CAT 2019 Slot 1 — QA Question 4
IndicesEasy
If m and n are integers such that (√2)19 34 42 9m 8n = 3n 16m (64)1/4, then m is
Answer & solution
- A
-16
-12
- C
-24
- D
-20
Solution
(√2)19 34 42 9m 8n = 3n 16m (64)1/4
∴ 219/2 34 24 32m 23n = 3n 24m 26/4
∴ 219/2 34 24 32m 23n = 3n 24m 23/2
∴ 2[(19/2) + 4 + 3n] 3(4 + 2m) = 2[4m + (3/2)] 3n
Equating the exponents of 2 and 3 on both sides, we get;
Powers of 2 : (19/2) + 4 + 3n = 4m + (3/2)
⇒ 6n + 24 = 8m ...(1)
Powers of 3 : 4 + 2m = n ...(2)
Solving (1) and (2), we get;
m = −12.
Hence, option (b).