CAT 1998 — QA Question 19
Direction: Answer the question based on the following information.
A, B, C and D collected one-rupee coins following the given pattern.
- Together they collected 100 coins.
- Each one of them collected even number of coins.
- Each one of them collected at least 10 coins.
- No two of them collected the same number of coins.
If A collected 54 coins, then the difference in the number of coins between the one who collected maximum number of coins and the one who collected the second highest number of coins must be at least
Answer & solution
- A
12
- B
24
30
- D
None of these
Since A has collected 54 coins out of 100, he should obviously be the person who collected the maximum number of coins. For the difference between him and the second highest person to be minimum, the second highest person should collect the maximum number of coins possible under the given conditions. And for this to happen, the remaining two should collect the minimum number of coins. So if the two of them collect 10 and 12 coins, i.e. 22 coins between themselves, the third person would have to collect (100 – 54 – 22) = 24 coins. Hence, the difference between him and the highest person should at least be (54 – 24) = 30.