A) 1
B) 2
C) 3
D) 4
Correct Answer: B
Solution :
Suppose that the added number be \[x\] then \[x+2,\ x+14,\ x+62\] be in G.P. Therefore \[{{(x+14)}^{2}}=(x+2)(x+62)\] \[\Rightarrow \] \[{{x}^{2}}+196+28x={{x}^{2}}+64x+124\] \[\Rightarrow \] \[36x=72\Rightarrow x=2\]. 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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