Question

A and B are two number when divided by 7 leaves a remainder 3 and 5. What will be the remainder when A-B is divided by 7 ?

Answer 1

A/7 == Quotient + remainder
A = Q*7 + 3
Similarly B = Q1*7 + 5
A - B = 7(Q-Q1) + (3-5)
(A-B)/7 = 7(Q-Q1)/7 + -2/7
Hence remainder will be equal to what we get when -2 is divided by 7, which is nothing but 7-2 = 5
Hope it helps.

Answer 2

The remainder when A-B is divided by 7 is 5.

Given - Divisor and remainder

Find - Remainder when A-B is divided by 7

Solution - As we know -

Dividend = Divisor*Quotient + Remainder

Let the quotient for number A be p and number B be q.

For number A

A = 7p + 3

For number B

B = 7q + 5

For A-B

A-B = 7p + 3 - 7q - 5

A-B = 7p - 7q - 2

A-B = 7(p-q) - 2

Here, the remainder is -2. But the divisor is 7, so the remainder should be between any number from 0 to 6.

A-B = 7(p-q-1+1) - 2

A-B = 7(p - q - 1) + 7 - 2

A-B = 7(p - q - 1) + 5

Hence, remainder when A-B is divided by 7 is 5. The quotient will be 7(p - q - 1).

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