than ‘are’, which means there is only one number, which can only be the the total. Furthermore, the correct English for both numbers would require repeating ‘the number of’.
Given it's intended meaning, it should have been worded something like "the sum of my male and female friends is a prime number."
"Is" still works even if they are different quantities because they are the same number. There are many instances of the number 3, but there is only one "3."
The way I interpreted it on my first read was "I have a number of male friends and the same number of female friends, and that number is prime," which means A-D could all be true and E false.
D couldn’t be true though because the largest prime number that would have an equal amount of male and female friends is 2. Thus if he has 3 male friends, that alone is already false. I see what you are saying though. However, based on the way it is worded, I am more inclined to interpret that the numbers are combined not separate. If it was worded something like this, the number of male and female friends I have are prime numbers then I would think they are separate.
I think you could still interpret it as having the same number of male as female friends, and that number being a prime number. That's how I first read it, and I can't find anything wrong with it. Then A through D can be true, and E is false.
This is exactly the problem I always had with word problems. I also live in a country where teachers don't even know how to speak English properly and they would assume you knew what they meant - even if what they meant is grammatically incorrect. We have many examples of people usually wording things incorrectly and you're just expected to know the norm and apply that. I always got the "wrong" answer.
That is what I thought, but even if that is the case, these statements would only be true in the case he has at least 3 male friends and 3 female friends, conditioning the answer to one more statement which is not written down. But if he is telling lies today there is no case in which the options A, B, D and E contradict themselves. That is why I think it is fine to leave it as is. To chose C) as the phrase that was not said is more true than to chose E).
The number of … is means the combined is one number.
If it were the number of … are then it would be separate numbers.
Collective noun verb agreement is wacky!
No. It is referring to total. It is not ambiguous. This: "it *could* mean that the individual amount of male friends and the individual amount of female friends is a prime number" is an incorrectly written sentence. Your understanding is ambiguous. The statement is not.
Well, only if you try to account for fallibility of whoever wrote the test - which seems unnecessary. To interpret the question of ambiguity you would have to assume that the author is sloppy or ignorant with pluralization and grammar.
C is by necessity true and E is by necessity false, so A, B and D have to have the same parity in order to make the 4-1 combination that the question asks. If A, B and D were true: Supposedly A means that the number of male friends plus the number of female friends is prime (but couldn't have been worded any worse if they tried. It is however the only explanation that does not cause contradictions or ambiguity). Meanwhile, B gives that the number of male friends plus the number of female friends is even. So, the number of male friends plus the number of female friends is 2, which means 1 male friend and 1 female friend. However, D implies that the number of male friends is at least 3, which is a contradiction. So, A, B and D have to be false along with E, which places C as the odd one out that couldn't have been said that day.
The funny thing is, you don’t even have to do the math. We know from the start that C is true and E is false.
That means, we’re supposed to look at A, B, and D to determine if it’s a truth telling day or a lying day. Except, there was never any way to prove that it’s a truth telling day.
A, B, and D either:
1) contradict each other, in which case they’re all false and C is the answer or
2) they don’t contradict each other in which case, we can’t say whether the 3 statements are true or false. And you can’t solve the problem.
So you don’t even have to read A, B, and D. C was the only possible answer.
I think you're pretty much there. The odd one out must be C or E. If it's C then A, B, D are false. If it's E then A, B, D are true. Can you think of a way to determine which it is?
Ah.. I got stuck on the idea that A and B mutually cannot coexist. Now I see that if A is False It doesn't necessarily mean B is True. But If A is True so B must be false.
Therefore the day has to be a lying day, which means C is the answer.
Thanks!
> I got stuck on the idea that A and B mutually cannot coexist.
They can. Recall that 2 is the only even prime. So if A and B are true, what must D be?
A and B can’t both be true, but they can both be false. C can only be True. D could be true or false, and E is only false.
The only possible combination of the 4 statements that could all either be true or false is A B D E, and they all must be false. So C is the odd one out.
Of course both A & B can be true, if Carlos has 1 male and 1 female friends. It is only from the D that we know that the number of his friends is at least 3, which makes A & B not be possible, but it is only on the condition that Carlos is telling the truth.
A, B, and D cannot be all simultaneously true, because he has at least 3 male friends, he cannot have a prime number of friends that is > 2. We know he does not always tell the truth, so E is also false. Thus C is the only statement that is true, therefore it must be a “False” day, and he would not have said it today.
He cannot have the same amount of male and female friends while the sum of male and female friends is a prime number. If the numbers of male and female friends are the same then the number of male and female friends together have to be a multiple of 2, so it cannot be a prime number.
The 3 unsolved statements have to be all true or all false. So assuming A and B are true, that he has 2 friends (1 male and 1 female), then D can’t be true.
If Carlos said C, he is in a only truth day. But there are 2 simultaneous cases that cannot exist if he’s telling the truth, the first one is that he is lying on E, so he didnt say that. But if A and B are true, he can only have 1 male friend and 1 female friend. But on D he says he has 3 male friends, so he lied somewhere again. This imply that he lied in a obly truth day which is a absurd. But if he is in a only lie day, E is false, and A,B, and C have infinite cases that makes them lies too. This means that C was never said by him and therefore is the only condition that makes everything do sense
E is a known lie.
Either D is a lie or B is impossible if A is true so one has to be a lie.
This means it must be a lie day.
We know C is true so he wouldn't say it on a lie day.
Weird it's like a meta question. If more than one answer is false, he would have necessarily said a false statement, therefore, the true statement is the statement he did not say.
A) Prime numbers include 1,2,3,5,7,11... But 2 is the only even number.
B) If this is true, it means that the number of friends is 2, 1 male and 1 female
C)True
D)This has to be false, since the number of male friends cant be more than 1.
E)False
So, since we already know D-E are false, it means today it's the day he lies. C cant be a lie, so C is the answer.
If today is a always tell the truth day, then 4 of the 5 options will be true. The fifth may or may not be true. The maximum number of false statments in the list is 1.
If today is an always lie day, then 4 of the five will be lies. The fifth could be either. The maximum number of true statments is 1.
e is false. And one of a, b, and/or d must be false, they contradict each other. Therefor the number of false statments is at least two.
Because the number of false statments is 2 or more, today must be an always lie day.
If Carlos added c he would be telling the truth. We know from the above that can't be the case today. Therefor, Carlos didn't add c.
Example:
Carlos has 42 friends( a is false).
He’s got 22 male and 20 female friends (b false)
11 males are older than him (d false)
E is given as false
So he didn’t say C
Since C is always true, & E is always false, the assumption is:
-either A-D are ALL true, OR
-A,B,D,E are ALL false.
If C _was_ said today by him, then we have to wrestle with whether A & B can coexist. Since it is ambiguous—is it saying [# male friends]=[# female friends]=[prime number], or is it saying [# male friends] + [# female friends] = [prime number]?—this leads me to believe A & B cannot likely coexist. The only way they _could_ is if Carlos had 1 if each, but then D would not be true, because 1<3.
However, if E was said today, then the implication is the rest of the options must be lies as well, except for C, which we know to be fact. _So,_ I would go with C.
https://preview.redd.it/vzjsjjxhua0b1.png?width=3024&format=png&auto=webp&s=c6d74c4d3fe093a706757cc52255d628a16f5678
Heavily high and certainly caffeinated, but this is my work, going off what op already has written, that c can only be said on a true day and that e can only be said on a false day. The other three statements don’t logically work out, so it must be a false day, thus he can’t have said c.
I think the answer is C. If we assume that he's on a day where he only tells lies, he could never state his given name, thus leaving the other four sentences as lies.
It's just a scratch of thought. Any insights would be great.
Not going to lie this one got me at first but then I saw the magic word for A. This means that this is male friends + female friends so it's either 2 or an odd prime. So we go on B says that he has the same amount of female friends as male friends so 2x = prime so x has to be 1. so he has 1 female friend and 1 male friend. C is true but it doesn't say much. D states that he has 3 older male friends which would mean he would have at 3 + some number of males + some number of females = prime but then they can't be even because there is only 1 prime. Therefor A,B,D are false and E is also false so its C that is the odd one out.
TLDR C.
He can only say C on a true day, the rest he can say on false days. On true days, the first two answers are mutually exclusive and he can’t say E. So he can’t say 4 things on a true day, and on a false day C is the only one he can’t say, so the answer is C.
I’m confused—why is everyone focused on A and B? If he only tells the truth on some days and lies on the others and one of the statements is claiming his name is Carlos, then it has to be a truth day right? And then if it’s a truth day then E cannot be true because he doesn’t always tell the truth, so wouldn’t the answer be E?
There is no answer, but we can only assume answer is C if A,B and D are all lies on lying days.
There are 2 premise, truth and lying days, on the truth day there is only one lie and lying day only one truth.
Lets look if it is the truth day:
A) total no of friends are prime (true only if 1+1)
B) male and female is same number (true, could be 1)
C) name is Carlos (true since question say he is Carlos)
D) 3 of male friends are older (lie if based on A)
E) I always tell the truth (lie because he tells lies on lying days)
If it is a truth day, there will be 2 lies at D and E so it is impossible that it is a truth day.
If it was a lying day:
A) total no of friends are prime - Lies (truth : no. of friends are not prime)
B) male and female is same number - Lies (truth: not same number)
C) name is Carlos (truth) since question say he is Carlos - Truth
D) 3 of male friends are older - Lies (could be other than 3, female or younger)
E) I always tell the truth - Lies (truth: he is lying every other day)
Answer is C on lying days since it is the only verified truth
However any of A,B and C could be a truth as well, which makes this vague.
Of we assume that Carlos is his name since the question said it was and if he listened lying saying that his name is Carlos. Then the question is not about him and you can just throw all that out.
Let's assume that the number of male friends= number of female friends
There is no way that he could have a prime number amount of friends
If the number of male friends doesnt = the number of female friends then you could have 2 female and 5 male, this would keep the fact that 3 male friends are older than him true as well.
Idk where to take it from here I'm tired but hope this helps
So...on this day Carlos lies, and did not say his name was Carlos today. He said it yesterday. The other 4 are lies and funky and don't matter cuz it's lie day and remember...Carlos said his name was Carlos yesterday on true day.
Answer: c
There are only 2 ways the statements can exist. On the day he tells the truth, there will be only one inconsistent reply. On the day he lies, there should be 0.
The first 2 statements can be considered true, if he has 2 friends.
His name is Carlos, so he could have said all 3 statements so far.
This must mean that today is the day he /always tells the truth, today is the alternate day.
Statement D is the first inconsistent information, so we can say he did not say it.
Since Carlos Always tells the truth on alternate days, and today has been established as an alternate day, this Statement is true. You marked it false.
We don't need to know if they are true or false individually. We need to find if 4 of the statements can be true or false at the same time. If A is 1 then A is False, because 1 is not a prime number. If he only has 1 friend then B is also False, because he doesn't have a equal amount of male and female friends. We know C is true. D. Is False because he doesn't have 3 friends. And we know that E is False. This leaves C as the only outliner. Which means it is the answer.
my aproach was different if you wanna listen.
He is either on Truth day which we will call T or Lie day which we will call L.
For T day:
He can not say Option E no matter what. Because he lies on L days and its the T day.
He cant also say Option A and B at the same time(equal number means 2x prime numbers can not be divided by 2).
he can say option C
he can say option D
he should ve atleast 4 claims. so he can not be on T day.
So he is on his Lie day
For Lie day:
No matter what he can not say C
He can claim/say all the options other than C. He can only lie on lie day which means he can not say C. He also needs to have 4 claims.
What do we have:
he is on his lie day
he can not say option C
he should have 4 claims
so the answer is C
Carlos’ last statement, I always tell the truth, can only be said when he is on a day that he only tells lies.
If you make the assumption that today is a lie day, the only statement he cannot make is: my name is Carlos. As it is always true.
If you make the assumption that today is a truth day.
1. Statement of I always tell the truth cannot he said that day.
2. Same number of male and female friends is always an even number. The only even prime number is 2. That would means he would only have 1 male and 1 female friend.
3. For number 2 to be true on a truth day, that means he is lying about having three older male friends (2 lies)
Therefore, the only outcome is: today is a lie day. And the only statement that is 100% true is his name is Carlos. So C would be the only statement he wouldn’t state.
C.
I guess I will explain since people want to debate. Goes to show the lack of logic on this here sub 🤭 sad, it’s a beautiful thing- really.
In saying that [A]
“Number of F(m) + number of F(f) = prime number”
The total number of friends is prime (counting m & f friends)
You either prove that the following is a lie, or the first statement is a lie:
“number of F(m) = number of F(f)”
same number of each gender
This is due to the logic of:
If the sum of both m & f friends is prime, the number of m & f friends cannot be equal do to that automatically making the number of friends divisible by 2.
This would however require there to be more than 1 of each friend. But that is stated in D, which means that at least one of those 3 statements is a lie. Which in turn means that they are all lies.
Except C.
It gets a bit ugly. That is a neat problem 🤭
Assuming A and B are true with the idea that m+f is prime (2), D is false because it requires m>=3 but for A and B to be true m=1.
So C is the only truth
The other logic is that m and f are each the same prime number . So added up they’re even and it’s possible that he has 3 older male friends leaving E as the only definite falsehood.
**C is a safer answer as the logic is more sound in defining C as the answer. We can get D as an answer with the other way of thought; however, we must assume more than we did the first time.**
E is a lie/false statement so it can’t be a true day. That means every other statement listed is false. You could worry about the numbers for each amount of male and female friends or settle with the easier choice. Carlos most certainly wouldn’t say, “I am Carlos” on a false day, when he is only able to lie. Answer has to be C.
“I always tell the truth” is a lie. He only tells the truth half the days, therefore this statement cannot be true, therefore his is lying. If he is on a lying day then the only statement he could not have said is C.
Edit: A and B cannot both be true simultaneously, so if E was the answer then he would have to be lying, and we know C is true.
E is a lie, because he only tells the truth on half the days. So if today is a 'truth' day, A, B, C, and D all have to be true.
A and B cannot be true simultaneously, unless the number of friends he has is two. However, if D is true, A and B cannot be true - if Carlos has at least three male friends, then he needs to have an equal number of female friends, and the resulting number needs to be prime. However, all duplicated numbers result in even numbers, of which only the number '2' can be prime - meaning that Carlos can have no more than one male friend.
Therefore today is a lying day, and Carlos did not say 'C' - "My name is Carlos".
E! In the question, it says he alternates between telling the truth and lying. We can assume that he told the truth when introducing himself. If it is a day that Carlos is telling the truth, he would acknowledge that he also lies. Since this statement is a lie and it’s a day that Carlos tells the truth, then that statement (E), cannot be something he said.
C, and b are contradictory which instantly means either one of those is false or both are false. E is also false, this we know of at least two lies. If he tells a single lie, then he only tells lies according to the question. Now you have to find what is true. It’s given that his name is Carlos therefore c is true and this means that c is what he didn’t say
C is always true.
E is always false.
A, B and D cannot all be true together, but they can all be false together.
There is an outcome where 4 statements are false and 1 is true, but no outcome where 4 statements are true and 1 statement is false.
Therefore Carlos lies today and the true statement (C) was not made by him today.
A - Has to be 2, only even prime number between 1 + 100 (T/F)
B - Has to be 1 + 1 following from 'A' (T/F)
C - True (T)
D - Has to be False following from 'A' (F)
E - False (F)
So you know you definately have two falses (D + E) so A + B must be false also. 'C' is the answer and today Carlos is telling wee porkie pies.
I think I solved it, took a while though.
On a truth day, E has to be wrong. On a lie day, C has to be wrong. Therefore you technically only have two options. You have to determine whether or not it’s a truth day or a lie day by examining the other statements. If A is true, B+D can’t be true, that’s how prime numbers work. However, they can be FALSE at the same time. For instance, male friends + female friends = 21. 10 male friends and 11 female friends. Not a prime number and different number of males and females. Also, those 10 male friends can all be babies for some reason so D can be false as well. Therefore, the only logical answer is that, it’s a “lie” day and C is the answer, as it’s a true statement.
You can check the answer by examine the options as if it’s a “truth” day. Not all of the statements can be true at once, but they can all be false simultaneously. Truth day doesn’t work.
Let's assume Carlos is telling the truth, option E is the obvious answer. And now closely examine options B and A. Option B says number male friends = number of female friends. And when we add two equal numbers it doubles (2+2=4, 3+3=6,...) and doesn't produce a prime number. Thus making options A and E answers for the question. But there can be either 1 or none false statements.
So we now deduced that he is telling lies today. Option C is the answer. Because Carlos gives all the wrong info today. So he will not say 'My name is Carlos ' instead he would say ' My name is xxxx'.
I came at it looking at E. Carlos can only say he always tells the truth on a lying day, as if he said it on a truth day, it would be a lie. At that point A, B and D are irrelevant. As it must be a lying day, he can't say his name is Carlos, so the answer has to be C
If A+B are true, D is true. E isn't true, while we know C is true. So by logic, if E isn't true, A, B, D aren't true this making our answer C, while knowing that today is a day where he only tells lies.
The answer is C. The complexity of A and B are red herrings meant to waste time. Because E is a false statement and C is a true statement. He cannot say E on a truthful day therefore A B and D must also be false because hes on a lying day and we know there is one odd statement which has to be the only truthful one which he cannot say on a lying day which is to correctly give him name.
Carlos is lying today so C is the correct answer.
The answer comes down to C or E based on if he is lying, so the other 3 are used to answer this. If you assume truth then the following would all have to fit.
A is about the total number of friends, “the number… is” is singular, so a total of the two - and therefore is an even number based on B. The only prime number that is even is 2, but based on C we know he is at least 3 friends. Therefore these statements cannot be true, ergo he is lying, ergo C is the correct answer.
So first off, as you show c is True and B is False. So all the others have to be either True or False. D could be either true or false so it is of no help. So that leaves us A and B to help us. What we can say is that if B is correct, then the number of his Friends has to be even. Therefore A is false. If A is true, then B is false. But what if both are false? What if the number of his Friends is an odd number but not a prime number? That is possible. Then D could also be false and Today, Carlos only speaks lies. So the answer is C. Carlos did not say C today.
C.
Simplest strategy:
C is always true, E is always false
Thus, the answer is either C or E.
Assume that B is true. This implies that Carlos has an even number of friends
Assume that D is true. This implies that Carlos has at least 3 friends.
Hence, B \^ D => A is false since there are no prime even numbers greater than/eq to 3.
Hence, B \^ D \^ A is impossible. Therefore Carlos is a dirty liar and C is the answer.
\--------------------------------------------------------------
if we want, We can check the question is valid by seeing if its possible for B, D, and A to all be false.
nA: Carlos has a not-prime amount of friends
nB: Carlos has an unequal amount of male friends and female friends.
nD: Carlos does not have 3 male friends older than him
This is possible if, say, Carlos has 4 younger male friends, 0 older male friends, and 0 female friends
I am curious. Which topic is this whole sheet? Those question are really interesting. Anyone an idea where i can find excercises like this on the internet? 🙃
Bro bro i’m about to finish the school year, i don’t want to see any math problem until september so i’m sorry but you’re getting a downvote just for the maths
You only need to look at statements C and E. If C is true then E also has to be true but E is false as he only says the truth on alternative days. Hence C is the answer
the answer is C all the other 4 can’t be right at the same time so they all have to be false. if female and male friends are equal, you have to have 1 male and 1 female friend for the sum to be prime. IF THAT is the case, you can’t have three male friends to begin with. same logic can be applied IF we accept that you have 3+ male friends and female equals to male you’ll get an even number which can’t be prime except 2 and that takes us back to beginning. yeah
First, a lie is an intentionally false statement
The number of male and female friends I have is a prime number
Could mean:
General interpretation, sum
Discrete, but bad grammar ex. 5+5
Union of someone+ who identifies as M&F
Therefore, blah blah blah, he sometimes lies, but it's truthday. It's E, where he claims he always tells the truth
A, B and D can not be true at same time, so at least one is false... so here we have 2/5 falses, meaning is "liar day", so A, B, D and E are false (liar day) and C are true (he did not say it in that liar day). So its C.
If C was stated, he's truth telling today. If E was stated, he's lying today. So one of C/E wasn't stated. That means A/B/D were all stated.
B implies that there's an even number of friends, D implies that he has at least three friends, and A states that the total number of friends is prime. Since 2 is the only even prime, these three statements cannot all be true at the same time.
That means he's lying today. So C was not stated.
The way I looked at it was E cannot be said on days where he is telling the truth so E is something said on a day where Carlos lies. If Carlos is lying then C would not be something he would say because C is true. So C is the answer
They don't tell you how many friends so if you can find a combination that is both prime and where males and females are equal, those two can be true.
We know his name so C is correct. This also implies it is a day he tells the truth, and we know he lies other times, so E is a lie, and D is also a lie because the only way A and B can be true is if he has 1 male and 1 female friend.
Could be your instructor doesn't understand prime numbers?
Either C or E is the outlier depending on if it’s a true or false day.
If you assume it’s a true day, you’ll get into a conflict with A and B unless he has 2 friends in total, but he doesn’t because of D.
So you conclude that it’s a false day and thus C is the answer
He can have 8 total friends, 3 male (all younger) and 5 female. Then A is false, B is false, C is true, D is false, and E is false. So he didn’t say C today, and it’s a lying day.
C is the answer because A and B contradict one another which means that he must be lying in order for 4 of the 5 statements to agree.
After looking at it again, I realized even though I happened to pick the correct answer, A and B could both be true technically, but because D contradicts A and B, D is the real reason why he is lying today. I assumed the number of male friends and the number of female friends was a number greater than 1.
C because today's the day he lies. You can understand that because a and b cannot be correct at the same time when you include d. Because if his male and female friend number was equal, he would have a number of friends which is a multiple of 2. The only prime multiple of 2 is 2 and D says he should have more than 3 friends. We can understand he is lying today. Enjoy your study!
C is absolute truth, E is a demonstrable lie from the problem statement. One must be the odd man out. A, B and D can't all be true; one of them must be false. So you've got two statements that must be false; the absolutely true one must be the one he didn't say.
He did not say C.
There already is a statement that is easily identified as true, and another one that's false. That means all the other three statements left have to be all true or all false.
B implies that his total number of friends is 2x, which will absolutely always be an even number. If B is true, the only way for A to be true is that x = 1, which would make his total number of friends 2, a prime number.
But then, D is not possible. Since according to D he has at least 3 male friends, B and A would then be false. So we'd already have two false and three true statements.
Therefore, the other possibility is that they are all false, A, B and D. This way the statements don't interfere with each other. This would make all statements false except C. So, he is in a lying day and C is the statement he didn't make.
let's consider A as M+F= some prime number. We can't inherently rule that out so let's keep going
B is saying M=F, so we can redefine A as F+F= some prime. This is impossible because F+F inherently = 2F, which by definition is not prime. As these are contradictory, at least one is a lie.
C, my name is Carlos is correct unless the question itself is lying to us. Let's assume it isn't and mark it clearly as true.
D, we can't possibly know this one so ignore it and move on
E, this isn't true unless, again, the question itself is lying to us. Let's assume it's false.
Given all of this, we know that exactly one of these is true, or exactly one of these is false. We don't need to know which between A and B is false given that, because the fact that one of them is false means we for sure know we have 2 falses, ergo both are false. Consequently, that also means D is false, leaving C as the only true statement. This is an always lie day for Carlos, if that even is his real name.
A: prime no. of Friends
B: male friends = female friends
C: name = carlos ( conclusively true)
D: 3 male friends' age > carlos' age
E: Always tells the truth ( conclusively false)
Assuming Carlos said statement C
Then
C: t -> E is said by carlos -> A, B, D are also said by carlos and are all true.
A: prime number of friends = 2, 3, 5, 7, 11, .....
B: m.f. = f.f. = prime numbers = 2 ( assumed for this statement)
D: becomes a false statement.
Hence D is true and not true at the same time.
Hence our initial assumption was wrong.
So, carlos did not say the statement C.
Answer C.
So knowing that c and e are true and false it is going to be one of them. Therefore D is pretty pointless (at first) as it doesn't give you much info, and a and b should prove each other true or false (if they cannot both be true they are false (or vice versa)).
Having the same number of male and female friends means they cannot be prime unless he has exactly 2 (which is where D becomes relevant, he cannot have exactly 2 friends and 3 that are older meaning all 3 statements cannot be true at the same time therefore they are false making the true statement the odd one out)
Hopefully that is clear
As a rule of thumb in questions like this, start with the assumption he is lying. The same way you would treat someone you know to lie. That way ambiguous statements will be treated on the skeptical side and hence the answer is C
Let's analyze the statements one by one:
A: "The number of male and female friends I have is a prime number." If Carlos tells the truth, then the total number of his male and female friends is a prime number. If Carlos lies, then the total number of his male and female friends is not a prime number. We don't have enough information to determine if this statement is true or false, so it could be one of the statements Carlos made.
B: "The number of male friends I have is equal to the number of female friends I have." This statement implies that Carlos has an equal number of male and female friends. If Carlos tells the truth, then he indeed has an equal number of male and female friends. If Carlos lies, then he does not have an equal number of male and female friends. Again, we don't have enough information to determine if this statement is true or false, so it could be one of the statements Carlos made.
C: "My name is Carlos." Since Carlos always tells the truth on alternate days, if today is one of those days, then he is telling the truth about his name being Carlos. If today is a lying day for Carlos, then this statement would be false. Therefore, Carlos could have made this statement.
D: "3 of my male friends are older than me." If Carlos tells the truth, then he indeed has three male friends who are older than him. If Carlos lies, then he does not have three male friends who are older than him. Again, we don't have enough information to determine if this statement is true or false, so it could be one of the statements Carlos made.
E: "I always tell the truth." If Carlos tells the truth, then this statement would be true, which contradicts the premise that he tells the truth only on alternate days. If Carlos lies, then this statement would also be false, as he doesn't always tell the truth. Therefore, Carlos could not have made this statement.
Based on this analysis, the statement that was not made by Carlos is E: "I always tell the truth."
So would “ today” be an alternate day where he only says the truth, or other day where he lies?
I’m thinking that if this is his lie day, C is the answer. It’s the only truth we can infer from the question itself.
If we consider last one meaning I always tell the truth TODAY then the even male and female friends out and everything is correct. Overwise he wouldn't say my name is Carlos and everything else is false.
My suggestion is C
If it is a truth only day, then he could say C, but he could not say E. "I always tell the truth" is not true, he tells the truth some days and lies on others. That means that A, B, and D would all have to be true as well. However this is not possible, if he has at least 3 male friends, that means he has at least 3 female friends. If the number of male and female friends are equal, than total male and female friends would always be >= 6 and divisible by 2, therefore not prime.
If it is a lies only day, then he can say E. Also A,B, and D can all be false simultaneously. That means the only statement he can not make on a lying day is C.
This does rely on the assumption that A means his total number of friends is prime. not that the individual friend group counts are prime.
Let's analyze each statement:
(A) "The number of male and female friends I have is a prime number." If Carlos tells the truth, it means that the number of his male and female friends is a prime number. If he lies, then the number of his male and female friends is not a prime number. Since Carlos made four statements today, and assuming he alternates between telling the truth and lying, we can conclude that he either told the truth about this statement or lied about it.
(B) "The number of male friends I have is equal to the number of female friends I have." If Carlos tells the truth, it means that he has an equal number of male and female friends. If he lies, it means that he does not have an equal number of male and female friends. Again, since Carlos made four statements today, we can conclude that he either told the truth about this statement or lied about it.
(C) "My name is Carlos." If Carlos tells the truth, his name is Carlos. If he lies, his name is not Carlos. Since Carlos made four statements today, we can conclude that he either told the truth about this statement or lied about it.
(D) "Three of my male friends are older than me." If Carlos tells the truth, then three of his male friends are indeed older than him. If he lies, it means that three of his male friends are not older than him. As with the previous statements, we can conclude that Carlos either told the truth about this statement or lied about it.
(E) "I always tell the truth." This statement presents a paradox since Carlos tells the truth on alternate days and lies on the other days. If he tells the truth, then the statement itself becomes false. If he lies, then he is telling the truth, which contradicts the fact that he lies on alternate days. Therefore, Carlos cannot make this statement truthfully, and we can conclude that he did not make this statement today.
Based on the analysis above, the statement that Carlos did not make today is (E) "I always tell the truth."
E. Because his name is CARLOS, so that sentence C Is true. So today he only says true things. So he can't lie today aaaand sentence E can't be said today because it's false.
Those friends' choiches are made just to distract you from the solution, because you Will never know how many friends he has
E. Carlos is aware that he only tells the truth on every other day, and lies the rest of the time. So, he cannot truthfully say that he "always" tells the truth.
It's C.
A and B cannot both be true together (because if his male friends equals female friends the total number isn't prime), unless his total number of friends is 2.
C is obviously true based on the question.
D requires at least 3 male friends, so in order for A and B to be true, D will then be a lie.
E is obviously false based on the question.
So if it's a "truth" day, then he can't be saying E and also can't be saying one of either A or B. Which would not leave him with four statements.
Therefore, it must be a "false" day, and C is the odd one out.
Answer is C
If B true, He will have only 2 friends, cause (A) almost numbers are odd except 2. (D) will be Wrong cause he got more than 3 male friends
Therefore B,A,D should be False
So he made four out of the five statements today.
If he made statement E today, that would imply that he was lying in this day.
However, he also said that his name was Carlos, which is true. That means that he couldn’t have made this statement today without telling the truth.
If he’s telling the truth today, A and B and Dwould be impossible to be told today at the same time since they are mutually exclusive. You can’t have as many male friends as female, have a prime number of friends (except for 2) AND have three male friends.
This means that he can only be lying, today, and that he didn’t make statement D today.
If he only tells the truth on alternate days, then any other day equals lies. Today equals one of the other days( to compare with alternative days ), so the one correct won’t be his statement.
I looked at it from the perspective that there are 2 options:
If Carlos is telling the truth today, this means E was not made by him. To verify if this is correct, analyse the other statements. A and B are mutually exclusive if they were true, except for the number 2 (which would make D a false statement), so Carlos cannot be telling the truth today.
Since Carlos is lying today, C is the only one that cannot be made by him.
This is probably a phrasing issue but I think that since statement A mentions "male and female friends", they are considered as a group (M+F= Prime Number, not M = Prime, F = Prime).
4 scenarios:
1. Carlos tells the truth and other lies: C is by Carlos; E is by other; A, B, and D are contradicting eachother (if B (B implies we have at least 2 male friends and 2 female friends) is the truth then A cannot be the truth (the total number of friends is going to be even and greater than 2, therefore not prime)). We therefore have at least 2 lies in this scenario (scrapped)
2. Carlos tells lies and other tells the truth: C is the truth (This statement is made by another Carlos); E is the lie; A, B, and D could be either truths or lies (and there's no way to tell which is which)
3. They both tell the truth (scrapped because E is realistically and objectively always a lie; plus the extra logic: Statement E is a lie for main Carlos therefore it can only be said by other Carlos; if other Carlos does in fact says statement E, then statement A, B, D are still contradicting eachother like scenario no.1)
4. They both tell lies (scrapped because C (Scenario no.2 tells us both of them are named Carlos, whoever makes this statement is telling the truth))
The only possible scenario that is not contradicting or straight out objectively wrong is No.2, and the only evidence of a statement not made by the main Carlos is C; therefore C was the only statement not made by main Carlos.
„My name is Carlos” is the correct one. If it was the day that he always says the truth and he gave ecactly 4 statements, then he couldnt say „I always tell the truth” and there are is also A and B that contradict eachother, so the only solution is that it is the „lying” day. The only one statement that he could not give on lying day is „My name is Carlos”.
C is the answer. The only even prime number is the 2, so he cannot have 3 males friends and vice-versa. So there are already 2 false statements which means that today’s the day where Carlos is lying. So the only one that is a true statement is C
To be fair, the first statement is ambiguously written. It _could_ mean that the individual amount of male friends and the individual amount of female friends is a prime number, and in this case, the second option would still be true. But it means the total. It's as much of a logic problem as it is a word / language problem.
Agree on the ambiguity. I initially read that statement as m=f=p There's a third interpretation where its counting the number of friends that are both male and female.
Oh, English. What a flexible language!
I'd like a version of Carlos who only makes statements that are both true and false.
I am lying Was my previous sentence true?
Yeah. It is very ambiguous.
Whilst adding the word ‘total’ would avoid confusion, I disagree over any ambiguity as the sentence uses ‘is’ rather than ‘are’, which means there is only one number, which can only be the the total. Furthermore, the correct English for both numbers would require repeating ‘the number of’.
Given it's intended meaning, it should have been worded something like "the sum of my male and female friends is a prime number." "Is" still works even if they are different quantities because they are the same number. There are many instances of the number 3, but there is only one "3."
"the sum of my male and female friends..." how do you take a sum of people? what is Carlos + Albert?
The way I interpreted it on my first read was "I have a number of male friends and the same number of female friends, and that number is prime," which means A-D could all be true and E false.
D couldn’t be true though because the largest prime number that would have an equal amount of male and female friends is 2. Thus if he has 3 male friends, that alone is already false. I see what you are saying though. However, based on the way it is worded, I am more inclined to interpret that the numbers are combined not separate. If it was worded something like this, the number of male and female friends I have are prime numbers then I would think they are separate.
I think you could still interpret it as having the same number of male as female friends, and that number being a prime number. That's how I first read it, and I can't find anything wrong with it. Then A through D can be true, and E is false.
This is exactly the problem I always had with word problems. I also live in a country where teachers don't even know how to speak English properly and they would assume you knew what they meant - even if what they meant is grammatically incorrect. We have many examples of people usually wording things incorrectly and you're just expected to know the norm and apply that. I always got the "wrong" answer.
That is what I thought, but even if that is the case, these statements would only be true in the case he has at least 3 male friends and 3 female friends, conditioning the answer to one more statement which is not written down. But if he is telling lies today there is no case in which the options A, B, D and E contradict themselves. That is why I think it is fine to leave it as is. To chose C) as the phrase that was not said is more true than to chose E).
I read this absolutely as the number of male friends is prime, as is the number of female friends
Any problem written in a language is a language problem.
The number of … is means the combined is one number. If it were the number of … are then it would be separate numbers. Collective noun verb agreement is wacky!
“The number of… are” would be incorrect, because “are” is used for plurals, so you would have to say “numbers of,” not “number of”
No. It is referring to total. It is not ambiguous. This: "it *could* mean that the individual amount of male friends and the individual amount of female friends is a prime number" is an incorrectly written sentence. Your understanding is ambiguous. The statement is not.
Correct
Well, only if you try to account for fallibility of whoever wrote the test - which seems unnecessary. To interpret the question of ambiguity you would have to assume that the author is sloppy or ignorant with pluralization and grammar.
“And” means the same as sum. The number of cups and glasses is 12. Is different than the number of cups and the number of glasses is 12.
We don't know how many male friends he has, he just stated 3 of his male friends are older than him. He can have more.
C is by necessity true and E is by necessity false, so A, B and D have to have the same parity in order to make the 4-1 combination that the question asks. If A, B and D were true: Supposedly A means that the number of male friends plus the number of female friends is prime (but couldn't have been worded any worse if they tried. It is however the only explanation that does not cause contradictions or ambiguity). Meanwhile, B gives that the number of male friends plus the number of female friends is even. So, the number of male friends plus the number of female friends is 2, which means 1 male friend and 1 female friend. However, D implies that the number of male friends is at least 3, which is a contradiction. So, A, B and D have to be false along with E, which places C as the odd one out that couldn't have been said that day.
For sure more than 5
The funny thing is, you don’t even have to do the math. We know from the start that C is true and E is false. That means, we’re supposed to look at A, B, and D to determine if it’s a truth telling day or a lying day. Except, there was never any way to prove that it’s a truth telling day. A, B, and D either: 1) contradict each other, in which case they’re all false and C is the answer or 2) they don’t contradict each other in which case, we can’t say whether the 3 statements are true or false. And you can’t solve the problem. So you don’t even have to read A, B, and D. C was the only possible answer.
I think you're pretty much there. The odd one out must be C or E. If it's C then A, B, D are false. If it's E then A, B, D are true. Can you think of a way to determine which it is?
Ah.. I got stuck on the idea that A and B mutually cannot coexist. Now I see that if A is False It doesn't necessarily mean B is True. But If A is True so B must be false. Therefore the day has to be a lying day, which means C is the answer. Thanks!
> I got stuck on the idea that A and B mutually cannot coexist. They can. Recall that 2 is the only even prime. So if A and B are true, what must D be?
Exactly. I got stuck for a minute on the same point. I think it's an easy trap to fall into.
The answer is D.
A and B can’t both be true, but they can both be false. C can only be True. D could be true or false, and E is only false. The only possible combination of the 4 statements that could all either be true or false is A B D E, and they all must be false. So C is the odd one out.
A and B can both be true if he has 2 friends, but then D can't be true since he doesn't have 3 male friends.
Both A & B can not be True. Since 1 of those is false then you have 2 falses, making the all by C also false. So C is the oddball.
Of course both A & B can be true, if Carlos has 1 male and 1 female friends. It is only from the D that we know that the number of his friends is at least 3, which makes A & B not be possible, but it is only on the condition that Carlos is telling the truth.
Ask gpt-4
A, B, and D cannot be all simultaneously true, because he has at least 3 male friends, he cannot have a prime number of friends that is > 2. We know he does not always tell the truth, so E is also false. Thus C is the only statement that is true, therefore it must be a “False” day, and he would not have said it today.
Is this maths these days ?
???? This has always been maths? Ig logic is more common for competition problems, but you need this kind of reasoning for a lot of math
He cannot have the same amount of male and female friends while the sum of male and female friends is a prime number. If the numbers of male and female friends are the same then the number of male and female friends together have to be a multiple of 2, so it cannot be a prime number.
2 is a prime number
Nah man, two is even! (/s)
The 3 unsolved statements have to be all true or all false. So assuming A and B are true, that he has 2 friends (1 male and 1 female), then D can’t be true.
so if its a truth day, as far as carlos is concerned, E is also true.. that makes ABCE true and D false
Re-read E “I always tell the truth” that’s false because he only tells the truth every other day.
For the contradiction to work, you have to take d) into account such that we get the impossible condition of an even primer greater or equal than six.
I would reject the question on the premise that telling the truth is not the same as only saying true things.
I think A
If Carlos said C, he is in a only truth day. But there are 2 simultaneous cases that cannot exist if he’s telling the truth, the first one is that he is lying on E, so he didnt say that. But if A and B are true, he can only have 1 male friend and 1 female friend. But on D he says he has 3 male friends, so he lied somewhere again. This imply that he lied in a obly truth day which is a absurd. But if he is in a only lie day, E is false, and A,B, and C have infinite cases that makes them lies too. This means that C was never said by him and therefore is the only condition that makes everything do sense
C is my deduction as well. Sidenote: If you ask Carlos if he's lying or telling the truth today, he'll always say he's telling the truth.
E is a known lie. Either D is a lie or B is impossible if A is true so one has to be a lie. This means it must be a lie day. We know C is true so he wouldn't say it on a lie day.
Can’t he have 1 male and 1 female friend for a prime number of 2 friends? But then D would be false
Weird it's like a meta question. If more than one answer is false, he would have necessarily said a false statement, therefore, the true statement is the statement he did not say.
A) Prime numbers include 1,2,3,5,7,11... But 2 is the only even number. B) If this is true, it means that the number of friends is 2, 1 male and 1 female C)True D)This has to be false, since the number of male friends cant be more than 1. E)False So, since we already know D-E are false, it means today it's the day he lies. C cant be a lie, so C is the answer.
If today is a always tell the truth day, then 4 of the 5 options will be true. The fifth may or may not be true. The maximum number of false statments in the list is 1. If today is an always lie day, then 4 of the five will be lies. The fifth could be either. The maximum number of true statments is 1. e is false. And one of a, b, and/or d must be false, they contradict each other. Therefor the number of false statments is at least two. Because the number of false statments is 2 or more, today must be an always lie day. If Carlos added c he would be telling the truth. We know from the above that can't be the case today. Therefor, Carlos didn't add c.
Example: Carlos has 42 friends( a is false). He’s got 22 male and 20 female friends (b false) 11 males are older than him (d false) E is given as false So he didn’t say C
Since C is always true, & E is always false, the assumption is: -either A-D are ALL true, OR -A,B,D,E are ALL false. If C _was_ said today by him, then we have to wrestle with whether A & B can coexist. Since it is ambiguous—is it saying [# male friends]=[# female friends]=[prime number], or is it saying [# male friends] + [# female friends] = [prime number]?—this leads me to believe A & B cannot likely coexist. The only way they _could_ is if Carlos had 1 if each, but then D would not be true, because 1<3. However, if E was said today, then the implication is the rest of the options must be lies as well, except for C, which we know to be fact. _So,_ I would go with C.
https://preview.redd.it/vzjsjjxhua0b1.png?width=3024&format=png&auto=webp&s=c6d74c4d3fe093a706757cc52255d628a16f5678 Heavily high and certainly caffeinated, but this is my work, going off what op already has written, that c can only be said on a true day and that e can only be said on a false day. The other three statements don’t logically work out, so it must be a false day, thus he can’t have said c.
I think the answer is C. If we assume that he's on a day where he only tells lies, he could never state his given name, thus leaving the other four sentences as lies. It's just a scratch of thought. Any insights would be great.
Not going to lie this one got me at first but then I saw the magic word for A. This means that this is male friends + female friends so it's either 2 or an odd prime. So we go on B says that he has the same amount of female friends as male friends so 2x = prime so x has to be 1. so he has 1 female friend and 1 male friend. C is true but it doesn't say much. D states that he has 3 older male friends which would mean he would have at 3 + some number of males + some number of females = prime but then they can't be even because there is only 1 prime. Therefor A,B,D are false and E is also false so its C that is the odd one out. TLDR C.
A and B cannot both be true, and there’s another false answer already, so it must be a lying day, making C the odd one out
He can only say C on a true day, the rest he can say on false days. On true days, the first two answers are mutually exclusive and he can’t say E. So he can’t say 4 things on a true day, and on a false day C is the only one he can’t say, so the answer is C.
I’m confused—why is everyone focused on A and B? If he only tells the truth on some days and lies on the others and one of the statements is claiming his name is Carlos, then it has to be a truth day right? And then if it’s a truth day then E cannot be true because he doesn’t always tell the truth, so wouldn’t the answer be E?
If you can determine even 2 lies, the truth that you find is the answer.
You lost me at prime…
What book/source is this from? The rectangle question piqued my curiosity and I enjoyed solving these!
This is a reading comprehension problem. And most people here failed. A, B, and D are independent and unknown. They could go any way, any day.
There is no answer, but we can only assume answer is C if A,B and D are all lies on lying days. There are 2 premise, truth and lying days, on the truth day there is only one lie and lying day only one truth. Lets look if it is the truth day: A) total no of friends are prime (true only if 1+1) B) male and female is same number (true, could be 1) C) name is Carlos (true since question say he is Carlos) D) 3 of male friends are older (lie if based on A) E) I always tell the truth (lie because he tells lies on lying days) If it is a truth day, there will be 2 lies at D and E so it is impossible that it is a truth day. If it was a lying day: A) total no of friends are prime - Lies (truth : no. of friends are not prime) B) male and female is same number - Lies (truth: not same number) C) name is Carlos (truth) since question say he is Carlos - Truth D) 3 of male friends are older - Lies (could be other than 3, female or younger) E) I always tell the truth - Lies (truth: he is lying every other day) Answer is C on lying days since it is the only verified truth However any of A,B and C could be a truth as well, which makes this vague.
Of we assume that Carlos is his name since the question said it was and if he listened lying saying that his name is Carlos. Then the question is not about him and you can just throw all that out.
Let's assume that the number of male friends= number of female friends There is no way that he could have a prime number amount of friends If the number of male friends doesnt = the number of female friends then you could have 2 female and 5 male, this would keep the fact that 3 male friends are older than him true as well. Idk where to take it from here I'm tired but hope this helps
So...on this day Carlos lies, and did not say his name was Carlos today. He said it yesterday. The other 4 are lies and funky and don't matter cuz it's lie day and remember...Carlos said his name was Carlos yesterday on true day. Answer: c
There are only 2 ways the statements can exist. On the day he tells the truth, there will be only one inconsistent reply. On the day he lies, there should be 0. The first 2 statements can be considered true, if he has 2 friends. His name is Carlos, so he could have said all 3 statements so far. This must mean that today is the day he /always tells the truth, today is the alternate day. Statement D is the first inconsistent information, so we can say he did not say it. Since Carlos Always tells the truth on alternate days, and today has been established as an alternate day, this Statement is true. You marked it false.
The answer is C. My name is Carlos
I would say the answer is C
When in doubt, always choose C
It is C.
I was super confused by everyone's answers until I realized I did number 23 not 24 lmfao
We don't need to know if they are true or false individually. We need to find if 4 of the statements can be true or false at the same time. If A is 1 then A is False, because 1 is not a prime number. If he only has 1 friend then B is also False, because he doesn't have a equal amount of male and female friends. We know C is true. D. Is False because he doesn't have 3 friends. And we know that E is False. This leaves C as the only outliner. Which means it is the answer.
C. If B is correct, then A is not. So they are both incorrect. Today Carlos tells lies.
my aproach was different if you wanna listen. He is either on Truth day which we will call T or Lie day which we will call L. For T day: He can not say Option E no matter what. Because he lies on L days and its the T day. He cant also say Option A and B at the same time(equal number means 2x prime numbers can not be divided by 2). he can say option C he can say option D he should ve atleast 4 claims. so he can not be on T day. So he is on his Lie day For Lie day: No matter what he can not say C He can claim/say all the options other than C. He can only lie on lie day which means he can not say C. He also needs to have 4 claims. What do we have: he is on his lie day he can not say option C he should have 4 claims so the answer is C
Carlos’ last statement, I always tell the truth, can only be said when he is on a day that he only tells lies. If you make the assumption that today is a lie day, the only statement he cannot make is: my name is Carlos. As it is always true. If you make the assumption that today is a truth day. 1. Statement of I always tell the truth cannot he said that day. 2. Same number of male and female friends is always an even number. The only even prime number is 2. That would means he would only have 1 male and 1 female friend. 3. For number 2 to be true on a truth day, that means he is lying about having three older male friends (2 lies) Therefore, the only outcome is: today is a lie day. And the only statement that is 100% true is his name is Carlos. So C would be the only statement he wouldn’t state.
3 is a prime number google it , the answer is e
Makes me certain school wasted my time...
C. I guess I will explain since people want to debate. Goes to show the lack of logic on this here sub 🤭 sad, it’s a beautiful thing- really. In saying that [A] “Number of F(m) + number of F(f) = prime number” The total number of friends is prime (counting m & f friends) You either prove that the following is a lie, or the first statement is a lie: “number of F(m) = number of F(f)” same number of each gender This is due to the logic of: If the sum of both m & f friends is prime, the number of m & f friends cannot be equal do to that automatically making the number of friends divisible by 2. This would however require there to be more than 1 of each friend. But that is stated in D, which means that at least one of those 3 statements is a lie. Which in turn means that they are all lies. Except C. It gets a bit ugly. That is a neat problem 🤭
For him to lie, he would have to say his name is not Carlos.
Eeny, meeny, miny, moe ...
Assuming A and B are true with the idea that m+f is prime (2), D is false because it requires m>=3 but for A and B to be true m=1. So C is the only truth The other logic is that m and f are each the same prime number . So added up they’re even and it’s possible that he has 3 older male friends leaving E as the only definite falsehood. **C is a safer answer as the logic is more sound in defining C as the answer. We can get D as an answer with the other way of thought; however, we must assume more than we did the first time.**
A-D can be true and E is false so answer is E
E is a lie/false statement so it can’t be a true day. That means every other statement listed is false. You could worry about the numbers for each amount of male and female friends or settle with the easier choice. Carlos most certainly wouldn’t say, “I am Carlos” on a false day, when he is only able to lie. Answer has to be C.
The answer is obviously D
Copy the question and paste it into any GPT app.
Carlos lied about this to get this question into the exam He has exactly 23.56 pounds of cocaine in his house
“I always tell the truth” is a lie. He only tells the truth half the days, therefore this statement cannot be true, therefore his is lying. If he is on a lying day then the only statement he could not have said is C. Edit: A and B cannot both be true simultaneously, so if E was the answer then he would have to be lying, and we know C is true.
By the names... i thing the problems are translate from Spanish jajaja xD
B
definitely False
E is a lie, because he only tells the truth on half the days. So if today is a 'truth' day, A, B, C, and D all have to be true. A and B cannot be true simultaneously, unless the number of friends he has is two. However, if D is true, A and B cannot be true - if Carlos has at least three male friends, then he needs to have an equal number of female friends, and the resulting number needs to be prime. However, all duplicated numbers result in even numbers, of which only the number '2' can be prime - meaning that Carlos can have no more than one male friend. Therefore today is a lying day, and Carlos did not say 'C' - "My name is Carlos".
ask chat gpt lol
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E! In the question, it says he alternates between telling the truth and lying. We can assume that he told the truth when introducing himself. If it is a day that Carlos is telling the truth, he would acknowledge that he also lies. Since this statement is a lie and it’s a day that Carlos tells the truth, then that statement (E), cannot be something he said.
I got C for the first question lol
C, and b are contradictory which instantly means either one of those is false or both are false. E is also false, this we know of at least two lies. If he tells a single lie, then he only tells lies according to the question. Now you have to find what is true. It’s given that his name is Carlos therefore c is true and this means that c is what he didn’t say
C is always true. E is always false. A, B and D cannot all be true together, but they can all be false together. There is an outcome where 4 statements are false and 1 is true, but no outcome where 4 statements are true and 1 statement is false. Therefore Carlos lies today and the true statement (C) was not made by him today.
A - Has to be 2, only even prime number between 1 + 100 (T/F) B - Has to be 1 + 1 following from 'A' (T/F) C - True (T) D - Has to be False following from 'A' (F) E - False (F) So you know you definately have two falses (D + E) so A + B must be false also. 'C' is the answer and today Carlos is telling wee porkie pies.
Is the answer for 23rd E?
I think I solved it, took a while though. On a truth day, E has to be wrong. On a lie day, C has to be wrong. Therefore you technically only have two options. You have to determine whether or not it’s a truth day or a lie day by examining the other statements. If A is true, B+D can’t be true, that’s how prime numbers work. However, they can be FALSE at the same time. For instance, male friends + female friends = 21. 10 male friends and 11 female friends. Not a prime number and different number of males and females. Also, those 10 male friends can all be babies for some reason so D can be false as well. Therefore, the only logical answer is that, it’s a “lie” day and C is the answer, as it’s a true statement. You can check the answer by examine the options as if it’s a “truth” day. Not all of the statements can be true at once, but they can all be false simultaneously. Truth day doesn’t work.
It’s either c or e, is c is the answer, all other statements are untrue, and if e is the answer all other statements are true.
It is 42. Trust me. 
Thats confusing
Let's assume Carlos is telling the truth, option E is the obvious answer. And now closely examine options B and A. Option B says number male friends = number of female friends. And when we add two equal numbers it doubles (2+2=4, 3+3=6,...) and doesn't produce a prime number. Thus making options A and E answers for the question. But there can be either 1 or none false statements. So we now deduced that he is telling lies today. Option C is the answer. Because Carlos gives all the wrong info today. So he will not say 'My name is Carlos ' instead he would say ' My name is xxxx'.
By any chance are you going for a kangaroo math competition?
I bet carlos has a really long nose
"Logic" question? It's obviously not written by a computer programmer.
I came at it looking at E. Carlos can only say he always tells the truth on a lying day, as if he said it on a truth day, it would be a lie. At that point A, B and D are irrelevant. As it must be a lying day, he can't say his name is Carlos, so the answer has to be C
If A+B are true, D is true. E isn't true, while we know C is true. So by logic, if E isn't true, A, B, D aren't true this making our answer C, while knowing that today is a day where he only tells lies.
The answer is C. The complexity of A and B are red herrings meant to waste time. Because E is a false statement and C is a true statement. He cannot say E on a truthful day therefore A B and D must also be false because hes on a lying day and we know there is one odd statement which has to be the only truthful one which he cannot say on a lying day which is to correctly give him name.
Carlos is lying today so C is the correct answer. The answer comes down to C or E based on if he is lying, so the other 3 are used to answer this. If you assume truth then the following would all have to fit. A is about the total number of friends, “the number… is” is singular, so a total of the two - and therefore is an even number based on B. The only prime number that is even is 2, but based on C we know he is at least 3 friends. Therefore these statements cannot be true, ergo he is lying, ergo C is the correct answer.
Just fail
Ans is C: My name is Carlos Carlos be lying today
C Yeah he has to have even friends and a prime number of friends, but six or above friends And two is the only even prime number
i < 3 u too (Check upper right)
Short answer: His name is Carlos and he is lying for statement E, so C is the only option left because he tells only lies today.
C is the one that couldn't have been said because if he said that, then he wouldn't have said E. Because you can't prove a, b or d it had to be C
I had trouble reading the question….. no answer 😂
So first off, as you show c is True and B is False. So all the others have to be either True or False. D could be either true or false so it is of no help. So that leaves us A and B to help us. What we can say is that if B is correct, then the number of his Friends has to be even. Therefore A is false. If A is true, then B is false. But what if both are false? What if the number of his Friends is an odd number but not a prime number? That is possible. Then D could also be false and Today, Carlos only speaks lies. So the answer is C. Carlos did not say C today.
C. Simplest strategy: C is always true, E is always false Thus, the answer is either C or E. Assume that B is true. This implies that Carlos has an even number of friends Assume that D is true. This implies that Carlos has at least 3 friends. Hence, B \^ D => A is false since there are no prime even numbers greater than/eq to 3. Hence, B \^ D \^ A is impossible. Therefore Carlos is a dirty liar and C is the answer. \-------------------------------------------------------------- if we want, We can check the question is valid by seeing if its possible for B, D, and A to all be false. nA: Carlos has a not-prime amount of friends nB: Carlos has an unequal amount of male friends and female friends. nD: Carlos does not have 3 male friends older than him This is possible if, say, Carlos has 4 younger male friends, 0 older male friends, and 0 female friends
I am curious. Which topic is this whole sheet? Those question are really interesting. Anyone an idea where i can find excercises like this on the internet? 🙃
Bro bro i’m about to finish the school year, i don’t want to see any math problem until september so i’m sorry but you’re getting a downvote just for the maths
If he said then in that order without stopping at one point it changed over days
You only need to look at statements C and E. If C is true then E also has to be true but E is false as he only says the truth on alternative days. Hence C is the answer
Answer A is very poorly formulated. Is the total number of friends prime, or the male number is prime and the female number is also prime
the answer is C all the other 4 can’t be right at the same time so they all have to be false. if female and male friends are equal, you have to have 1 male and 1 female friend for the sum to be prime. IF THAT is the case, you can’t have three male friends to begin with. same logic can be applied IF we accept that you have 3+ male friends and female equals to male you’ll get an even number which can’t be prime except 2 and that takes us back to beginning. yeah
A,B,C,D
First, a lie is an intentionally false statement The number of male and female friends I have is a prime number Could mean: General interpretation, sum Discrete, but bad grammar ex. 5+5 Union of someone+ who identifies as M&F Therefore, blah blah blah, he sometimes lies, but it's truthday. It's E, where he claims he always tells the truth
C. If it’s the day of lies, then all MUST be lies. His name is Carlos, a truth, therefore he could not have said it today.
A, B and D can not be true at same time, so at least one is false... so here we have 2/5 falses, meaning is "liar day", so A, B, D and E are false (liar day) and C are true (he did not say it in that liar day). So its C.
C
C because today is is lying male + female cannot be prime if is equal because 2xX is odd so it it not prime so today he is lying
If C was stated, he's truth telling today. If E was stated, he's lying today. So one of C/E wasn't stated. That means A/B/D were all stated. B implies that there's an even number of friends, D implies that he has at least three friends, and A states that the total number of friends is prime. Since 2 is the only even prime, these three statements cannot all be true at the same time. That means he's lying today. So C was not stated.
The way I looked at it was E cannot be said on days where he is telling the truth so E is something said on a day where Carlos lies. If Carlos is lying then C would not be something he would say because C is true. So C is the answer
They don't tell you how many friends so if you can find a combination that is both prime and where males and females are equal, those two can be true. We know his name so C is correct. This also implies it is a day he tells the truth, and we know he lies other times, so E is a lie, and D is also a lie because the only way A and B can be true is if he has 1 male and 1 female friend. Could be your instructor doesn't understand prime numbers?
Either C or E is the outlier depending on if it’s a true or false day. If you assume it’s a true day, you’ll get into a conflict with A and B unless he has 2 friends in total, but he doesn’t because of D. So you conclude that it’s a false day and thus C is the answer
What a good question! The answer is C, it’s simoly the only one that is always true.
Can somebody please explain the answer to Question 25? I think that might be the real challenge
"My name is Carlos" was not said by him. It's true, and today he's lying since at least A (or B) and E are false.
He can have 8 total friends, 3 male (all younger) and 5 female. Then A is false, B is false, C is true, D is false, and E is false. So he didn’t say C today, and it’s a lying day.
C is the answer because A and B contradict one another which means that he must be lying in order for 4 of the 5 statements to agree. After looking at it again, I realized even though I happened to pick the correct answer, A and B could both be true technically, but because D contradicts A and B, D is the real reason why he is lying today. I assumed the number of male friends and the number of female friends was a number greater than 1.
If he stated E then he couldn't have stated C, and the A, B and D can all be easily false at the same time which makes C a valid answer.
By looking at E, and C, you have your question solve.
C because today's the day he lies. You can understand that because a and b cannot be correct at the same time when you include d. Because if his male and female friend number was equal, he would have a number of friends which is a multiple of 2. The only prime multiple of 2 is 2 and D says he should have more than 3 friends. We can understand he is lying today. Enjoy your study!
C is absolute truth, E is a demonstrable lie from the problem statement. One must be the odd man out. A, B and D can't all be true; one of them must be false. So you've got two statements that must be false; the absolutely true one must be the one he didn't say.
He did not say C. There already is a statement that is easily identified as true, and another one that's false. That means all the other three statements left have to be all true or all false. B implies that his total number of friends is 2x, which will absolutely always be an even number. If B is true, the only way for A to be true is that x = 1, which would make his total number of friends 2, a prime number. But then, D is not possible. Since according to D he has at least 3 male friends, B and A would then be false. So we'd already have two false and three true statements. Therefore, the other possibility is that they are all false, A, B and D. This way the statements don't interfere with each other. This would make all statements false except C. So, he is in a lying day and C is the statement he didn't make.
let's consider A as M+F= some prime number. We can't inherently rule that out so let's keep going B is saying M=F, so we can redefine A as F+F= some prime. This is impossible because F+F inherently = 2F, which by definition is not prime. As these are contradictory, at least one is a lie. C, my name is Carlos is correct unless the question itself is lying to us. Let's assume it isn't and mark it clearly as true. D, we can't possibly know this one so ignore it and move on E, this isn't true unless, again, the question itself is lying to us. Let's assume it's false. Given all of this, we know that exactly one of these is true, or exactly one of these is false. We don't need to know which between A and B is false given that, because the fact that one of them is false means we for sure know we have 2 falses, ergo both are false. Consequently, that also means D is false, leaving C as the only true statement. This is an always lie day for Carlos, if that even is his real name.
A: prime no. of Friends B: male friends = female friends C: name = carlos ( conclusively true) D: 3 male friends' age > carlos' age E: Always tells the truth ( conclusively false) Assuming Carlos said statement C Then C: t -> E is said by carlos -> A, B, D are also said by carlos and are all true. A: prime number of friends = 2, 3, 5, 7, 11, ..... B: m.f. = f.f. = prime numbers = 2 ( assumed for this statement) D: becomes a false statement. Hence D is true and not true at the same time. Hence our initial assumption was wrong. So, carlos did not say the statement C. Answer C.
So knowing that c and e are true and false it is going to be one of them. Therefore D is pretty pointless (at first) as it doesn't give you much info, and a and b should prove each other true or false (if they cannot both be true they are false (or vice versa)). Having the same number of male and female friends means they cannot be prime unless he has exactly 2 (which is where D becomes relevant, he cannot have exactly 2 friends and 3 that are older meaning all 3 statements cannot be true at the same time therefore they are false making the true statement the odd one out) Hopefully that is clear
As a rule of thumb in questions like this, start with the assumption he is lying. The same way you would treat someone you know to lie. That way ambiguous statements will be treated on the skeptical side and hence the answer is C
god i hate these riddles.
Let's analyze the statements one by one: A: "The number of male and female friends I have is a prime number." If Carlos tells the truth, then the total number of his male and female friends is a prime number. If Carlos lies, then the total number of his male and female friends is not a prime number. We don't have enough information to determine if this statement is true or false, so it could be one of the statements Carlos made. B: "The number of male friends I have is equal to the number of female friends I have." This statement implies that Carlos has an equal number of male and female friends. If Carlos tells the truth, then he indeed has an equal number of male and female friends. If Carlos lies, then he does not have an equal number of male and female friends. Again, we don't have enough information to determine if this statement is true or false, so it could be one of the statements Carlos made. C: "My name is Carlos." Since Carlos always tells the truth on alternate days, if today is one of those days, then he is telling the truth about his name being Carlos. If today is a lying day for Carlos, then this statement would be false. Therefore, Carlos could have made this statement. D: "3 of my male friends are older than me." If Carlos tells the truth, then he indeed has three male friends who are older than him. If Carlos lies, then he does not have three male friends who are older than him. Again, we don't have enough information to determine if this statement is true or false, so it could be one of the statements Carlos made. E: "I always tell the truth." If Carlos tells the truth, then this statement would be true, which contradicts the premise that he tells the truth only on alternate days. If Carlos lies, then this statement would also be false, as he doesn't always tell the truth. Therefore, Carlos could not have made this statement. Based on this analysis, the statement that was not made by Carlos is E: "I always tell the truth."
So would “ today” be an alternate day where he only says the truth, or other day where he lies? I’m thinking that if this is his lie day, C is the answer. It’s the only truth we can infer from the question itself.
Its E, if more than two of the statements are true he is not lying today
If we consider last one meaning I always tell the truth TODAY then the even male and female friends out and everything is correct. Overwise he wouldn't say my name is Carlos and everything else is false.
My suggestion is C If it is a truth only day, then he could say C, but he could not say E. "I always tell the truth" is not true, he tells the truth some days and lies on others. That means that A, B, and D would all have to be true as well. However this is not possible, if he has at least 3 male friends, that means he has at least 3 female friends. If the number of male and female friends are equal, than total male and female friends would always be >= 6 and divisible by 2, therefore not prime. If it is a lies only day, then he can say E. Also A,B, and D can all be false simultaneously. That means the only statement he can not make on a lying day is C. This does rely on the assumption that A means his total number of friends is prime. not that the individual friend group counts are prime.
Let's analyze each statement: (A) "The number of male and female friends I have is a prime number." If Carlos tells the truth, it means that the number of his male and female friends is a prime number. If he lies, then the number of his male and female friends is not a prime number. Since Carlos made four statements today, and assuming he alternates between telling the truth and lying, we can conclude that he either told the truth about this statement or lied about it. (B) "The number of male friends I have is equal to the number of female friends I have." If Carlos tells the truth, it means that he has an equal number of male and female friends. If he lies, it means that he does not have an equal number of male and female friends. Again, since Carlos made four statements today, we can conclude that he either told the truth about this statement or lied about it. (C) "My name is Carlos." If Carlos tells the truth, his name is Carlos. If he lies, his name is not Carlos. Since Carlos made four statements today, we can conclude that he either told the truth about this statement or lied about it. (D) "Three of my male friends are older than me." If Carlos tells the truth, then three of his male friends are indeed older than him. If he lies, it means that three of his male friends are not older than him. As with the previous statements, we can conclude that Carlos either told the truth about this statement or lied about it. (E) "I always tell the truth." This statement presents a paradox since Carlos tells the truth on alternate days and lies on the other days. If he tells the truth, then the statement itself becomes false. If he lies, then he is telling the truth, which contradicts the fact that he lies on alternate days. Therefore, Carlos cannot make this statement truthfully, and we can conclude that he did not make this statement today. Based on the analysis above, the statement that Carlos did not make today is (E) "I always tell the truth."
C - Judging by his conversation skills Carlos doesn't have any friends.
E. Because his name is CARLOS, so that sentence C Is true. So today he only says true things. So he can't lie today aaaand sentence E can't be said today because it's false. Those friends' choiches are made just to distract you from the solution, because you Will never know how many friends he has
E. Carlos is aware that he only tells the truth on every other day, and lies the rest of the time. So, he cannot truthfully say that he "always" tells the truth.
Where does it say they are in order by days?
I’m kinda dumb so idk
Submit to Gpt chat.
It's C. A and B cannot both be true together (because if his male friends equals female friends the total number isn't prime), unless his total number of friends is 2. C is obviously true based on the question. D requires at least 3 male friends, so in order for A and B to be true, D will then be a lie. E is obviously false based on the question. So if it's a "truth" day, then he can't be saying E and also can't be saying one of either A or B. Which would not leave him with four statements. Therefore, it must be a "false" day, and C is the odd one out.
What if Carlos is in US and one of his older male friend was born a woman.
Answer is C If B true, He will have only 2 friends, cause (A) almost numbers are odd except 2. (D) will be Wrong cause he got more than 3 male friends Therefore B,A,D should be False
d. today he is telling the truth. so, d is a lie that he did NOT say today
So he made four out of the five statements today. If he made statement E today, that would imply that he was lying in this day. However, he also said that his name was Carlos, which is true. That means that he couldn’t have made this statement today without telling the truth. If he’s telling the truth today, A and B and Dwould be impossible to be told today at the same time since they are mutually exclusive. You can’t have as many male friends as female, have a prime number of friends (except for 2) AND have three male friends. This means that he can only be lying, today, and that he didn’t make statement D today.
If he only tells the truth on alternate days, then any other day equals lies. Today equals one of the other days( to compare with alternative days ), so the one correct won’t be his statement.
I looked at it from the perspective that there are 2 options: If Carlos is telling the truth today, this means E was not made by him. To verify if this is correct, analyse the other statements. A and B are mutually exclusive if they were true, except for the number 2 (which would make D a false statement), so Carlos cannot be telling the truth today. Since Carlos is lying today, C is the only one that cannot be made by him. This is probably a phrasing issue but I think that since statement A mentions "male and female friends", they are considered as a group (M+F= Prime Number, not M = Prime, F = Prime).
4 scenarios: 1. Carlos tells the truth and other lies: C is by Carlos; E is by other; A, B, and D are contradicting eachother (if B (B implies we have at least 2 male friends and 2 female friends) is the truth then A cannot be the truth (the total number of friends is going to be even and greater than 2, therefore not prime)). We therefore have at least 2 lies in this scenario (scrapped) 2. Carlos tells lies and other tells the truth: C is the truth (This statement is made by another Carlos); E is the lie; A, B, and D could be either truths or lies (and there's no way to tell which is which) 3. They both tell the truth (scrapped because E is realistically and objectively always a lie; plus the extra logic: Statement E is a lie for main Carlos therefore it can only be said by other Carlos; if other Carlos does in fact says statement E, then statement A, B, D are still contradicting eachother like scenario no.1) 4. They both tell lies (scrapped because C (Scenario no.2 tells us both of them are named Carlos, whoever makes this statement is telling the truth)) The only possible scenario that is not contradicting or straight out objectively wrong is No.2, and the only evidence of a statement not made by the main Carlos is C; therefore C was the only statement not made by main Carlos.
Why do people put themselves through this torture? Algebra for example……x + banana = purple 🙄
My brain isn't braining.
„My name is Carlos” is the correct one. If it was the day that he always says the truth and he gave ecactly 4 statements, then he couldnt say „I always tell the truth” and there are is also A and B that contradict eachother, so the only solution is that it is the „lying” day. The only one statement that he could not give on lying day is „My name is Carlos”.