# Q. If the sum of the two-digit numbers AB and CD is the three-digit number 1CE, where the letters A, B, C, D, E denote distinct digits, then what is the value of A?

a) 9

b) 8

c) 7

d) Cannot be determined due to insufficient data

Correct answer: a) 9

##### Question from UPSC Prelims 2024 CSAT Paper

**Explanation:**

## Sum of the two-digit numbers AB and CD

The solution considers two cases:

Case 1: No carry-over from B+D

In this case:

A + C = 1C

A + C = 10 + C

A = 10

However, A = 10 is not possible because A must be a single digit.

Case 2: There’s a carry-over of 1 from B+D

In this case:

A + C + 1 = 1C

A + C + 1 = 10 + C

A = 9

Case 2 provides a valid solution where A = 9.

This solution efficiently eliminates Case 1 and proves that Case 2 must be true, leading to the conclusion that A = 9.