# Quantitative Aptitude – Modern Maths – Progressions – Let x, y, z be three positive real ## Slot -1 – Quantitative Aptitude – Modern Maths – Progressions – Let x, y, z be three positive real numbers

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?

a) 5/2
b) 1/6
c) 3/2
d) 3/6

Solution:
Given x,y, z are in GP . let common ratio of this GP is r so y=xr & z=xr^2
Now 5x, 16y and 12z are in A.P. So
12z-16y=16y-5x
32y=12z+5x
32xr=12xr^2+5x
12r^2-32r+5=0
(6r-1)(2r-5)=0
So r=1/6 or 5/2
As given x < y < z so r >1
Thus r = 5/2
Option a) 5/2 is correct

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