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When positive integer x is divided by positive integer y,

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Joined: 03 Sep 2018
Posts: 23
WE: Analyst (Consulting)
Re: When positive integer x is divided by positive integer y,  [#permalink]

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New post 04 Nov 2018, 08:06
ajit257 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


Answer:

given: x/y = 96.12
implies, x = 96.12*y = 96y + .12y
this further implies that remainder when x is divided by 12 is equal to .12y, i.e. 9 =.12y
Hence y = 75
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Re: When positive integer x is divided by positive integer y,  [#permalink]

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New post 31 Dec 2018, 09:15
Top Contributor
ajit257 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


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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Re: When positive integer x is divided by positive integer y, &nbs [#permalink] 31 Dec 2018, 09:15

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