A number when divided by 82 it gives a remainder of 80. What is the remainder if that number is divided by 41?

(a) 40

(b) 39

(c) 28

(d) 34

Question

A number when divided by 82 it gives a remainder of 80. What is the remainder if that number is divided by 41? 

(a) 40

(b) 39

(c) 28

(d) 34

ONLiNE UPSC · Accepted Answer

We are told that a number leaves a remainder of 80 when divided by 82, 

Which means the number is 80 more than a multiple of 82. 

So, we can write the number as 82k + 80 for some integer k. 

Now, we want to find the remainder when this number is divided by 41. 

Since 82 is divisible by 41 (because 82 = 2 &times; 41), the term 82k is also divisible by 41 and leaves no remainder. 

So, the remainder when the number is divided by 41 will be the same as the remainder when 80 is divided by 41. 

Dividing 80 by 41 gives 1 as the quotient and 39 as the remainder. 

Hence, the final answer is 39.

So, option b is correct.

Number System

Remainder Theorem

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