John and Mark each own a collection of baseball cards. The two collect

Hi SajjadAhmad,

This question can be solved by TESTing THE ANSWERS. To help decide which answer to TEST first, it's worth noting that the prompt describes that - after a rather small 'trade' of cards - John would have 22 MORE cards than Mark. Since they have a total of 120 cards, and the question asks for the number of cards that Mark started with, we should start with an answer that is LESS than half of the total (since John would have more than half and Mark would have less than half).

Let's TEST Answer D: 46 cards

IF....
Mark starts with 46 cards....
John starts with 120 - 46 = 74 cards

John gives 5 cards to Mark and Mark gives 2 cards to John....
Mark = 46 + 5 - 2 = 49 cards
John = 74 - 5 + 2 = 71 cards
John now has 22 more cards than Mark. This is an exact match for what we were told, so this MUST be the answer...

Final Answer:
GMAT assassins aren't born, they're made,
Rich

We can let the number of cards Mark has = m and the number of cards John has = j.

Since they have a combined 120 cards, m + j = 120.

We are also given that 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. Thus:

j - 5 + 2 = m - 2 + 5 + 22

j - 3 = m + 25

j = m + 28

We can substitute m + 13 for j in the equation m + j = 120 and we have:

m + m + 28 = 120

2m = 92

m = 46

Answer: D