CAT 2018 Slot 1 — QA Question 34
Geometric ProgressionEasy
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
Answer & solution
- A
1/6
5/2
- C
3/6
- D
3/2
Solution
Let the common ratio be ‘k’.
⇒ x = y/k and z = yk
Now considering the AP, 5x = 5y/k, 16y and 12z = 12yk are in arithmetic progression,
∴ 2 × 16y = 5y/k + 12yk
⇒ 32 = 5/k + 12k
⇒ 12k2 – 32k + 5 = 0
⇒ (2k – 5)(6k – 1) = 0
⇒ k = 5/2 or 1/6
As x < y < z, k has to be greater than 1.
∴ k = 5/2
Hence, option (b).