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CAT 1998 — QA Question 20

Even OddEasy
Passage / Data

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 and B collected two more coins than twice the number of coins collected by C, then the number of coins collected by B could be

Answer & solution

Correct answer: 22

  • A

    28

  • B

    20

  • C

    26

  • 22

Solution

If A has collected 54 coins, the remaining three of them should collect (100 – 54) = 46 coins between themselves.
Let us assume that C has collected 10 coins. So B will collect (2 × 10) + 2 = 22. So A will collect (46 – 10 – 22) = 14 coins, which is a possible combination.

Let us now assume that C picks up 12 coins. So B should pick up (2 × 12) + 2 = 26. So A will have to collect (46 – 12 – 26) = 8 coins. 
This combination is not possible. It can be concluded that C cannot pick up more than 10 coins and hence B has to pick up 22 coins to satisfy the given condition.

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CAT 1998 QA Q20: If A collected 54 coins and B collected two more coins than twice the number of coins collected by C, then the — Solution | TheCATExam