1355 - Data Sufficiency

Data Sufficiency MCQ No. : 50215

If m and n are positive integers, is (√M )n an integer?

(1) (√M ) is an integer.

(2) (√n ) is an integer.

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Correct Answer: A

Explanation:

Arithmetic Properties of numbers

  • (1) If (√M ) is an integer and n is a positive integer, then (√M )n is an integer because an integer raised to a positive integer is an integer; SUFFICIENT.
  • (2) The information that (√n ) is an integer is not helpful in answering the question. For example, if m = 2 and n = 9, -√9 = 3, which is an integer, but (√29 ) = (l6 √2), which is not an integer. But if m = 4and n=9, then √9 = 3, which is an integer, and (√4 )9 = 29 = 512 is an integer; NOT sufficient.

The correct answer is A; statement 1 alone is sufficient.

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