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

A12

B13

C15

D14

Answer:

C. 15

Read Explanation:

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

x17\frac{x}{17}=7q + 1517\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


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