The number which should be added to the number added to the numbers 2, 14, 62

Question -

The number which should be added to the number added to the numbers 2, 14, 62 so that the resulting numbers may be in G.P. is

Options:

A . 1

B . 2

C . 3

D . 4

Answer: Option B
:
B

Suppose that the added number be x

then x + 2, x + 14, x + 62 be in G.P.

Therefore $(x + 14)^{2}$ = (x + 2)(x + 62)

$\Rightarrow x^{2} + 196 + 28 x$ = $x^{2} + 64 x + 124$

$\Rightarrow 36 x$ = 72 $\Rightarrow x$ = 2

Trick : (a) Let 1 is added, then the numbers will be 3, 15, 63 which are obviously not in G.P.

(b) Let 2 is added, then the numbers will be 4, 16, 64 which are obviously in G.P.

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