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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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New post Updated on: 09 Feb 2013, 01:56
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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

Originally posted by ajit257 on 18 Dec 2010, 08:13.
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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Re: Remainder problem  [#permalink]

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New post 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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Re: PS Integers and remainder  [#permalink]

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New post 24 Sep 2013, 08:50
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1
3
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: Remainder problem  [#permalink]

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New post 18 Dec 2010, 08:28
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Re: Remainder problem  [#permalink]

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New post 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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Re: Remainder problem  [#permalink]

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

anshumishra....thanks for the hint. i feel better now.
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Re: Remainder problem  [#permalink]

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New post 19 Dec 2010, 13:49
2
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

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


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Re: Remainder problem  [#permalink]

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New post 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

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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New post 06 May 2011, 11:38
1
x = y Q + 9

x/y = 96.12

thus 0.12 * y = 9

y = 900/ 12 = 75

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Re: PS Integers and remainder  [#permalink]

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New post 06 May 2011, 11:45
2
2
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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New post 11 May 2011, 06:51
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x = 96y + 0.12y

= 96y + 12y/100

12y/100 = 9

3y/25 = 9

=> y = 75

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

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New post 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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New post 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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New post 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]

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

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

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New post 04 Oct 2013, 10:10
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


A concept that can be applied here is: -

Remainder = Divisor * decimal part

For example, 5/2 = 2.5. Here, 2 is quotient and 1 is remainder. So, Remainder/Divisor --> 1/2 = 0.5.

In the question, it is given that remainder is 9, divisor is y and decimal part is 0.12. Applying the concept, 9 = y * 0.12. On solving this, y comes out to be 75.
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Re: When positive integer x is divided by positive integer y,  [#permalink]

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New post 23 Oct 2013, 18:13
3
3
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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Re: Remainder problem  [#permalink]

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New post 19 Dec 2013, 09:08
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.


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.

Thanks in advance.
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Re: Remainder problem  [#permalink]

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New post 19 Dec 2013, 09:11
1
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.

Answer: B.


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.

Thanks in advance.


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: Remainder problem   [#permalink] 19 Dec 2013, 09:11

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