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dividing of integers

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dividing of integers

by Lattefah84 » Thu Jan 14, 2010 9:02 am
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 tried to solved as y= xq+r (q-quotient, r- remainder),

1=xq/y + r, 1=96.12q + 9/y ...


and I can't continue... where did I make a mistake?
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by Brent@GMATPrepNow » Thu Jan 14, 2010 9:11 am
Lattefah84 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 tried to solved as y= xq+r (q-quotient, r- remainder),

1=xq/y + r, 1=96.12q + 9/y ...
and I can't continue... where did I make a mistake?
There are a few ways to tackle this question.
One way is to examine a few other fractions.
7/2 = 3 1/2 = 3.5 (notice that 0.5 = 1/2)
11/4 = 2 3/4 = 2.75 (notice that 0.75 = 3/4)

So, we know that x/y = 96 9/y = 96.12 (we get the 9 part from the question, where it say the remainder is 9)

This means that 9/y = 0.12 or 9/y = 12/100
When we solve for y, we get y=75
Brent Hanneson - Creator of GMATPrepNow.com
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by Lattefah84 » Thu Jan 14, 2010 11:54 am
Brent Hanneson wrote:
Lattefah84 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 tried to solved as y= xq+r (q-quotient, r- remainder),

1=xq/y + r, 1=96.12q + 9/y ...
and I can't continue... where did I make a mistake?
There are a few ways to tackle this question.
One way is to examine a few other fractions.
7/2 = 3 1/2 = 3.5 (notice that 0.5 = 1/2)
11/4 = 2 3/4 = 2.75 (notice that 0.75 = 3/4)

So, we know that x/y = 96 9/y = 96.12 (we get the 9 part from the question, where it say the remainder is 9)

This means that 9/y = 0.12 or 9/y = 12/100
When we solve for y, we get y=75

thank you for the answer, but I still don't get it :( ... How can I conclude that x/y=96 and 9/y = 0.12?
the equation 1=xq/y + r is not correct? n it could be 93 + 3.12, or 52 + 44.12, or...
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by ace_gre » Thu Jan 14, 2010 1:21 pm
Hi, Here is my approach..Similar to Brent's

given x = k*y + 9, where k is the quotient when x is divided by y---(1)
Also given x/y = 96.12 ==>96+ 0.12---(2)

Now ky is a whole number and is equal to 96 in eq 2.
So the fractional part is the remainder

0.12y=9
y=9/0.12 = 75.
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by joyseychow » Wed Jan 20, 2010 7:14 pm
Yup. It's 75.

In remainder questions, the value after decimal represents the remainder. In this case, it's 0.12.

x/y=96.12
x=y(96+0.12)

0.12y=9
y=75.
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