Question

Two numbers when divided by a certain divisor leave remainders of 431 and 379 respectively. When the sum of these two numbers is divided by the same divisor, the remainder is 211. What is the divisor?

Answer 1

Let A be the divisor, X and Y be the two numbers. ( A is an integer) 
We have: X= Ax + 431 
Y= Ay+ 379 
X+Y= Az + 211= A(x+y) + 810 ( x, y and z and integers) 
---> A ( z-x-y)= 810-211= 599

Answer 2

Concept:

Number = divisor × quotient + remainder

Given:

Two numbers when divided by a certain divisor leave remainders of 431 and 379 respectively.

When their sum is divided by the same divisor, the remainder is 211.

Find:

We need to find the divisor.

Step-by-step explanation:

Let A be the divisor

and

X and Y be the two numbers.

ATQ, we have:

X = A x + 431

Y = A y+ 379

X + Y = A z + 211

Also,

A z + 211 = A ( x + y ) + 810

We get that:

A ( z - x - y ) = 810 - 211 = 599

Therefore, the divisor is 599.

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