Question

When a number is divided by 119, the remainder remains 15. When the same number is divided by 17, What will be the remainder?

• A. 12
• B. 13
• C. 15
• D. 14

Answer 1

Answer:

C. 15

Let, the Number be x, Quotient be q

Divisor, d = 119

Remainder, r = 15

We know, x = (d $\times$ q) + r

⇒ x = (119 $\times$ q) + 15 = (17 $\times$ 7 $\times$ q) + 15

Same number when divided by 17

$\frac{x}{17}$=7q + $\frac{15}{17}$

∴ Remainder is 15.

Alternate Method 

Alternative 1:

Assume any number which when divided by 119 gives remainder 15

As we know, 

All the numbers were completely divided by itself,

Let the number be 119 + 15 = 134 (as 15 remainder was given in the question)

Now, 

When 134 is divided by 17 leaves remainder 15 

So, 15 is the right answer.

 

Alternative 2:

As we know that the given number 119 is completely divided by 17 (the other number)

Then in this case, Remainder will also be same as 15