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  • Question
  • Given below is an equation where the letters represent digits. (PQ) . (RQ) = XXX. Determine the sum of P + Q + R + X.
    I. X = 9.
    II. The digits are unique. [3]


  • Options
  • A. Statement I alone is sufficient to answer the question.
  • B. Statement II alone is sufficient to answer the question.
  • C. Statement I and Statement II together are sufficient, but neither of the two alone is sufficient to answer the question.
  • D. Either Statement I or Statement I alone is sufficient to answer the question.

  • Correct Answer
  •  

    Explanation

    Given relationship is (PQ)(RQ) = XXX
    Since X can take 9 values from 1 to 9 hence we have 9 possibilities
    111 = 3 x 37 444 = 12 x 37 777 = 21 x 37
    222 = 6 x 37 555 = 15 x 37 888 = 24 x 37
    333 = 9 x 37 666 = 18 x 18 999 = 27 x 37
    But out of these 9 cases only in 999, we get the unit's digit of two numbers the same. Since it is a unique value, hence we need neither statement I nor statement II to answer the question.


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