ziyuenlau 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.

Source : Veritas
OA=B

Great question.

Statement 1: Ralph has 40 Valentine's Day cards to give out.

Clearly insufficient.

Say Ralph has 40 friends and 40 cards; each gets only one card.

If Ralph has 20 friends and 40 cards; each gets two cards. No unique answer. Insufficient.

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

Case 1: ONLY ONE card to each scenario:

Say Ralph has one friend and one card.

If the number of friends were doubled, ie. number of friends = 2, he cannot give one card to each. The answer is NO, Ralph did not give more than one card to each.

Case 2: MORE THAN ONE card to each scenario:

Say Ralph has one friend and two cards. Thus, each one gets two cards.

If the number of friends were doubled, ie. number of friends = 2, he can give one card to each. So this scenario is not a valid one. It points to the fact that Ralph gave only one card to each.

You may try with one friend and three cards. But you cannot have a valid scenario. Thus, Ralph gave only one card to each. The answer is NO, Ralph did not give more than one card to each.

The correct answer: B

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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