# Q. A 3-digit number ABC, on multiplication with D gives 37DD where A, B, C and D are different non-zero digits. What is the value of A+B+C?

(a) 18

(b) 16

(c) 15

(d) Cannot be determined due to insufficient data

Correct Answer: (a) 18

#### Question from UPSC Prelims 2023 CSAT

**Explanation : **

## 3-digit number ABC

The problem states that when a 3-digit number ABC is multiplied by D, it gives 37DD. Here, A, B, C, and D are different non-zero digits.

To solve this, we need to find a value for D such that 37DD is a 4-digit number. The only possible values for D are 1, 2, 3, 4, 5, 6, 7, 8, and 9.

If D = 1, then 37DD is not a 4-digit number. If D = 2, then 37DD is not a 4-digit number. If D = 3, then 37DD is not a 4-digit number.

If D = 4, then 37DD = 3744, which is a 4-digit number. Therefore, D = 4.

Now, we need to find a 3-digit number ABC such that ABC * 4 = 3744.

The only 3-digit number that satisfies this equation is 936. Therefore, A = 9, B = 3, and C = 6.

Finally, we need to find the value of A + B + C.

A + B + C = 9 + 3 + 6 = 18.

Therefore, the correct answer is (a) 18.