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# When positive integer x is divided by positive integer y,

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When positive integer x is divided by positive integer y, [#permalink]

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18 Dec 2010, 08:13
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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
[Reveal] Spoiler: OA

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Last edited by Bunuel on 09 Feb 2013, 01:56, edited 2 times in total.
Renamed the topic and edited the question.

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18 Dec 2010, 19:03
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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

Any faster way to solve this ?

Think of it this way:
$$\frac{x}{y} = 96.12 = 96 \frac{12}{100}$$ (in mixed fraction format)$$= 96 \frac{3}{25}$$
This means when x is divided by y, quotient obtained is 96 and remainder is 3 if y is 25. If remainder is 9, y must be 75.
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18 Dec 2010, 08:28
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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

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.

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Re: PS Integers and remainder [#permalink]

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24 Sep 2013, 08:50
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Easy it is

x/y = 96 + .12..... (1)

Remember here:

x = yQ + R

Can also be written as

x/y = Q + R/y ..... (2)

Comparing (1) and (2)

Q=96 and
R/y=.12

We know that Remainder is 9 , hence R=9

y=75
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Re: When positive integer x is divided by positive integer y [#permalink]

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09 May 2013, 21:01
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laythesmack23 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

As we know, $$Decimal Part$$ $$=$$ $$\frac{Remainder}{Divisor}$$

Therefore, .12 = $$\frac{x}{y}$$

or $$\frac{12}{100}$$ = $$\frac{x}{y}$$

or $$\frac{3}{25}$$ = $$\frac{x}{y}$$

or $$\frac{9}{75}$$ = $$\frac{x}{y}$$

Hence, 75 ... Hence, B ..........
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Re: When positive integer x is divided by positive integer y, [#permalink]

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23 Oct 2013, 18:13
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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

when you are given a remainder from a fraction, and the remainder is in decimal form, you can solve for like this:

$$\frac{Remainder}{denominator}$$=[decimal of quotient]

So in this case; $$\frac{9}{y}$$=.12
=
$$\frac{9}{y}$$= $$\frac{12}{100}$$
=
$$\frac{9}{y}$$= $$\frac{3}{25}$$
=
3y=225
=
y=75

B

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19 Dec 2010, 13:49
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ajit257 wrote:
thanks guys....

anshumishra....thanks for the hint. i feel better now.

Great ! I am happy that it helped.

Here is another similar problem. Try to solve yourself first.

If s and t are positive integer such that s/t=64.12, which of the following could be the remainder when s is divided by t?
(A) 2
(B) 4
(C) 8
(D) 20
(E) 45

[Reveal] Spoiler:
Ans: E
0.12 = 12/100 = r/t => t = 100*r/12 (where r & t are both integers)
Only E has the integral soln.

Thanks

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Re: PS Integers and remainder [#permalink]

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06 May 2011, 11:45
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x = qy + 9
x = 96.12y

Equating remainders of above two equations we have

0.12y =9
=> y = 75

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Re: PS Integers and remainder [#permalink]

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11 May 2011, 06:51
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x = 96y + 0.12y

= 96y + 12y/100

12y/100 = 9

3y/25 = 9

=> y = 75

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Re: When positive integer x is divided by positive integer y, [#permalink]

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16 Aug 2013, 22:55
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Galiya wrote:
Quote:
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);

Bunuel
why did you assume that q=96? while solving the question I threw away the thought that q=96 because reminders were different

Hi Galiya,

For this i will give u a example
When 23/2 =11.5 (Q = 11 and Remainder = 1)
Here Quotient = 11 and Remainder = .5 * 2 (Divisor) = 1

Hence in the original problem q = 96
x/y = 96.12-->
X= q *y (divisor) + Remainder (.12* Divisor)

Hope its clear.

Regards,
Rrsnathan.

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Re: When positive integer x is divided by positive integer y, [#permalink]

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17 Aug 2013, 11:57
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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

12/100 = 3/25 = 9/75 = remainder/quotient
so , y = 75
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19 Dec 2013, 09:11
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aeglorre 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.

Are there any other questions similar to this one? I just simply cannot seem to wrap my head around the concept, so practicing on more examples would probably help.

Check this one: if-s-and-t-are-positive-integers-such-that-s-t-64-12-which-135190.html

Hope it helps.
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Re: When positive integer x is divided by positive integer y, [#permalink]

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07 Jun 2016, 11:10
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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

This problem will be best solved using the remainder formula. Let’s first state the remainder formula:

When positive integer x is divided by positive integer y, if integer Q is the quotient and r is the remainder, then x/y = Q + r/y.

In this problem we are given that when positive integer x is divided by positive integer y, the remainder is 9. So we can say:

x/y = Q + 9/y

We also are given that x/y = 96.12. Using the remainder formula we can say:

x/y = 96.12

x/y = 96 + 0.12

x/y = 96 + 12/100

Because Q is always an integer, we see that Q must be 96, and thus the remainder 9/y must be 12/100. We can now equate 9/y to 12/100 and determine the value of y.

9/y = 12/100

12y = 9 x 100

y = 900/12 = 75

Note: Had we simplified 12/100 to 3/25 first, we would have also obtained the same answer. See below.

9/y = 3/25

3y = 9 x 25

y = 3 x 25 = 75

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Re: When positive integer x is divided by positive integer y, [#permalink]

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10 Jun 2016, 00:06
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x/y,r=9

x=qy+9

divide LHS and RHS by y

x/y=q+9/y

96.12--->0.12 is the remainder part.

9/y=0.12

or y=9/0.12=75

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18 Dec 2010, 12:08
ajit257,
That is the easiest way - as Bunuel solved.

Now try to solve the same question with one change that you don't know the remainder. Believe me, that would be an even better question (and you have the same options as answers).

It will make your concepts more clear.

Thanks

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19 Dec 2010, 13:44
thanks guys....

anshumishra....thanks for the hint. i feel better now.
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19 Dec 2010, 14:11
anshumishra wrote:
ajit257 wrote:
thanks guys....

anshumishra....thanks for the hint. i feel better now.

Great ! I am happy that it helped.

Here is another similar problem. Try to solve yourself first.

If s and t are positive integer such that s/t=64.12, which of the following could be the remainder when s is divided by t?
(A) 2
(B) 4
(C) 8
(D) 20
(E) 45

[Reveal] Spoiler:
Ans: E
0.12 = 12/100 = r/t => t = 100*r/12 (where r & t are both integers)
Only E has the integral soln.

Thanks

Please try to discuss one question per thread. This question was discussed here: remainders-105400.html#p823773
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Re: PS Integers and remainder [#permalink]

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06 May 2011, 11:38
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x = y Q + 9

x/y = 96.12

thus 0.12 * y = 9

y = 900/ 12 = 75

B
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Re: When positive integer x is divided by positive integer y, [#permalink]

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08 Feb 2013, 22:11
I got B as well but I set it up a little bit differently.

If x/y has remainder 9, then the remainder is 9 "Y-ths"
Also, if the remainder is .12 then .12 = 12/100 = 3/25.

I set up the equation 9/Y = 3/25 therefore Y= (9*25)/3 after cancellation Y=3*25=75

That said, the correct answer is supposed to be D but everyone else also seems to be getting B so I have no idea what's going on. I would love to hear from someone who got D

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Re: When positive integer x is divided by positive integer y, [#permalink]

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16 Aug 2013, 02:53
Quote:
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);

Bunuel
why did you assume that q=96? while solving the question I threw away the thought that q=96 because reminders were different

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Re: When positive integer x is divided by positive integer y,   [#permalink] 16 Aug 2013, 02:53

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