Algebra - Surds & Indices - Previous Year CAT/MBA Questions

Answer: Option A

Video Explanation

Text Explanation :

Let us prime factorize all the terms under the cube root sign.
      
7^a × (35)^(b+1) × (20)^(c+2) = 7^a × 5^b+1 × 7^b+1 × 2^2(c+2) × 5^c+2

= 2^2(c+2) × 5^b+c+3 × 7^a+b+1

We have to calculate cube-root of this expression, hence powers of all prime numbers should be divisible by 3 for cube-root to be a whole number.

∴ 2(c + 2), (b + c + 3) and (a + b + 1) all should be multiples of 3.

Only option (a) satisfies this given condition.

Hence, option (a).