GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Mar 2019, 13:06 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # When positive integer x is divided by positive integer y,

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 8982
Location: Pune, India
Re: Remainder problem  [#permalink]

### Show Tags

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/
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Manager  Joined: 07 Apr 2014
Posts: 105
Re: When positive integer x is divided by positive integer y,  [#permalink]

### Show Tags

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 V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13755
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: When positive integer x is divided by positive integer y,  [#permalink]

### Show Tags

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

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 Follow
Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Intern  Joined: 16 Feb 2015 Posts: 9 Re: When positive integer x is divided by positive integer y, [#permalink] ### Show Tags 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 D Joined: 16 Oct 2010 Posts: 8982 Location: Pune, India Re: When positive integer x is divided by positive integer y, [#permalink] ### Show Tags 1 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 Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Manager  Joined: 21 Sep 2015 Posts: 76 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 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 G Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2826 Re: When positive integer x is divided by positive integer y, [#permalink] ### Show Tags 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 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 Head of GMAT Instruction Jeff@TargetTestPrep.com See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews Intern  Joined: 28 Dec 2015 Posts: 39 Re: When positive integer x is divided by positive integer y, [#permalink] ### Show Tags 1 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 Manager  B Joined: 12 Oct 2012 Posts: 112 WE: General Management (Other) When positive integer x is divided by positive integer y, [#permalink] ### Show Tags 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  B 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 x/y=96.12 .12 =9 12/100=9/y 12y=900 y= 75 Manager  B 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 Here is a video explanation for the problem: Senior Manager  G Joined: 26 Dec 2015 Posts: 254 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 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  B 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 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  G Joined: 02 Sep 2016 Posts: 664 Re: When positive integer x is divided by positive integer y, [#permalink] ### Show Tags 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  B 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 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! Wisconsin(Madison) School Moderator S Joined: 06 Mar 2017 Posts: 195 Concentration: Operations, General Management Schools: Terry '21 (M$)
Re: When positive integer x is divided by positive integer y,  [#permalink]

### Show Tags

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.

Why can I not take it as 95+1.12 or 94+2.12.......?
hope you understood my query?
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 8982
Location: Pune, India
Re: When positive integer x is divided by positive integer y,  [#permalink]

### Show Tags

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.

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

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Intern  B
Joined: 24 Oct 2014
Posts: 16
Location: Spain
Schools: LBS '21 (II)
Re: When positive integer x is divided by positive integer y,  [#permalink]

### Show Tags

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 . 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.
Intern  B
Joined: 01 May 2017
Posts: 34
When positive integer x is divided by positive integer y,  [#permalink]

### Show Tags

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)
Target Test Prep Representative G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2826
Re: When positive integer x is divided by positive integer y,  [#permalink]

### Show Tags

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

_________________

# Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews Re: When positive integer x is divided by positive integer y,   [#permalink] 11 Dec 2017, 11:50

Go to page   Previous    1   2   3    Next  [ 42 posts ]

Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.  