# Q. AB and CD are 2-digit numbers. Multiplying AB with CD results in a 3-digit number DEF. Adding DEF to another 3-digit number GHI results in 975. Further A, B, C, D, E, F, G, H, I are distinct digits. If E = 0, F = 8, then what is A+B+C equal to ?

(a) 6

(b) 7

(c) 8

(d) 9

Correct Answer: (a) 6

#### Question from UPSC Prelims 2023 CSAT

**Explanation : **

## Since E = 0 and F = 8, the product of AB and CD must be a number in the form of 08X, where X is a digit from 1 to 9.

The only way to get a product of 08X is if one of the numbers (AB or CD) is a multiple of 4 and the other number ends with 2 or 7.

The possible pairs of numbers are (12, 34), (17, 24), (24, 17), (34, 12).

However, since the sum of DEF and GHI is 975, the sum of the digits D, G, H, I must be 9 (since E = 0 and F = 8).

The only pair of numbers that satisfies this condition is (12, 34), which gives a product of 408.

Therefore, A = 1, B = 2, C = 3, D = 4.

So, A + B + C = 1 + 2 + 3 = 6.

Therefore, the correct answer is (a) 6.