Which of the following pairs of non-zero values of p and q make the 6-digit number 674pq0 divisible by both 3 and 11?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 05 Dec 2022 Shift 1)

Answer 1

Given:

674pq0 is divisible by both 3 and 11

Concept used:

If the sum of digits of a number is a multiple of 3, the number will be completely divisible by 3

If the difference of the sum of alternative digits of a number is 0 or divisible by 11, then that number is divisible by 11 completely.

Calculation:

As 674pq0 divisible by 3

So, 6 + 7 + 4 + p + q + 0

⇒ 17 + p + q also divisible by 3

Now,

Possible values of p + q = 4, 7, 10, 13, 16

From the options

Option 1 and Option 4 is satisfying

Now,

For Option 1

The number is 674220

So, 6 + 4 + 2 - 7 - 2 = 3 Not divisible by 11

For Option 4

The number is 674520

So, 6 + 4 + 2 - 7 - 5 = 0 divisible by 11

∴ The required answer is Option 4.

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