# Test of Divisibility : XAT, TANCET Number Properties

The question is from the topic Number Systems. It is a question on tests of divisibility.

#### Question

What is the value of M and N respectively? If M39048458N is divisible by 8 and 11; where M and N are single digit integers?

- 7, 8
- 8, 6
- 6, 4
- 5, 4
- 4, 6

Correct Answer -

**6, 4**. Choice (3)

#### Explanatory Answer

**Test of Divisibility by 8**: If the last three digits of a number are divisible by 8, then the number is divisible by 8.

Here, last three digits 58N are divisible by 8 if N = 4 because 584 is divisible by 8.

**Test of Divisibility by 11**If the digits at odd and even places of a given number are equal or differ by a number divisible by 11, then the given number is divisible by 11.

Therefore, (M + 9 + 4 + 4 + 8) - (3 + 0 + 8 + 5 + N) = (M + 5) should be divisible by 11; this condition is satisfied when M = 6.

Correct answer choice (3)

Level of difficulty : Moderate

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