Question

a three digit number is divisible by 18 leaves remainder is 5 and divided by 16 how many different possible values it can have?
a.0
b.1
c.4
d.8​

Answer 1

Given:

A three digit number is divisible by 18.

It leaves a remainder 5 when divisible by 16.

To Find:

How many different possible values can it have?

Solution:

Let the unknown 3 digit number be A.

Given A is divisible by 18.

Therefore,

• A = 18k - (1)

Also When A is divided by 16, it leaves a remainder 5.

Then,

• A = 16m + 5 - (2)

Lets equate (1)  and (2)

• 18k = A = 16m + 5
• k = (16m + 5) / 18

Here 16 x m + 5 should be divisible by 18 , for k to be an integer value.

• 16 x m will be an even number.
• An even number + odd number = always n odd number.
• 16m + 5 is an odd number.
• Hence it will not be divisible by 18.

Hence the number of possible values the three digit number can have is 0.