Q27
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: B
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.