Which of the following statements is true?A) The number 49,836 is divisible by 5, but not by 9.
B) The number 49,836 is divisible by 5 and 9.
C) The number 49,836 is divisible by 3, 6, and 9.
D) The number 49,836 is divisible by 2, 3, and 6.

Option D

ANSWER:  

The number 49,836 is divisible by 2, 3, and 6.

SOLUTION:

Let us check one by one statement.

Consider Option (A)

The number 49,836 is divisible by 5, but not by 9.

Given, 49,836 is divisible by 5.

Divisibility rule for 5 is, last digit of the number should be either 0 or 5.

But here last digit is 6, so given number is not divisible by 5

Hence, this statement is not true.

Consider Option (B)

The number 49,836 is divisible by 5 and 9.

Here again given that, 49,836 is divisible by 5, but we know that it is not divisible by 5.

Hence, this statement is also wrong.

Consider Option (C)

The number 49,836 is divisible by 3, 6, and 9.

Given, 49,836 is divisible by 3.

Divisibility rule for 3 is, sum of the digits must be a multiple of 3.

Now sum of digits = 4+9+8+3+6 = 30.

Since, 30 is an multiple of 3, given number is divisible by 3.

And, 49,836 is divisible by 6.

Divisibility rule for 6 is, the number should be divisible by both 2 and 3.

First let us check divisibility with 2,

Divisibility rule for 2 is, the last digit of the number must any one of 0,2,4,6,8

Here, last digit is 6, so it is divisible by 2

And it is also divisible by 3 as we proved above.

So, the given number is divisible by 6.

And 49,836 is divisible by 9.

Divisibility rule for 9 is, sum of the digits must be a multiple of 9.

Sum of digits = 30 which is not a multiple of 9

So, given number is not divisible by 9

Hence, this statement is wrong.

Consider Option (D)

The number 49,836 is divisible by 2, 3, and 6.

Given, 49,836 is divisible by 2, 3, and 6.

As we have already seen in above case that, 49,836 is divisible by 2, 3 and 6  .Hence statement D is correct.