Question

The greatest five-digit number, when divided by 5, 6 and 7 leaves the remainder 2, is

• A. 99952
• B. 99962
• C. 99982
• D. 99752

Answer 1

The correct option is B 99962

LCM (5, 6, 7) = 5 × 6 × 7 = 210

So, the multiple of 210 added to 2 would give remainder 2 when divided by any of these three numbers 5, 6, and 7.

Now, the greatest 5-digit number is 99999.

On dividing 99999 by 210, remainder is 39.

∴ 99999 – 39 = 99960 is completely divisible by 210

So, 99960 + 2 = 99962 leaves remainder 2 when divided by 210.

∴ 99962 is the greatest five-digit number, which when divided by 5, 6 and 7 leaves remainder 2.

Hence, the correct answer is option (b).