### XAT 2011 Question 94

Instructions

are followed by two statements labelled as I and II. Decide if these statements are sufficient to conclusively answer the question. Choose the appropriate answer from the options given below:

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 II alone is sufficient to answer the question.
E. Neither Statement I nor Statement II is necessary to answer the question.

Question 94

# 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.

Solution

Given relationship is $$(PQ)(RQ) = XXX$$

Since, X can take nine values from 1 to 9, thus we have 9 possibilities.

$$111 = 3 \times 37$$                    $$666 = 18 \times 37$$

$$222 = 6 \times 37$$                    $$777 = 21 \times 37$$

$$333 = 9 \times 37$$                    $$888 = 24 \times 37$$

$$444 = 12 \times 37$$                  $$999 = 27 \times 37$$

$$555 = 15 \times 37$$

But, out of these 9 cases, only in 999, we get the unit's digit of the two numbers same. Since it is a unique value,

Thus, we need neither statement I nor II to answer the question.

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