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Remainder Question

by sanchu » Mon Feb 10, 2014 3:58 pm
When positive integer x is divided by positive integer y, the remainder is 9. If x/y=96.12, what is the value of y?
a) 96
b)75
c) 48
d)25
e) 12

I'm having a tough time visualizing this one.
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by Bill@VeritasPrep » Mon Feb 10, 2014 4:11 pm
sanchu wrote:When positive integer x is divided by positive integer y, the remainder is 9. If x/y=96.12, what is the value of y?
a) 96
b)75
c) 48
d)25
e) 12

I'm having a tough time visualizing this one.
I used to forgot the relationship between the remainder and decimal forms fairly regularly, but you can always derive it using simple values.

7/4 = 1 R 3

7/4 = 1.75

Using pieces from the remainder form, how do I get the decimal .75? It must be the remainder of 3 divided by the divisor of 4.

decimal = remainder / divisor

.12 = 9/y

12/100 = 9/y

3/25 = 9/y

3y = 9*25

y=3*25

y=75
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by ceilidh.erickson » Tue Feb 11, 2014 2:16 pm
Another way you could solve this is as a system of equations.

If, when we divide x by y, we get a remainder of 9, we could say that y times something plus 9 equals x:
ny + 9 = x

Then we're told that x/y = 96.12, which means that n must equal 96:
96y + 9 = x

We can also rearrange our given equation to say 96.12y = x.

Since both equations are equal to x, we can say:

96y + 9 = 96.12y
9 = 0.12y
y = 75
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by ceilidh.erickson » Tue Feb 11, 2014 2:17 pm
For more on remainders, see: https://www.beatthegmat.com/tricky-remai ... tml#695422
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by GMATGuruNY » Tue Feb 11, 2014 2:38 pm
sanchu wrote:When positive integer x is divided by positive integer y, the remainder is 9. If x/y=96.12, what is the value of y?
a) 96
b)75
c) 48
d)25
e) 12
I would probably use Bill's approach, as I did here:
https://www.beatthegmat.com/dealing-with ... 69971.html

Another approach:

96.12 = 9612/100 = 4806/50 = 2403/25.

Since x/y = 2403/25 -- and x and y are integers -- y must be a multiple of 25.
Eliminate A, C and E.
If y=25 -- as stated in answer choice D -- then x=2403, in which case the remainder for x/y will be 3.
Eliminate D.

The correct answer is B.
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