Question

When a is divided by c the remainder is 11. when b is divided by c the remainder is 21. when a+b is divided by c the remainder is 4. then c=?

Answer 1

Answer:

c=31

Step-by-step explanation:

Given that 11 is the remainder when a is divided by c.

So, a can be expressed as

a=mc+11, where m is an integer

Also given that 21 is the remainder when b is divided by c.

So, b can be expressed as

b=nc+21, where n is an integer.

Now, given that 4 is the remainder when a+b is divided by c.

a+b=(m+n)c+35

When this is divided by c, the remainder will be same when 35 is divided by c as (m+n)c is already divisible by c.

So, the remainder is 4 when 35 is divided by c.

So,           35=kc+4

implies,    31=kc

Therefore, c is a factor of 31 and as 31 is a prime number, hence

c=31

Hope this helps!