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Darknight123
The integers 573921 and 575713 when divided by a 3 digit number leave the same remainder. What could be that 3 digit number?

A.206
B.274
C.256
D.189
E.219

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If 2 numbers are divisible by a number it should also divide the sum and difference

and the difference provides = 1792 which is divisible by 256 since 1792 = 256*7

Therefore IMO C
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The integers 573921 and 575713 when divided by a 3 digit number leave the same remainder.

Dividend = Divisor * Quotient + Remainder

=> 573921 = x*a + r (where x is the divided, a is the quotient and r is the remainder)
=> 575713 = x*b + r (where x is the divided, b is the quotient and r is the remainder)

575713 - 573921 = xb + r - (xa + r) = xb - xa = x*(b-a)
=> 1792 = x*(b-a)
=> x must divide a factor of 1792 = 256 * 7
=> Number can be 256

So, Answer will be C
Hope it helps!

Watch the following video to MASTER Remainders

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