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

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8079
Location: Pune, India

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19 Dec 2013, 18:20
Expert's post
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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 post. It discusses another similar question and the concept involved in detail (including a discussion on some fundamental gaps many students have): http://www.veritasprep.com/blog/2011/05 ... emainders/
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Karishma
Veritas Prep | GMAT Instructor
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 07 Apr 2014 Posts: 119 Re: When positive integer x is divided by positive integer y, [#permalink] ### Show Tags 11 Sep 2014, 07:12 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 x/y = 96.12 can be written as x= 96y +.12y where .12y is a remainder already given remainder is 9 so (0.12)y= 9 y= 75 EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 11663 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: When positive integer x is divided by positive integer y, [#permalink] ### Show Tags 02 Jan 2015, 13:46 Hi All, It looks like most of the posts have provided similar algebra explanations. Here's a way to use Number Properties, the answer choices and "brute force" to find the solution. In this prompt, we're told that X and Y are INTEGERS. Since X/Y = 96.12, we can rewrite the equation as... X = 96.12(Y) The Y has to "multiply out" the .12 so that X becomes an integer. Since .12 is such a weird value, there can't be that many numbers that X could be. Since none of the answers ends in 00, we need to find another way to multiply out the .12 - the only way to do it is with a multiple of 25. Eliminate A, C and E. Between B and D, we just need to find the one that matches the rest of the info in the prompt (X/Y = 96.12 and X/Y has a remainder of 9) Answer B: If Y = 75, then X = 7209...... 7209/75 gives a remainder of 9 THIS IS A MATCH Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Intern
Joined: 16 Feb 2015
Posts: 9
Re: When positive integer x is divided by positive integer y, [#permalink]

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27 Feb 2015, 11:48
I'm still confused....

The main formula that we're using is
Dividend/Divisor = Quotient + Remainder/Divisor OR Dividend = Quotient*Divisor + Remainder

For the first part of the question, we can use the 2nd formula to derive x = Qy+9. I'm ok with this.

For the second part of the question, using the 2nd formula, why don't we get x = 96y+.12 (in the same vein as the first part)? I know it should be .12y, but I don't see how it goes along with the formula, the formula says Remainder, NOT remainder/Divisor. Not to mention, isn't the divisor 100? As in 12/100? Doesn't that make .12y redundant because it's 12/100*100?

The first and the second part of the questions are exactly alike, except the first part is missing the quotient that we end up finding after we do the second part.

Thanks!
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8079
Location: Pune, India
Re: When positive integer x is divided by positive integer y, [#permalink]

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02 Mar 2015, 00:23
1
KUDOS
Expert's post
aces021 wrote:
I'm still confused....

The main formula that we're using is
Dividend/Divisor = Quotient + Remainder/Divisor OR Dividend = Quotient*Divisor + Remainder

For the first part of the question, we can use the 2nd formula to derive x = Qy+9. I'm ok with this.

For the second part of the question, using the 2nd formula, why don't we get x = 96y+.12 (in the same vein as the first part)? I know it should be .12y, but I don't see how it goes along with the formula, the formula says Remainder, NOT remainder/Divisor. Not to mention, isn't the divisor 100? As in 12/100? Doesn't that make .12y redundant because it's 12/100*100?

The first and the second part of the questions are exactly alike, except the first part is missing the quotient that we end up finding after we do the second part.

Thanks!

Consider this: If 5 is divided by 4, you get quotient 1 and remainder 1

5 = 4*1 + 1

But when you write it in terms of decimals, 5/4 = 1.25
Is the remainder .25 here? No. Then, do you think it is correct to write 5 as 1*y + .25? This is what you have done above.

What is .25? It is the fraction of divisor that is leftover -> 25%. Since the divisor is 4, 25% of it i.e. 1 is leftover. So remainder is 1.

Similarly, when you have 96.12, we can say that 12% of the divisor is leftover.
12% of divisor = 9
Divisor = 75
_________________

Karishma
Veritas Prep | GMAT Instructor
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 21 Sep 2015 Posts: 81 Location: India GMAT 1: 730 Q48 V42 GMAT 2: 750 Q50 V41 Re: When positive integer x is divided by positive integer y, [#permalink] ### Show Tags 28 May 2016, 02:23 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 x/y = q + r/y x/y = 96 + (3/25) Therefore 3/25 = 9/y y = 75 _________________ Appreciate any KUDOS given ! Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2442 Re: When positive integer x is divided by positive integer y, [#permalink] ### Show Tags 07 Jun 2016, 11:10 1 This post received KUDOS Expert's post 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. _________________ Jeffery Miller Head of GMAT Instruction GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Intern Joined: 28 Dec 2015 Posts: 41 Re: When positive integer x is divided by positive integer y, [#permalink] ### Show Tags 10 Jun 2016, 00:06 1 This post received KUDOS 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 Current Student Joined: 12 Oct 2012 Posts: 120 WE: General Management (Other) When positive integer x is divided by positive integer y, [#permalink] ### Show Tags 21 Jun 2016, 20:21 JeffTargetTestPrep 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 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. If we were not given remainder 9, and the question would only state If x/y = 96.12, what is the value of y? In this case, x = 96y + $$\frac{12}{100}$$*y $$\frac{12y}{100}$$ =>$$\frac{3y}{25}$$. Since, we do not have an equation to find the value of y, can we say that R = Multiple of 3 & Divisor is 25 ? TIA Intern Joined: 09 Dec 2014 Posts: 5 WE: Information Technology (Health Care) Re: When positive integer x is divided by positive integer y, [#permalink] ### Show Tags 31 Dec 2016, 08:37 x/y=96.12 .12 =9 12/100=9/y 12y=900 y= 75 Manager Joined: 25 Jun 2016 Posts: 61 GMAT 1: 780 Q51 V46 Re: When positive integer x is divided by positive integer y, [#permalink] ### Show Tags 14 Jan 2017, 13:04 Here is a video explanation for the problem: Senior Manager Joined: 26 Dec 2015 Posts: 280 Location: United States (CA) Concentration: Finance, Strategy WE: Investment Banking (Venture Capital) Re: When positive integer x is divided by positive integer y, [#permalink] ### Show Tags 16 Jan 2017, 17:58 This specific q is easier than it looks. The problem mentions that x/y gives you a remainder of 9 AND that x/y = 96.12. That means we can set both remainders EQUAL to each other. 9 = .12y --> 9 = (12/100)y --> 900 = 12y --> y = 75 Intern Joined: 09 Dec 2014 Posts: 5 WE: Information Technology (Health Care) Re: When positive integer x is divided by positive integer y, [#permalink] ### Show Tags 29 Mar 2017, 20:58 Remainder Problems always gives me a bit of trouble The first think to do is write the equation to identify all the parts 1. dividend/divisor = Quotient + Remainder 2. What is the problem asking for ( Divisor) 3. Get the Divisor - y by itself (X = Qx Y + R) 4. 96Y +.12Y = 9 4. Notice that Q = 96.12. The decimal in the quotient is always the reminder. This means that R=.12=9 5. Put it all together x= 96.12y= .12y= 9= 75 Director Joined: 02 Sep 2016 Posts: 745 Re: When positive integer x is divided by positive integer y, [#permalink] ### Show Tags 01 Apr 2017, 07:02 x=yq+9 .........eq.1 (q=Quotient) x/y= 96.12 .......eq.2 Finding a relation between the two equations x/y=96+0.12 (means the same as 96.12) There is one more we can write the equation (x=yq+9) x/y= q/y+9/y 96.12=q+9/y 96+0.12=q+9/y 9/y=12/100 y=100*9/12 y=75 _________________ Help me make my explanation better by providing a logical feedback. If you liked the post, HIT KUDOS !! Don't quit.............Do it. Intern Joined: 24 Oct 2016 Posts: 12 Location: India WE: Research (Investment Banking) Re: When positive integer x is divided by positive integer y, [#permalink] ### Show Tags 12 Apr 2017, 22:46 The solution that came to my head: x/y=96.12=9612/100=2403/25 2403/25 has remainder 3 For remainder 9, 25*3=75 SIMPLE! Intern Joined: 06 Mar 2017 Posts: 29 Location: India Schools: ISB '20 GMAT 1: 650 Q49 V30 GPA: 3.9 Re: When positive integer x is divided by positive integer y, [#permalink] ### Show Tags 21 Jun 2017, 08:24 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. Why can I not take it as 95+1.12 or 94+2.12.......? hope you understood my query? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8079 Location: Pune, India Re: When positive integer x is divided by positive integer y, [#permalink] ### Show Tags 21 Jun 2017, 22:11 siddreal 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. Why can I not take it as 95+1.12 or 94+2.12.......? hope you understood my query? We split it up into 96 and .12 to separate out the integer and the decimal part. The decimal part is the one that gives the remainder. If we split it as 95 + 1.12, it doesn't serve the purpose since the decimal part has still not been separated out. For more on this, check: https://www.veritasprep.com/blog/2011/0 ... emainders/ _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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

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12 Nov 2017, 14:12
I solved it in a different way:

If 9 is the reminder, and the first number after the comma is 1, that means that the solution:
- Cannot be bigger than 90. Ergo cross out A).
- Cannot be smaller than 90/2, because then it would be 96.[(>1)]2. Ergo cross out D) and E).

Now you have only B) and C). The second number after the 1 in 96.12 is a [2]. Check for each:
- B): 90-75=15, plug a 0 -> 150/75 = 2 . Ergo right answer!!!!
- C): 90-48=42, plug a 0 -> 420/48 <> 2. Ergo cross C).

What do you think?

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

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16 Nov 2017, 07:49
for a number of form a $$\frac{x}{y}$$ remember following:

a = Quotient
x = Remainder
y = Dividend

So in this question, we need to find the value of y given a = 96 and x = 9:

Decimal number 96.12 can be written as 96 $$\frac{12}{100}$$

Above fraction can be simplified as following:

96 $$\frac{(2 * 2 * 3)}{(2 * 2 * 5 * 5)}$$

In order to have remainder = 9, we need to multiply and divide both the numerator and denominator with 3:

96 $$\frac{(2 * 2 * 3 * 3)}{(2 * 2 * 5 * 5 * 3)}$$

Now simplify the number while keeping 3*3 in numerator, So 2 * 2 is cancelled from both numerator and denominator; hence, we are left with:

96 $$\frac{(3 * 3)}{(5 * 5 * 3)}$$

hence we have a = 96, x = 9 and y = 75 (option B)
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Re: When positive integer x is divided by positive integer y, [#permalink]

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11 Dec 2017, 11:50
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 to 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:

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] 11 Dec 2017, 11:50

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