CAT 2018 Quant Questions

Question:
Let x, y, z be three positive real numbers in a geometric progression such that x < y < z. If 5x, 16y, and 12z are in an arithmetic progression then the common ratio of the geometric progression is

3/6
3/2
5/2
1/6
Show Answer
Correct Answer: 3

Since x, y ,and z are in G.P.  and x<y<z, let x = a, y=ar and z=ar2, where a>0 and r>1.

It is also given that, 15x, 16y and 12z are in A.P.

Therefore, 2×16y=5x+12z

Substituting the values of x, y and z we get,

$32ar=5a + 12ar^2$

$\Rightarrow 32 r=5+12 r^{2}$

$\Rightarrow 12 r^{2}-32 r+5=0$

On solving the above quadratic equation we get r=1/6 or 5/2.

Since r>1, therefore r=5/2.


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