Question

The integers 34041 and 32506, when divided by a 3 - digit integer n, leave the same remainder. What can be the value of n?
1. 289
2. 307
3. 367
4. 493

Answer 1

Correct Answer - Option 2 : 307

Given:

3-digit integer = n

Two integers = 34041 and 32506

Concept used:

Whenever we divide any two numbers with a common divisor and the remainder comes out to be same then the difference of those two numbers is a multiple of the divisor.

Calculation:

Let the common remainder be x.

32506 – x is divisible by n.

34041 – x is divisible by n.

Difference of (32506 – x) and (34041 – x) = (32506 – x) – (34041 – x)

⇒ 32506 – x – 34041 + x

⇒ 32506 – 34041

⇒ 1535 

Factors of 1535 = 1 × 5 × 307 × 1535

3-digit number = 307

⇒ n = 307

∴ The value of n is 307.