QUESTION

CSAT

Easy

Maths

Prelims 2021

Consider all 3-digit numbers (without repetition of digits) obtained using three non-zero digits which are multiples of 3. Let S be their sum. Which of the following is/are correct?

S is always divisible by 74.
S is always divisible by 9.

Select the correct answer using the code given below:

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Explanation

Three non-zero digits which are multiples of 3 are: 3, 6, and 9.

Using these 3 digits, we can make $3!$ , i.e. 6 three-digit numbers.

So their sum, $S = 369 + 396 + 639 + 693 + 936 + 963 = 3996$

We can see that, S is divisible by both 74 and 9.

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