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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

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.
_________________

Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________

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.

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

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07 Jun 2016, 11:10

1

This post received KUDOS

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

Answer is B.
_________________

Jeffrey Miller Jeffrey Miller Head of GMAT Instruction

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).

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

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

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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