CAT 2020 Slot 3 — QA Question 7

Assuming, k = 14^a = 36^b = 84^c

⇒ 14 = k^1/a

⇒ 36 = 6² = k^1/b or 6 = k^1/2b 

⇒ 84 = k^1/c

We know, 84 = 6 × 14

⇒ k^1/c = k^1/2b × k^1/a

⇒ k^{1/c – 1/a} = k^1/2b

⇒ $\frac{1}{c}-\frac{1}{a}=\frac{1}{2b}$

⇒ $2\mathrm{b}\left(\frac{1}{\mathrm{c}}-\frac{1}{\mathrm{a}}\right)$ = 1

Hence, $6\mathrm{b}\left(\frac{1}{\mathrm{c}}-\frac{1}{\mathrm{a}}\right)$ = 3

Hence, 3.