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CAT 2002 — QA Question 27

Simple EquationsEasy

A thief was stealing diamonds from a jewellery store. On his way out, he encountered three guards, each was given half of the existing diamonds and two over it by the thief. In the end, he was left with one diamond. How many did the thief steal?

Answer & solution

Correct answer: 36

  • A

    40

  • 36

  • C

    42

  • D

    38

Solution

Assume that the thief had stolen x diamonds.

The 1st watchman got = x/2 + 2

Diamonds left = x − (x/2 + 2) = x/2 – 2

The 2nd watchman got = (x/2 − 2)/2 + 2 = x/4 + 1

Diamonds left = (x/2 − 2) − (x/4 + 1) = x/4 − 3

The 3rd watchman got = (x/4 − 3)/2 + 2 = x/8 + 1/2

Diamonds left = (x/4 − 3) − (x/8 + 1/2) = x/8 − 7/2 = 1

∴ x/8 = 9/2

∴ x = 36

Hence, option (b).


Alternatively,

One may proceed by substituting the options that are even.

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CAT 2002 QA Q27: A thief was stealing diamonds from a jewellery store. On his way out, he encountered three guards, each was gi — Solution | TheCATExam