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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Remainder Question
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Bill@VeritasPrep
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I used to forgot the relationship between the remainder and decimal forms fairly regularly, but you can always derive it using simple values.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.
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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ceilidh.erickson
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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
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
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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ceilidh.erickson
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For more on remainders, see: https://www.beatthegmat.com/tricky-remai ... tml#695422
Ceilidh Erickson
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Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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GMATGuruNY
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I would probably use Bill's approach, as I did here: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
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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As a tutor, I don't simply teach you how I would approach problems.
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