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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.
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Re: When positive integer x is divided by positive integer y, the result i [#permalink]

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10 Apr 2015, 02:32

x/y = 96.12 x/y ==> 9612/100 ==> x/y = 96 12/100 From that you can see that the reminder is 12. If you make the reminder 9, that means that you multiply 12 by 3/4 Multiply 100 also by 3/4 and you get 75.

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13 Jun 2016, 13:20

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Re: When positive integer x is divided by positive integer y, the result i [#permalink]

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17 Jun 2016, 06:46

Bunuel wrote:

When positive integer x is divided by positive integer y, the result is 59.32. What is the sum of all possible 2-digit remainders for x/y?

A. 560 B. 616 C. 672 D. 728 E. 784

Kudos for a correct solution.

After I saw the solution..I got to know what exactly the question was asking for..somehow..I feel that this question should ask it in a better way..if thats not the case, then please help me comprehend such abridged questions.
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Re: When positive integer x is divided by positive integer y, the result i [#permalink]

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07 Jul 2016, 03:18

1

This post received KUDOS

Hi everyone!

A question here...

I don't really get what the Q is asking, since 8/25, 16/50 etc all represent the same exact number! so, how come we are summing numbers from 8 to 96? for what? They would reduce to the simplest fraction 8/25, so how can those be different numbers (remainders in this case)?

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21 Aug 2017, 12:20

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: When positive integer x is divided by positive integer y, the result i [#permalink]

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21 Aug 2017, 13:25

iliavko wrote:

Hi everyone!

A question here...

I don't really get what the Q is asking, since 8/25, 16/50 etc all represent the same exact number! so, how come we are summing numbers from 8 to 96? for what? They would reduce to the simplest fraction 8/25, so how can those be different numbers (reminders in this case)?

i found a better explanation

32/100 reduces down to 8/25

you can not use 8 because that is not a double-digit number, but you want to look for everything that could l reduce down to 8/25 which represent all the other numbers that could be the remainers

the easy way is to multiply by all numbers, 1* 8/ 25= 8/25. 2* 8/25 = 16/50 ...... 12* 8/25 = 96/ 300, and you can not use 13 because that is greater than two digits.

so basically you then add up all those values in between

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