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16 Sep 2013, 02:24
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B
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52% (01:50) correct
48%
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wrong
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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.
(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.
16 Sep 2013, 02:52
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honchos
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?
General Discussion
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.
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.
16 Sep 2013, 02:47
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honchos
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)
