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N is the number, which when divided by 3 and 8 leaves the remainder 1 and 6, then which statement(s) is/are correct? A) If N is the largest two digit number, then sum of digit of N is 12. B) If N is the smallest three digit number, which when divided by 5, then remainder will be 3. C) If N is the largest two digit number, then N is an even number. Which statement(s) is/are true?

N is the number, which when divided by 3 and 8 leaves the remainder 1 and 6, then which statement(s) is/are correct? A) If N is the largest two digit number, then sum of digit of N is 12. B) If N is the smallest three digit number, which when divided by 5, then remainder will be 3. C) If N is the largest two digit number, then N is an even number. Which statement(s) is/are true? Correct Answer Only B and C

Given,

N is the number, which when divided by 3 and 8 leaves the remainder 1 and 6.

Formula:

Largest two digit number is 99.

Smallest three digit number is 100.

Calculation:

LCM of 3 and 8

3 = 1 × 3

8 = 2 × 2 × 2

LCM = 2 × 2 × 2 × 3 = 24

When we divide 99 by 24 we get 3 in remainder.

The largest two digit number which when divided by 24 = 99 – 3 = 96

If N is divided by 3 and 8 leaves the remainder 1 and 6, then = 3 – 1 = 8 – 6 = 2

The largest two digit number which when divided by 3 and 8 leaves 1 and 6 remainder = 96 – 2 = 94

Statement C is correct because 94 is even number.

The sum of 94 = 9 + 4 = 13

Statement A is wrong.

When we divide 100 by 24 we get 4 in remainder.

The smallest three digit number which when divided by 24 = 100 – 4 + 24 = 120

If N is divided by 3 and 8 leaves the remainder 1 and 6, then = 3 – 1 = 8 – 6 = 2

The smallest three digit number which when divided by 3 and 8 leaves 1 and 6 remainder = 120 – 2 = 118

When we divide 118 by 5 we get remainder 3.

Statement B is correct.

∴ Only statement B and C are correct.

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