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.


Get one day FREE Trial of CAT online Full course FREE Registration
Also Check: 841+ CAT Quant Questions with Solutions


CAT Quant Online Course


  • 1000+ Practice Problems
  • Detailed Theory of Every Topics
  • Online Live Sessions for Doubt Clearing
  • All Problems with Video Solutions
₹ 2999

CAT 2018 Questions Paper with Solution PDF Download


CAT 2018 Quant Questions with Solutions

CAT 2018 Slot-1


CAT 2018 Slot-2


Back to Main Page



Try CAT 2020 online course for 1 day for FREE

Please provide your details to get FREE Trial of Bodhee Prep's Online CAT Course for one day. We will inform you about the trial on your whatsApp number with the activation code.