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Ralph is giving out Valentine’s Day cards to his friends.

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Ralph is giving out Valentine’s Day cards to his friends. [#permalink] New post  16 Sep 2013, 02:24
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Ralph is giving out Valentine’s Day cards to his friends. Each friend gets the same number of cards and no cards were leftover. If each friend gets at least one card, was the number of cards received by each friend more than one?

(1) Ralph has 40 Valentine’s Day cards to give out.
(2) If the number of friends were doubled, it would not be possible for each friend to get at least one card.
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Re: Ralph is giving out Valentine’s Day cards to his friends. [#permalink] New post  16 Sep 2013, 02:52
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honchos wrote:
Ralph is giving out Valentine’s Day cards to his friends. Each friend gets the same number of cards and no cards were leftover. If each friend gets at least one card, was the number of cards received by each friend more than one?

(1) Ralph has 40 Valentine’s Day cards to give out.
(2) If the number of friends were doubled, it would not be possible for each friend to get at least one card.

The correct answer is said to be B-
The correct response is (B). Clearly, statement 1 is not sufficient, as with 40 cards Ralph could give 20 each to two friends or 1 each to 40 friends, for example, so we cannot determine whether everyone got more than one.

Statement 2 is tricky but sufficient. The sufficiency lies in some of the information hidden in the question stem. Because each friend gets the same number of cards and no cards are left over, the possibilities here are limited. If, currently, each friend were to get two cards and then the number of friends were doubled, then each friend would only get one. Try it with numbers:

10 friends, 20 cards total --> 2 cards each double the friends: 20 friends, 20 cards, 1 card each

18 friends, 36 cards total --> 2 cards each double the friends: 36 friends, 36 cards, 1 card each

And in these cases, each friend still gets "at least one card," so each friend getting two cards is not compatible with statement 2. Increasing the number of cards:

10 friends, 40 cards total --> 4 cards each double the friends: 20 friends, 40 cards, 2 cards each

Is still not possible. So the only way that the given information AND statement 2 can be true is if each friend only gets one card to start:

10 friends, 10 cards --> 1 card each double the friends: 20 friends for only 10 cards, not everyone can have one

The correct answer is B, and beware the trap here with statement 1. Many test-takers will choose C because statement 1 makes the math easier, but you don't actually need the number of cards in order to solve the problem. The facts that all friends get at least one card, that they get the same number of cards,and that there is no remainder all add up to mean that the only way statement 2 can be true is if each friend currently gets one card.


However I still find that correct answer is C.
It is Yes No question.

Lets choose 7 people and 21 Valentine days Card, If we give each friends same number of card, they will get 3 cards.
Lets double the Number of friends = 14, each people will get the same number of cards i.e. 1 and at-least one card situation is also satisfied by(as mentioned in the condition B). So from B we get YES or NO so B alone is not sufficient. Hence C is correct.


Notice that (2) says: "if the number of friends were doubled, it would NOT be possible for each friend to get at least one card". But in your example (7 friends, 21 cards), when the number of friends is doubled to 14, it's still possible for each friend to get at least one card.

Stem says that: \(\frac{(# \ of \ cards)}{(# \ of \ friends)}=integer\geq{1}\).

(2) says that: \(\frac{(# \ of \ cards)}{2*(# \ of \ friends)}<{1}\) --> \(\frac{(# \ of \ cards)}{(# \ of \ friends)}<{2}\), thus \(\frac{(# \ of \ cards)}{(# \ of \ friends)}=integer={1}\).

Does this make sense?
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Re: Ralph is giving out Valentine’s Day cards to his friends. [#permalink] New post  16 Sep 2013, 02:27
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The correct answer is said to be B-
The correct response is (B). Clearly, statement 1 is not sufficient, as with 40 cards Ralph could give 20 each to two friends or 1 each to 40 friends, for example, so we cannot determine whether everyone got more than one.

Statement 2 is tricky but sufficient. The sufficiency lies in some of the information hidden in the question stem. Because each friend gets the same number of cards and no cards are left over, the possibilities here are limited. If, currently, each friend were to get two cards and then the number of friends were doubled, then each friend would only get one. Try it with numbers:

10 friends, 20 cards total --> 2 cards each double the friends: 20 friends, 20 cards, 1 card each

18 friends, 36 cards total --> 2 cards each double the friends: 36 friends, 36 cards, 1 card each

And in these cases, each friend still gets "at least one card," so each friend getting two cards is not compatible with statement 2. Increasing the number of cards:

10 friends, 40 cards total --> 4 cards each double the friends: 20 friends, 40 cards, 2 cards each

Is still not possible. So the only way that the given information AND statement 2 can be true is if each friend only gets one card to start:

10 friends, 10 cards --> 1 card each double the friends: 20 friends for only 10 cards, not everyone can have one

The correct answer is B, and beware the trap here with statement 1. Many test-takers will choose C because statement 1 makes the math easier, but you don't actually need the number of cards in order to solve the problem. The facts that all friends get at least one card, that they get the same number of cards,and that there is no remainder all add up to mean that the only way statement 2 can be true is if each friend currently gets one card.


However I still find that correct answer is C.
It is Yes No question.

Lets choose 7 people and 21 Valentine days Card, If we give each friends same number of card, they will get 3 cards.
Lets double the Number of friends = 14, each people will get the same number of cards i.e. 1 and at-least one card situation is also satisfied by(as mentioned in the condition B). So from B we get YES or NO so B alone is not sufficient. Hence C is correct.
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Re: Ralph is giving out Valentine’s Day cards to his friends. [#permalink] New post  16 Sep 2013, 02:47
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honchos wrote:
The correct answer is said to be B-
The correct response is (B). Clearly, statement 1 is not sufficient, as with 40 cards Ralph could give 20 each to two friends or 1 each to 40 friends, for example, so we cannot determine whether everyone got more than one.

Statement 2 is tricky but sufficient. The sufficiency lies in some of the information hidden in the question stem. Because each friend gets the same number of cards and no cards are left over, the possibilities here are limited. If, currently, each friend were to get two cards and then the number of friends were doubled, then each friend would only get one. Try it with numbers:

10 friends, 20 cards total --> 2 cards each double the friends: 20 friends, 20 cards, 1 card each

18 friends, 36 cards total --> 2 cards each double the friends: 36 friends, 36 cards, 1 card each

And in these cases, each friend still gets "at least one card," so each friend getting two cards is not compatible with statement 2. Increasing the number of cards:

10 friends, 40 cards total --> 4 cards each double the friends: 20 friends, 40 cards, 2 cards each

Is still not possible. So the only way that the given information AND statement 2 can be true is if each friend only gets one card to start:

10 friends, 10 cards --> 1 card each double the friends: 20 friends for only 10 cards, not everyone can have one

The correct answer is B, and beware the trap here with statement 1. Many test-takers will choose C because statement 1 makes the math easier, but you don't actually need the number of cards in order to solve the problem. The facts that all friends get at least one card, that they get the same number of cards,and that there is no remainder all add up to mean that the only way statement 2 can be true is if each friend currently gets one card.


However I still find that correct answer is C.
It is Yes No question.

Lets choose 7 people and 21 Valentine days Card, If we give each friends same number of card, they will get 3 cards.
Lets double the Number of friends = 14, each people will get the same number of cards i.e. 1 and at-least one card situation is also satisfied by(as mentioned in the condition B). So from B we get YES or NO so B alone is not sufficient. Hence C is correct.


I think your interpretation of statement 2 is not correct.

(2) If the number of friends were doubled, it would not be possible for each friend to get at least one card.

This means if the number of friends is doubled, the number of cards would be less than the number of friends. That is, each friend will not get at least 1 card. You will not be able to distribute the cards such that each friend gets one card.
So we cannot have 7 people and 21 cards.
Say we have 10 friends and 20 cards. If you double the number of friends, the number of friends is 20 and each friend can still get a card. So this is not the case. You must have had 20 friends if you have 20 cards/ 30 friends if you have 30 cards, 40 friends if you have 40 cards etc.

So the question is: was the number of cards received by each friend more than one? Answer: No. Each friend got only one card. Statement II alone is sufficient

Answer (B)
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Re: Ralph is giving out Valentine’s Day cards to his friends. [#permalink] New post  16 Sep 2013, 02:55
Bunuel wrote:
honchos wrote:
Ralph is giving out Valentine’s Day cards to his friends. Each friend gets the same number of cards and no cards were leftover. If each friend gets at least one card, was the number of cards received by each friend more than one?

(1) Ralph has 40 Valentine’s Day cards to give out.
(2) If the number of friends were doubled, it would not be possible for each friend to get at least one card.

The correct answer is said to be B-
The correct response is (B). Clearly, statement 1 is not sufficient, as with 40 cards Ralph could give 20 each to two friends or 1 each to 40 friends, for example, so we cannot determine whether everyone got more than one.

Statement 2 is tricky but sufficient. The sufficiency lies in some of the information hidden in the question stem. Because each friend gets the same number of cards and no cards are left over, the possibilities here are limited. If, currently, each friend were to get two cards and then the number of friends were doubled, then each friend would only get one. Try it with numbers:

10 friends, 20 cards total --> 2 cards each double the friends: 20 friends, 20 cards, 1 card each

18 friends, 36 cards total --> 2 cards each double the friends: 36 friends, 36 cards, 1 card each

And in these cases, each friend still gets "at least one card," so each friend getting two cards is not compatible with statement 2. Increasing the number of cards:

10 friends, 40 cards total --> 4 cards each double the friends: 20 friends, 40 cards, 2 cards each

Is still not possible. So the only way that the given information AND statement 2 can be true is if each friend only gets one card to start:

10 friends, 10 cards --> 1 card each double the friends: 20 friends for only 10 cards, not everyone can have one

The correct answer is B, and beware the trap here with statement 1. Many test-takers will choose C because statement 1 makes the math easier, but you don't actually need the number of cards in order to solve the problem. The facts that all friends get at least one card, that they get the same number of cards,and that there is no remainder all add up to mean that the only way statement 2 can be true is if each friend currently gets one card.


However I still find that correct answer is C.
It is Yes No question.

Lets choose 7 people and 21 Valentine days Card, If we give each friends same number of card, they will get 3 cards.
Lets double the Number of friends = 14, each people will get the same number of cards i.e. 1 and at-least one card situation is also satisfied by(as mentioned in the condition B). So from B we get YES or NO so B alone is not sufficient. Hence C is correct.


Notice that (2) says: "if the number of friends were doubled, it would NOT be possible for each friend to get at least one card". But in your example (7 friends, 21 cards), when the number of friends is doubled to 14, it's still possible for each friend to get at least one card.

Stem says that: \(\frac{(# \ of \ cards)}{(# \ of \ friends)}=integer\geq{1}\).

(2) says that: \(\frac{(# \ of \ cards)}{2*(# \ of \ friends)}<{1}\) --> \(\frac{(# \ of \ cards)}{(# \ of \ friends)}<{2}\), thus \(\frac{(# \ of \ cards)}{(# \ of \ friends)}=integer={1}\).

Does this make sense?


Yes, Veritas questions have high degree of analytical challenge, I believe they have the best questions among so many brands in the market. I mis interpreted statement B, I have jotted down this question, explanation is amazing.
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Re: Ralph is giving out Valentine’s Day cards to his friends. [#permalink] New post  16 Sep 2013, 03:02
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honchos wrote:
Bunuel wrote:
honchos wrote:
Ralph is giving out Valentine’s Day cards to his friends. Each friend gets the same number of cards and no cards were leftover. If each friend gets at least one card, was the number of cards received by each friend more than one?

(1) Ralph has 40 Valentine’s Day cards to give out.
(2) If the number of friends were doubled, it would not be possible for each friend to get at least one card.

The correct answer is said to be B-
The correct response is (B). Clearly, statement 1 is not sufficient, as with 40 cards Ralph could give 20 each to two friends or 1 each to 40 friends, for example, so we cannot determine whether everyone got more than one.

Statement 2 is tricky but sufficient. The sufficiency lies in some of the information hidden in the question stem. Because each friend gets the same number of cards and no cards are left over, the possibilities here are limited. If, currently, each friend were to get two cards and then the number of friends were doubled, then each friend would only get one. Try it with numbers:

10 friends, 20 cards total --> 2 cards each double the friends: 20 friends, 20 cards, 1 card each

18 friends, 36 cards total --> 2 cards each double the friends: 36 friends, 36 cards, 1 card each

And in these cases, each friend still gets "at least one card," so each friend getting two cards is not compatible with statement 2. Increasing the number of cards:

10 friends, 40 cards total --> 4 cards each double the friends: 20 friends, 40 cards, 2 cards each

Is still not possible. So the only way that the given information AND statement 2 can be true is if each friend only gets one card to start:

10 friends, 10 cards --> 1 card each double the friends: 20 friends for only 10 cards, not everyone can have one

The correct answer is B, and beware the trap here with statement 1. Many test-takers will choose C because statement 1 makes the math easier, but you don't actually need the number of cards in order to solve the problem. The facts that all friends get at least one card, that they get the same number of cards,and that there is no remainder all add up to mean that the only way statement 2 can be true is if each friend currently gets one card.


However I still find that correct answer is C.
It is Yes No question.

Lets choose 7 people and 21 Valentine days Card, If we give each friends same number of card, they will get 3 cards.
Lets double the Number of friends = 14, each people will get the same number of cards i.e. 1 and at-least one card situation is also satisfied by(as mentioned in the condition B). So from B we get YES or NO so B alone is not sufficient. Hence C is correct.


Notice that (2) says: "if the number of friends were doubled, it would NOT be possible for each friend to get at least one card". But in your example (7 friends, 21 cards), when the number of friends is doubled to 14, it's still possible for each friend to get at least one card.

Stem says that: \(\frac{(# \ of \ cards)}{(# \ of \ friends)}=integer\geq{1}\).

(2) says that: \(\frac{(# \ of \ cards)}{2*(# \ of \ friends)}<{1}\) --> \(\frac{(# \ of \ cards)}{(# \ of \ friends)}<{2}\), thus \(\frac{(# \ of \ cards)}{(# \ of \ friends)}=integer={1}\).

Does this make sense?


Yes, Veritas questions have high degree of analytical challenge, I believe they have the best questions among so many brands in the market. I mis interpreted statement B, I have jotted down this question, explanation is amazing.


Yes, I do agree. VeritasPrep questions are very good.
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Re: Ralph is giving out Valentine’s Day cards to his friends. [#permalink] New post  16 Sep 2013, 04:23
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In my opinion the best way to solve this is to draw --- for example there are 3 friends and 6 cards (once you draw you can see that even if the number of friends doubles everyone still gets one card).

However, if there are 3 friends and 3 cards, if you double the number of friends there are three friends left without any cards.

So if we remember the statement that everyone has the same number of cards we can conclude that "B" gives us enough information :)

Hope this helps
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Re: Ralph is giving out Valentine’s Day cards to his friends. [#permalink] New post  03 Jan 2014, 06:00
honchos wrote:
The correct answer is said to be B-
The correct response is (B). Clearly, statement 1 is not sufficient, as with 40 cards Ralph could give 20 each to two friends or 1 each to 40 friends, for example, so we cannot determine whether everyone got more than one.

Statement 2 is tricky but sufficient. The sufficiency lies in some of the information hidden in the question stem. Because each friend gets the same number of cards and no cards are left over, the possibilities here are limited. If, currently, each friend were to get two cards and then the number of friends were doubled, then each friend would only get one. Try it with numbers:

10 friends, 20 cards total --> 2 cards each double the friends: 20 friends, 20 cards, 1 card each

18 friends, 36 cards total --> 2 cards each double the friends: 36 friends, 36 cards, 1 card each

And in these cases, each friend still gets "at least one card," so each friend getting two cards is not compatible with statement 2. Increasing the number of cards:

10 friends, 40 cards total --> 4 cards each double the friends: 20 friends, 40 cards, 2 cards each

Is still not possible. So the only way that the given information AND statement 2 can be true is if each friend only gets one card to start:

10 friends, 10 cards --> 1 card each double the friends: 20 friends for only 10 cards, not everyone can have one

The correct answer is B, and beware the trap here with statement 1. Many test-takers will choose C because statement 1 makes the math easier, but you don't actually need the number of cards in order to solve the problem. The facts that all friends get at least one card, that they get the same number of cards,and that there is no remainder all add up to mean that the only way statement 2 can be true is if each friend currently gets one card.


However I still find that correct answer is C.
It is Yes No question.

Lets choose 7 people and 21 Valentine days Card, If we give each friends same number of card, they will get 3 cards.
Lets double the Number of friends = 14, each people will get the same number of cards i.e. 1 and at-least one card situation is also satisfied by(as mentioned in the condition B). So from B we get YES or NO so B alone is not sufficient. Hence C is correct.


What is the source of such questions?
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Re: Ralph is giving out Valentine’s Day cards to his friends. [#permalink] New post  03 Jan 2014, 06:04
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crunchboss wrote:
honchos wrote:
The correct answer is said to be B-
The correct response is (B). Clearly, statement 1 is not sufficient, as with 40 cards Ralph could give 20 each to two friends or 1 each to 40 friends, for example, so we cannot determine whether everyone got more than one.

Statement 2 is tricky but sufficient. The sufficiency lies in some of the information hidden in the question stem. Because each friend gets the same number of cards and no cards are left over, the possibilities here are limited. If, currently, each friend were to get two cards and then the number of friends were doubled, then each friend would only get one. Try it with numbers:

10 friends, 20 cards total --> 2 cards each double the friends: 20 friends, 20 cards, 1 card each

18 friends, 36 cards total --> 2 cards each double the friends: 36 friends, 36 cards, 1 card each

And in these cases, each friend still gets "at least one card," so each friend getting two cards is not compatible with statement 2. Increasing the number of cards:

10 friends, 40 cards total --> 4 cards each double the friends: 20 friends, 40 cards, 2 cards each

Is still not possible. So the only way that the given information AND statement 2 can be true is if each friend only gets one card to start:

10 friends, 10 cards --> 1 card each double the friends: 20 friends for only 10 cards, not everyone can have one

The correct answer is B, and beware the trap here with statement 1. Many test-takers will choose C because statement 1 makes the math easier, but you don't actually need the number of cards in order to solve the problem. The facts that all friends get at least one card, that they get the same number of cards,and that there is no remainder all add up to mean that the only way statement 2 can be true is if each friend currently gets one card.


However I still find that correct answer is C.
It is Yes No question.

Lets choose 7 people and 21 Valentine days Card, If we give each friends same number of card, they will get 3 cards.
Lets double the Number of friends = 14, each people will get the same number of cards i.e. 1 and at-least one card situation is also satisfied by(as mentioned in the condition B). So from B we get YES or NO so B alone is not sufficient. Hence C is correct.


What is the source of such questions?


This is VeritasPrep question as indicated here:
It's also mentioned in the posts above.
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Re: Ralph is giving out Valentine’s Day cards to his friends. [#permalink] New post  03 Jan 2014, 12:45
Nice question...

Statement 1... Its very easy to eliminate this choice. because we dont have information of friends.

Statement 2 .. very tricky.. bt i tuk around 3 mints to manipulate this choice because i was sure there is smthing is this choice that will make it sufficient..My sixth sense :P

My explantion for option b.. If we double the number and no any friends will get atleast one card, and question stem said that they all have same number of cards, so that means, no anyone has 2 card now.. How ? if each person wud have 2 cards , and if we double the friends still they cud get atleast one.. So this statement is sufficient. Ans is B.

This thing force me to choose option B..
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Re: Ralph is giving out Valentine’s Day cards to his friends. [#permalink] New post  22 Oct 2015, 13:51
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Ralph is giving out Valentine’s Day cards to his friends. Each friend gets the same number of cards and no cards were leftover. If each friend gets at least one card, was the number of cards received by each friend more than one?

(1) Ralph has 40 Valentine’s Day cards to give out.
(2) If the number of friends were doubled, it would not be possible for each friend to get at least one card.

There are 2 variables (no. of friends, no. of cards given), and 2 equations are given, so there is high chance (C) will be our answer. If we combine the 2 conditions,
the answer to the question becomes 'yes' as 40=8*5 (8 friends get 5 cards each), but 'no' for 40=40*1. Therefore the conditions are insufficient, and the answer becomes (E). The question is weird here...
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Re: Ralph is giving out Valentine’s Day cards to his friends. [#permalink] New post  06 Dec 2015, 10:16
great algebraic solution by Bunuel, plenty of kudos to you, guru
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Re: Ralph is giving out Valentine’s Day cards to his friends. [#permalink] New post  06 Apr 2017, 22:42
Ralph is giving out Valentine’s Day cards to his friends. Each friend gets the same number of cards and no cards were leftover. If each friend gets at least one card, was the number of cards received by each friend more than one?

(1) Ralph has 40 Valentine’s Day cards to give out.
Clearly NS as there is no mention of no. of friends.

(2) If the number of friends were doubled, it would not be possible for each friend to get at least one card.
Surely there are less cards than friends if no of friends is doubled.
So, certainly each friend got one card each.

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Re: Ralph is giving out Valentine’s Day cards to his friends. [#permalink] New post  04 Apr 2019, 01:22
honchos wrote:
Ralph is giving out Valentine’s Day cards to his friends. Each friend gets the same number of cards and no cards were leftover. If each friend gets at least one card, was the number of cards received by each friend more than one?

(1) Ralph has 40 Valentine’s Day cards to give out.
(2) If the number of friends were doubled, it would not be possible for each friend to get at least one card.


Let's say there are 7 Friends and each one gets an equal number of cards: Total #Cards MUST be >= 7.

Now, if we double the friends, i.e., from 7 to 14: NOT everyone will get at least one card ---> Someone will be WITHOUT any card.
Thus, the range of cards MUST be in between 7(including) and 14(excluding), i.e.,
    Anything from the set: {7, 8, 9, 10, 11, 12, 13} - Considering JUST the 1st range of possible cards
    Another possible set can be {14, 15, 16, 17, 18, 19, 20}

The role of this vital sentence comes in the picture:
    Each friend gets the same number of cards and NO cards were leftover.

Since the number of cards received by each of the friends is the SAME since the beginning, the number of cards need to be MULTIPLE of the number of friends.
    ELSE, the number of cards received by each of the friends will NOT be the SAME.

Thus, B is sufficient to answer.
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Re: Ralph is giving out Valentine’s Day cards to his friends. [#permalink] New post  19 Sep 2020, 04:46
Bunuel wrote:
honchos wrote:
Ralph is giving out Valentine’s Day cards to his friends. Each friend gets the same number of cards and no cards were leftover. If each friend gets at least one card, was the number of cards received by each friend more than one?

(1) Ralph has 40 Valentine’s Day cards to give out.
(2) If the number of friends were doubled, it would not be possible for each friend to get at least one card.

The correct answer is said to be B-
The correct response is (B). Clearly, statement 1 is not sufficient, as with 40 cards Ralph could give 20 each to two friends or 1 each to 40 friends, for example, so we cannot determine whether everyone got more than one.

Statement 2 is tricky but sufficient. The sufficiency lies in some of the information hidden in the question stem. Because each friend gets the same number of cards and no cards are left over, the possibilities here are limited. If, currently, each friend were to get two cards and then the number of friends were doubled, then each friend would only get one. Try it with numbers:

10 friends, 20 cards total --> 2 cards each double the friends: 20 friends, 20 cards, 1 card each

18 friends, 36 cards total --> 2 cards each double the friends: 36 friends, 36 cards, 1 card each

And in these cases, each friend still gets "at least one card," so each friend getting two cards is not compatible with statement 2. Increasing the number of cards:

10 friends, 40 cards total --> 4 cards each double the friends: 20 friends, 40 cards, 2 cards each

Is still not possible. So the only way that the given information AND statement 2 can be true is if each friend only gets one card to start:

10 friends, 10 cards --> 1 card each double the friends: 20 friends for only 10 cards, not everyone can have one

The correct answer is B, and beware the trap here with statement 1. Many test-takers will choose C because statement 1 makes the math easier, but you don't actually need the number of cards in order to solve the problem. The facts that all friends get at least one card, that they get the same number of cards,and that there is no remainder all add up to mean that the only way statement 2 can be true is if each friend currently gets one card.


However I still find that correct answer is C.
It is Yes No question.

Lets choose 7 people and 21 Valentine days Card, If we give each friends same number of card, they will get 3 cards.
Lets double the Number of friends = 14, each people will get the same number of cards i.e. 1 and at-least one card situation is also satisfied by(as mentioned in the condition B). So from B we get YES or NO so B alone is not sufficient. Hence C is correct.


Notice that (2) says: "if the number of friends were doubled, it would NOT be possible for each friend to get at least one card". But in your example (7 friends, 21 cards), when the number of friends is doubled to 14, it's still possible for each friend to get at least one card.

Stem says that: \(\frac{(# \ of \ cards)}{(# \ of \ friends)}=integer\geq{1}\).

(2) says that: \(\frac{(# \ of \ cards)}{2*(# \ of \ friends)}<{1}\) --> \(\frac{(# \ of \ cards)}{(# \ of \ friends)}<{2}\), thus \(\frac{(# \ of \ cards)}{(# \ of \ friends)}=integer={1}\).

Does this make sense?


But do we know that before doubling the cards we everyone had got at least one card in (B)?
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Re: Ralph is giving out Valentine’s Day cards to his friends. [#permalink] New post  27 Sep 2020, 08:00
Assume total cards = c
Assume total friends = f
ATS, c is divisible by f.
Mathematically, c/f = a positive integer, say c/f= a
Q= Is ‘a’ greater than 1?

St1: c= 40, Insufficient

St2: c/2f < 1
As c/f = a, c/2f = a/2
Rewriting above inequality: a/2 <1
Thus, a<2
a is a positive integer less than 2. So only possible value of a is 1.
Ans is No
Sufficient.
Ans B
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Re: Ralph is giving out Valentine’s Day cards to his friends. [#permalink] New post  27 Sep 2020, 11:40
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honchos wrote:
Ralph is giving out Valentine’s Day cards to his friends. Each friend gets the same number of cards and no cards were leftover. If each friend gets at least one card, was the number of cards received by each friend more than one?

(1) Ralph has 40 Valentine’s Day cards to give out.
(2) If the number of friends were doubled, it would not be possible for each friend to get at least one card.


Let C = the number of cards and F = the number of friends.

Statement 1:
Clearly insufficient.

Statement 2:
Since the number of cards is not sufficient for double the number of friends, we get:
C < 2F
Thus:
C = F
Since the number of cards is equal to the number of friends, each friend must get EXACTLY 1 CARD -- the only way to satisfy the condition that each friend receives at least one card.
Thus, the answer to the question stem is NO.
SUFFICIENT.

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B

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Re: Ralph is giving out Valentine’s Day cards to his friends. [#permalink] New post  01 Jul 2021, 12:25
VeritasKarishma wrote:
honchos wrote:
The correct answer is said to be B-
The correct response is (B). Clearly, statement 1 is not sufficient, as with 40 cards Ralph could give 20 each to two friends or 1 each to 40 friends, for example, so we cannot determine whether everyone got more than one.

Statement 2 is tricky but sufficient. The sufficiency lies in some of the information hidden in the question stem. Because each friend gets the same number of cards and no cards are left over, the possibilities here are limited. If, currently, each friend were to get two cards and then the number of friends were doubled, then each friend would only get one. Try it with numbers:

10 friends, 20 cards total --> 2 cards each double the friends: 20 friends, 20 cards, 1 card each

18 friends, 36 cards total --> 2 cards each double the friends: 36 friends, 36 cards, 1 card each

And in these cases, each friend still gets "at least one card," so each friend getting two cards is not compatible with statement 2. Increasing the number of cards:

10 friends, 40 cards total --> 4 cards each double the friends: 20 friends, 40 cards, 2 cards each

Is still not possible. So the only way that the given information AND statement 2 can be true is if each friend only gets one card to start:

10 friends, 10 cards --> 1 card each double the friends: 20 friends for only 10 cards, not everyone can have one

The correct answer is B, and beware the trap here with statement 1. Many test-takers will choose C because statement 1 makes the math easier, but you don't actually need the number of cards in order to solve the problem. The facts that all friends get at least one card, that they get the same number of cards,and that there is no remainder all add up to mean that the only way statement 2 can be true is if each friend currently gets one card.


However I still find that correct answer is C.
It is Yes No question.

Lets choose 7 people and 21 Valentine days Card, If we give each friends same number of card, they will get 3 cards.
Lets double the Number of friends = 14, each people will get the same number of cards i.e. 1 and at-least one card situation is also satisfied by(as mentioned in the condition B). So from B we get YES or NO so B alone is not sufficient. Hence C is correct.


I think your interpretation of statement 2 is not correct.

(2) If the number of friends were doubled, it would not be possible for each friend to get at least one card.

This means if the number of friends is doubled, the number of cards would be less than the number of friends. That is, each friend will not get at least 1 card. You will not be able to distribute the cards such that each friend gets one card.
So we cannot have 7 people and 21 cards.
Say we have 10 friends and 20 cards. If you double the number of friends, the number of friends is 20 and each friend can still get a card. So this is not the case. You must have had 20 friends if you have 20 cards/ 30 friends if you have 30 cards, 40 friends if you have 40 cards etc.

So the question is: was the number of cards received by each friend more than one? Answer: No. Each friend got only one card. Statement II alone is sufficient

Answer (B)


We should consider that the stem "no cards were leftover"
If there were 40 cards and 8 friends, then each friend gets 5
If doubled, then 40 cant be divided equally among 16 friends without keeping leftovers. So "Yes", more than one card.

However, if there were 40 cards and 40 friends, then all get 1 each. The answer is "No", and it satisfies that doubling it can result in no friend getting even 1 card.

IMO E
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Re: Ralph is giving out Valentine’s Day cards to his friends. [#permalink] New post  01 Jul 2021, 12:42
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coolwhizRaj wrote:
We should consider that the stem "no cards were leftover"
If there were 40 cards and 8 friends, then each friend gets 5
If doubled, then 40 cant be divided equally among 16 friends without keeping leftovers. So "Yes", more than one card.

However, if there were 40 cards and 40 friends, then all get 1 each. The answer is "No", and it satisfies that doubling it can result in no friend getting even 1 card.

IMO E


The condition in blue applies only to the ACTUAL distribution of the cards, as discussed in the prompt:
Ralph is giving out Valentine’s Day cards to his friends. Each friend gets the same number of cards and no cards were leftover.
Statement 2 refers not to the actual distribution but to a HYPOTHETICAL distribution:
If the number of friends were doubled, it would not be possible for each friend to get at least one card.
Statement 2 does NOT indicate that -- in the hypothetical case above -- no cards must be left over.
The only condition in Statement 2 is that -- if the number of friends doubles -- it is not possible to give each friend at least one card.
The red case above does not satisfy this condition:
If there are 16 cards and 40 friends, it is possible for each friend to receive at least 1 card.
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Re: Ralph is giving out Valentine’s Day cards to his friends. [#permalink] New post  11 Sep 2021, 05:40
Can someone please explain why B is correct and not E. If we have 8 friends then each friend will get 5 cards, but if we double the friends to 16, we will no longer be able to distribute cards evenly and hence won't be able to give 1 card to each friend.
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Re: Ralph is giving out Valentine’s Day cards to his friends. [#permalink]
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