John and Mark each own a collection of baseball cards. The two collections combined contain 120 cards.

[BTGmoderatorDC]

John and Mark each own a collection of baseball cards. The two collections combined contain 120 cards. If John were to trade 5 cards to Mark and receive 2 of Mark’s cards in return, John would have 22 more cards than Mark does. How many cards does Mark possess before the proposed trade?

A. 85
B. 74
C. 52
D. 46
E. 35


OA D

Source: Princeton Review

[Jay@ManhattanReview]

John and Mark each own a collection of baseball cards. The two collections combined contain 120 cards. If John were to trade 5 cards to Mark and receive 2 of Mark’s cards in return, John would have 22 more cards than Mark does. How many cards does Mark possess before the proposed trade?

A. 85
B. 74
C. 52
D. 46
E. 35

OA D

Source: Princeton Review

Say John has J cards and Mark has M cards; thus, J + M = 120 --- (1)

After the trading of cards, John has J – 5 + 2 = J – 3; thus, Mark has (M + 3) cards.

=> J – 3 = M + 3 + 22

= J – M = 28 ---(2)

From (1) and (2), we have J = 74 and M = 46.

Correct answer: D

Hope this helps!

-Jay
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