## When positive integer $$x$$ is divided by positive integer $$y,$$ the remainder is 9. If $$x/y = 96.12,$$ what is...

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### When positive integer $$x$$ is divided by positive integer $$y,$$ the remainder is 9. If $$x/y = 96.12,$$ what is...

by Gmat_mission » Sun Sep 12, 2021 9:27 am

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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

Source: Official Guide

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### Re: When positive integer $$x$$ is divided by positive integer $$y,$$ the remainder is 9. If $$x/y = 96.12,$$ what is...

by [email protected] » Sun Sep 12, 2021 12:18 pm
Gmat_mission wrote:
Sun Sep 12, 2021 9:27 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

Source: Official Guide
There are a few ways to tackle this question.

One way is to examine a few other fractions.
7/2 = 3 with remainder 1.
7/2 = 3 1/2 = 3.5
Notice that 0.5 = 1/2

Another example:
11/4 = 2 with remainder 3.
11/4 = 2 3/4 = 2.75
Notice that 0.75 = 3/4

Now onto the question....

So, we know that x/y = some value with remainder 9
If x/y = 96.12, we can conclude that 0.12 = 9/y
Now solve for y.
0.12 = 9/y
12/100 = 9/y [rewrite 0.12 as 12/100]
Simplify to get: 3/25 = 9/y
At this point, we might already see that y = 75.

If we don't spot this, we can always cross-multiply to get: 3y = (25)(9)
Solve to get y = 75

Cheers,
Brent

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