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Question

A, B, C, D, and E play a game of cards. B has 6 cards less than E and A has 6 cards less than D. A and B together have a third of the number of cards D and E have. If B has two cards less than what C has and the total number of cards is 30, how many cards does B have?

A
5
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B
3
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C
4
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D
2
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Solution

The correct option is C 4
We denote:
Person A B C D E
Number of cards a b c d e

Now, we know that B has 6 cards less than E and A has 6 cards less than D.

b=e6 a=d6

We also know that A and B together have a third of the number of cards D and E have.

a+b=d+e3

Combining the two equations, we find:

(e6)+(d6)=d+e3(d+e)12=d+e32×(d+e)3=12d+e=12×32d+e=18

Using this, we can caluclate the total number of cards A and B together have:

a+b=d+e3=183=6

Next, we know that B has 2 cards less than what C has.

b=c2c=b+2

And finally, we know that the total number of cards they have together is 30.

a+b+c+d+e=30(a+b)+(c)+(d+e)=30(6)+(b+2)+(18)=30(b+2)+24=30b=3026b=4

Hence, B has 4 cards.

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