Exams › SSC CGL (Prelims) › General

In the 7-digit number 89476_2, what is the smallest digit that can replace the blank so that the entire number is divisible by 8?

1. 2
2. 1
3. 4
4. 3

Correct answer: 3

Solution

Divisibility by 8 depends only on the last three digits: 6_2 = 600 + 10d + 2. We need (602 + 10d) ÷ 8 = integer. 602 mod 8 = 2; 10d mod 8 = 2d. So 2 + 2d ≡ 0 (mod 8) → 2d ≡ 6 (mod 8) → d ≡ 3 (mod 4). Smallest single digit is d = 3. Check: 632 ÷ 8 = 79 ✓.

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