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Manager  Joined: 28 Aug 2010
Posts: 149
When positive integer x is divided by positive integer y,  [#permalink]

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182 00:00

Difficulty:   35% (medium)

Question Stats: 72% (01:39) correct 28% (01:57) wrong based on 3172 sessions

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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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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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15
1
5
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
##### General Discussion
Math Expert V
Joined: 02 Sep 2009
Posts: 59720

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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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Manager  Joined: 25 Jun 2010
Posts: 75

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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
Manager  Joined: 28 Aug 2010
Posts: 149

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thanks guys....

anshumishra....thanks for the hint. i feel better now.
Manager  Joined: 25 Jun 2010
Posts: 75

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1
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
Math Expert V
Joined: 02 Sep 2009
Posts: 59720

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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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1
1
x = y Q + 9

x/y = 96.12

thus 0.12 * y = 9

y = 900/ 12 = 75

B
Director  Joined: 01 Feb 2011
Posts: 531
Re: PS Integers and remainder  [#permalink]

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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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1
3
x = 96y + 0.12y

= 96y + 12y/100

12y/100 = 9

3y/25 = 9

=> y = 75

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Posts: 2
Re: When positive integer x is divided by positive integer y,  [#permalink]

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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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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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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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1
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.
Senior Manager  Joined: 10 Jul 2013
Posts: 282
Re: When positive integer x is divided by positive integer y,  [#permalink]

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1
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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1
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.
Manager  Joined: 26 Sep 2013
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Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41 Re: When positive integer x is divided by positive integer y,  [#permalink]

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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
Manager  Joined: 12 Jan 2013
Posts: 142

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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.

Math Expert V
Joined: 02 Sep 2009
Posts: 59720

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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.

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

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