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When positive integer x is divided by positive integer y, the remainde

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Re: When positive integer x is divided by positive integer y, the remainde [#permalink] New post   18 Oct 2021, 07:42
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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


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Answer: Option B

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Re: When positive integer x is divided by positive integer y, the remainde [#permalink] New post   21 Mar 2022, 09:24
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Hi GMATters,

Here is my video explanation of this problem:

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Re: When positive integer x is divided by positive integer y, the remainde [#permalink] New post   24 Oct 2022, 18:27
Bunuel wrote:
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

Any faster way to solve this ?


When positive integer x is divided by positive integer y, the remainder is 9 --> x=qy+9;
x/y=96.12 --> x=96y+0.12y (so q above equals to 96);

0.12y=9 --> y=75.

Answer: B.


Bunuel
I realize that this question is elementary, but if I follow your approach...

(X/Y)=Q+9
--> X=QY+9Y
Why don't you multiply the 9 by Y?

Thank you.
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Re: When positive integer x is divided by positive integer y, the remainde [#permalink] New post   25 Oct 2022, 14:13
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woohoo921 wrote:
Bunuel wrote:
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

Any faster way to solve this ?


When positive integer x is divided by positive integer y, the remainder is 9 --> x=qy+9;
x/y=96.12 --> x=96y+0.12y (so q above equals to 96);

0.12y=9 --> y=75.

Answer: B.


Bunuel
I realize that this question is elementary, but if I follow your approach...

(X/Y)=Q+9
--> X=QY+9Y
Why don't you multiply the 9 by Y?

Thank you.


Hi woohoo921,

In this prompt, the '9' is the remainder (it's the 'left-over' piece outside of the division that takes place), so you don't end up multiplying it when getting rid of the fraction. You can prove this concept by TESTing VALUES. For example:

15/6 = 2 r 3
15 = 6(2) + 3

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Contact Rich at: Rich.C@empowergmat.com
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Re: When positive integer x is divided by positive integer y, the remainde [#permalink] New post   22 Jul 2023, 03:11
x/y = yxk + 9 and x/y = 96 + 12/100

that means, 9 = 12/100y
-> y = 900/12 = 75
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Re: When positive integer x is divided by positive integer y, the remainde [#permalink] New post   28 Dec 2023, 04:00
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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?

\(\frac{x}{y}\) = 96.12
=> x = 96.12y = (96 + 0.12)y = 96y + 0.12y

=> x when divided by y gives 96 as the quotient and 0.12y as the remainder
=> 0.12y = 9
=> y = \(\frac{9}{0.12}\) = 75

So, Answer will be B
Hope it helps!

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Re: When positive integer x is divided by positive integer y, the remainde [#permalink]
28 Dec 2023, 04:00
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