Data Sufficiency: Integer Product and Sum

XAT 2019 · QADI · Medium · Data Sufficiency

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We have two unknown positive integers mm and nn, whose product is less than 100.

There are two additional statement of facts available:

  • Statement 1: mnmn is divisible by six consecutive integers {j,j+1,…,j+5}\{j, j + 1, \dots, j + 5\}
  • Statement 2: m+nm + n is a perfect square.

Which of the two statements above, alone or in combination shall be sufficient to determine the numbers mm and nn?

  1. A.

    Each statement alone is sufficient to answer the question.

  2. B.

    Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

  3. C.

    Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.

  4. D.

    Statements 1 and 2 together are not sufficient, and additional data is needed to answer the question.

  5. E.

    Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.

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