Two numbers when divided by a certain divisor leave remainders 4375 and 2986 respectively, but when the sum of the two numbers is divided by the same divisor, the remainder is 2361. What is the divisor?
A
Correct answer
Explanation
Let n be the divisor and the numbers be a and b. We have a ≡ 4375 (mod n) and b ≡ 2986 (mod n). So (a+b) ≡ 4375+2986 ≡ 7361 (mod n). But we're told (a+b) ≡ 2361 (mod n). Therefore 7361 ≡ 2361 (mod n), meaning n divides (7361-2361) = 5000. Since n > 4375 (remainder must be less than divisor), n = 5000.