CSAT 2021

Q. Consider all 3-digit numbers (without repetition of digits) obtained using three non-zero digits) obtained using three non-zero digits which are multiples of 3. Let S be their sum.

Which of the following is/are correct?
1. S is always divisible by 74.
2. S is always divisible by 9.
Select the correct answer using the code given below:
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
Correct Answer: (c) Both 1 and 2

Question from UPSC Prelims 2021 CSAT Paper

Explanation:

Sum of 3-Digit Numbers with Digits 3, 6, and 9

The three non-zero digits which are multiples of 3 are 3, 6, and 9. The possible 3-digit numbers (without repetition of digits) obtained using these three digits are: 369, 396, 639, 693, 936, and 963.

The sum S of these numbers is:

S = (369 + 396 + … + 963) = 3996.

S is divisible by both 74 and 9.

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