If two numbers are each divided by the same divisor, then the remainder are 6 and 7, respectively. If the sum of the two numbers be divided by the same divisor, then the remainder is 5. The divisor is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 8.
Let the divisor be D, and the two numbers be a and b.
When a is divided by D, the remainder = 6
⇒ a = kD + 6 for some integer k
When b is divided by D, the remainder = 7
⇒ b = mD + 7 for some integer m
The sum of the two numbers = a + b = kD + 6 + mD + 7 = (k + m)D + 13
When a + b is divided by D, the remainder = 5
Remainder of 13 divided by D = 5
This means
⇒ 13 − 5 = 8 is divisible by D
The divisors of 8 are (D) = 1, 2, 4, 8
Since the value of D must be greater than the largest remainder (7),
the only valid value D = 8