Question

How to solve:

64329 is divided by a certain number. While dividing the numbers, 175, 114 and 213 appear as three successive remainders. The divisor is
(1) 184 (2) 224
(3) 234 (4) 296

Whats the trick behind this to solve faster. Thank you in Advance.

Answer 1

The first 3 digits are 643, and the remainder after subtracting out the first digit of the quotient * the divisor is 175. That means

643-175 = divisor * a single digit. If we try 296 first, 1*296 is too small, 2*296 = 594, and 643-594 = a two digit number, so 296 is not the divisor.

We can try 184 next:
643-175 = divisor * a single digit. We could try 3 as the first digit of the quotient: 3*184 = 552, but 643-552 = a two digit number, so 184 is not the divisor

Etc.

Answer 2

hey, its for intrview preparation, means to be done fast... got any tricks for this?

Answer 3

\(643 = 175 \mod k\)
\(1752 = 114 \mod k\)
\(1149 = 213 \mod k\)

Answer 4

Well, I did the problem that way in less than a minute, but maybe I'm quicker at arithmetic than you are. Took much longer to describe what I did than to do it!