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

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

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28 Jan 2015, 07:40
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Difficulty:

95% (hard)

Question Stats:

58% (01:59) correct 42% (05:07) wrong based on 243 sessions

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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

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

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28 Jan 2015, 09:59
1
ans B 616...
remainders = .32=32/100=8/25=16/50 and so on..
so two digit remainders are 16+24+32+....+96..
=8(2+3+4....+12)=616
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Re: When positive integer x is divided by positive integer y, the result i [#permalink]

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28 Jan 2015, 16:58
chetan2u wrote:
ans B 616...
remainders = .32=32/100=8/25=16/50 and so on..
so two digit remainders are 16+24+32+....+96..
=8(2+3+4....+12)=616

Why would we not count the 8/25? I got 624. Wouldn't it be =8(1+2+3+4....12)?

****Nevermind reread question and see that it is only 2 digit answers that we are using so then B=616
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Re: When positive integer x is divided by positive integer y, the result i [#permalink]

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28 Jan 2015, 22:09
1
Here we go---

Remainder/Divisor = decimal part

Say remainder = r

r/y = 0.32 --> 32/100

so we can have 16+24+32+40+48+56+64+72+80+88+96 = 616

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

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02 Feb 2015, 03:03
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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.

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

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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04 Feb 2015, 01:50
$$\frac{32}{100} = \frac{16}{50} = \frac{24}{75} =$$ .....

Two digit remainder addition = 16+24+32+40+48+56+64+72+80+88+96 = 8*2 + ................ + 8*12 = 8(2+.......+12) = 77*8 = 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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When positive integer x is divided by positive integer y, the result i [#permalink]

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Updated on: 21 Aug 2017, 14:53
.32 reduces to 8/25, 16/50, 24/75, 32/100....96/300
the sum of all 2 digit multiples of 8≤96=11*(16+96)/2=616
B

Originally posted by gracie on 13 Jun 2016, 15:16.
Last edited by gracie on 21 Aug 2017, 14:53, edited 5 times in total.
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Re: When positive integer x is divided by positive integer y, the result i [#permalink]

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13 Jun 2016, 17:22
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.

Reminder of x/y= 32/100= 8/25

First two digits multiple of 8 = 16
Last two digit multiple of 8 = 96 (8*12)

Total = Average * Total number of digits in the set

Since its a uniformly arranged set, average = 1st digit+last digit/2= 16+96/2
Total number of digits= 11

Total= 16+96/2*11= 616

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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
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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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
Re: When positive integer x is divided by positive integer y, the result i   [#permalink] 21 Aug 2017, 13:25
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