When positive integer x is divided by positive integer y, the result i

VERITAS PREP OFFICIAL SOLUTION:

An important division concept that the GMAT likes to test is that the remainder divided by the divisor becomes the decimal places. (Try this with smaller numbers like 5 divided by 4. The remainder is 1, which when divided by 4 becomes .25. Those are the decimal places in the result 1.25.)

Here you're given the decimal places as .32, which translates to "thirty-two hundredths" or 32/100. Since 32/100 reduces to 8/25, you know that in order to have a two-digit remainder you must have a divisor that's a multiple of 25 and a remainder that's a multiple of 8 and that's a two-digit number. That leaves you with these possibilities:

16/50

24/75

32/100

40/125

etc.

Which should tell you that the possible remainders are all multiples of 8 from 16 to 96. To sum those values, take the number of terms (there are 11 of them, since that's 2 * 8 through 12 * 8) and multiply by the middle value (56, the average of 16 and 96) and the answer is 616.