UPSC Prelims 2024 · CSAT
Question 35: Basic Numeracy
Let X be a two-digit number and Y be another two-digit number formed by interchanging the digits of X. If (X + Y) is the greatest two-digit number, then what is the number of possible values of X ?
AnswerUPSC’s answer is (d).
Let X = 10a + b; then Y = 10b + a and X + Y = 11(a + b). The greatest two-digit number is 99, so a + b = 9. The pairs (a, b) are (1,8), (2,7), (3,6), (4,5), (5,4), (6,3), (7,2), (8,1) and (9,0). X = 90 would make Y = 09, which is not a two-digit number, so it is excluded. That leaves 8 values: 18, 27, 36, 45, 54, 63, 72 and 81.
Why each option is right or wrong
- (a) Wrong. 2 counts only some of the pairs; there are 8.
- (b) Wrong. 4 counts only half of the pairs.
- (c) Wrong. 6 misses two valid values.
- (d) Right. 18, 27, 36, 45, 54, 63, 72, 81 (90 is excluded as Y would be 09).
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2024, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.