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CAT 1991 — QA Question 15

Simple EquationsEasy

Iqbal dealt some cards to Mushtaq and himself from a full pack of playing cards and laid the rest aside. Iqbal then said to Mushtaq. “If you give me a certain number of your cards, I will have four times as many cards as you will have. If I give you the same number of cards, I will have thrice as many cards as you will have “. Of the given choices, which could represent the number of cards with Iqbal?

Answer & solution

Correct answer: 31

  • A

    9

  • 31

  • C

    12

  • D

    35

Solution

Let Mushtaq has M cards while Iqbal has got I cards with him.

Let number of cards exchanged be x.

Case 1: I + x = 4(M – x) ... (i)

Case 2: I – x = 3(M + x) ... (ii)

From (i) and (ii)

I = 31x

Since I + M has to be less than or equal to 52, the only possible value for I could be 31.

Hence, option (b).

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CAT 1991 QA Q15: Iqbal dealt some cards to Mushtaq and himself from a full pack of playing cards and laid the rest aside. Iqbal — Solution | TheCATExam