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XAT 2019 — QA & DI Question 5

IndicesEasy

If 7a×(35)(b+1)×(20)(c+2)3 is a whole number then which one of the statements below is consistent with it?

Answer & solution

  • a = 3, b = 2, c = 1

  • B

    a = 3, b = 1, c = 1

  • C

    a = 2, b = 1, c = 2

  • D

    a = 2, b = 1, c = 1

  • E

    a = 1, b = 2, c = 2

Solution

Let us prime factorize all the terms under the cube root sign.
      
7a × (35)(b+1) × (20)(c+2) = 7a × 5b+1 × 7b+1 × 22(c+2) × 5c+2

= 22(c+2) × 5b+c+3 × 7a+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).

XAT 2019 QA & DI Q5: If 7 a × ( 35 ) ( b + 1 ) × ( 20 ) ( c + 2 ) 3 is a whole number then which one of the statements — Solution | TheCATExam