CDS 2026 · PYQ · Data Sufficiency / Number Properties · medium
A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.
Question: Let XYZ be a 3-digit number and the difference between XYZ and ZYX is equal to PQR. Is (P + R) equal to Q?
Statement-I: P = 3
Statement-II: R = 6
Which one of the following is correct in respect of the above Question and the Statements?
A.The Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
B.The Question can be answered by using either Statement alone
C.The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
D.The Question can be answered even without using both the Statements✓ Correct
Explanation
XYZ - ZYX = (100X + 10Y + Z) - (100Z + 10Y + X) = 99(X - Z). So PQR = 99(X - Z). The multiples of 99 that are 3-digit numbers are 198, 297, 396, 495, 594, 693, 792, 891. In each case, the middle digit is 9 and the sum of first and last digits is 9. So P + R = 9 = Q always. The answer is YES, and this conclusion can be reached without using either statement.
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