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There are between 100 and 110 cards in a collection of cards. If they are counted out 3 at a time, there...

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by AAPL » Mon Nov 23, 2020 4:20 am
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There are between 100 and 110 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?

A. 101
B. 103
C. 106
D. 107
E. 109

OA A
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Re: There are between 100 and 110 cards in a collection of cards. If they are counted out 3 at a time, there...

by Scott@TargetTestPrep » Mon Nov 30, 2020 10:47 am
AAPL wrote: ↑
Mon Nov 23, 2020 4:20 am
 GMAT Paper Tests

There are between 100 and 110 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?

A. 101
B. 103
C. 106
D. 107
E. 109

OA A
Solution:

Since there is a remainder of 2 when divided by 3, the number of cards will be 2 more than a multiple of 3, so there could be 101, 104, or 107 cards. Since there is a remainder of 1 when divided by 4 the number of cards will be 1 more than a multiple of 4, so there could be 101, 105, or 109 cards. Thus, there are 101 cards.

Answer: A

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