Find all School-related info fast with the new School-Specific MBA Forum

It is currently 17 Sep 2014, 23:55

Close

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
Your Progress

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

One-fourth of a solution that was 10% by weight was replaced

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
avatar
Joined: 10 Apr 2012
Posts: 279
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
Followers: 2

Kudos [?]: 115 [0], given: 323

GMAT ToolKit User Premium Member CAT Tests
One-fourth of a solution that was 10% by weight was replaced [#permalink] New post 13 Mar 2013, 12:52
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

53% (02:33) correct 47% (01:39) wrong based on 168 sessions
One fourth of a solution that was 10% sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight?

A. 34%
B. 24%
C. 22%
D. 18%
E. 8.5%

[Reveal] Spoiler:
I am trying to solve it using Allegation method , but not quit sure how to get the end result , Please help . Also, elaborate the steps so that I can understand the approach .
many thanks !



I started with 10% ------------ x% in the first row

16% in the second row

and x-16% and 6% in the last one

this gives me x-16/6= ? "stuck here "
[Reveal] Spoiler: OA

Last edited by Bunuel on 14 Mar 2013, 01:15, edited 1 time in total.
Edited the question.
1 KUDOS received
Intern
Intern
avatar
Joined: 28 Jan 2013
Posts: 8
Location: United States
Concentration: Strategy, Technology
GMAT Date: 04-20-2013
GPA: 3.2
WE: Analyst (Computer Software)
Followers: 0

Kudos [?]: 8 [1] , given: 4

Re: One-fourth of a solution that was 10% by weight was replaced [#permalink] New post 13 Mar 2013, 17:30
1
This post received
KUDOS
guerrero25 wrote:
One-fourth of a solution that was 10% by weight was replaced by a second solution resulting in a solution that was 16% sugar by weight. The second solution was what percent sugar by weight.

34%
24%
22%
18%
8.5%

I am trying to solve it using Allegation method , but not quit sure how to get the end result , Please help . Also, elaborate the steps so that I can understand the approach .
many thanks !



I started with 10% ------------ x% in the first row

16% in the second row

and x-16% and 6% in the last one

this gives me x-16/6= ? "stuck here "


This is the first question I trying to explain here, so please bear with my mistakes.

The best I could think of solving this is using nos.

Lets say we have a 100 ml of solution and it has 10 gm of sugar.

100 ml ---- 10 gm
75 ml ------- 7.5 gm
25 ml ------- 2.5 gm

Once we remove 25 ml, we have only 7.5 gm sugar left to make 16% of 100 ml solution we need 8.5 gm more sugar.
so we need 8.5 gm in 25 ml, which is 8.5 * 4 = 34 gm/ (25 * 4).

Ans A) 34 %
Expert Post
4 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4772
Location: Pune, India
Followers: 1111

Kudos [?]: 5044 [4] , given: 164

Re: One-fourth of a solution that was 10% by weight was replaced [#permalink] New post 13 Mar 2013, 19:52
4
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
guerrero25 wrote:
One-fourth of a solution that was 10% by weight was replaced by a second solution resulting in a solution that was 16% sugar by weight. The second solution was what percent sugar by weight.

34%
24%
22%
18%
8.5%

I am trying to solve it using Allegation method , but not quit sure how to get the end result , Please help . Also, elaborate the steps so that I can understand the approach .
many thanks !



I started with 10% ------------ x% in the first row

16% in the second row

and x-16% and 6% in the last one

this gives me x-16/6= ? "stuck here "


The allegation formula is this:

w1/w2 = (A2 - Aavg)/(Aavg - A1)
w1/w2 is the ratio of weights of the two solutions. Here, since 1/4 of the first solution is replaced, the weight of the first solution is 3/4 and that of the second solution is 1/4 so w1/w2 = 3/1

A2 - Concentration of second solution which we have to find here
Aavg - Concentration of mixture which is 16%
A1 - Concentration of first solution which is 10%

3/1 = (A2 - 16)/(16 - 10)
A2 = 34%

To find out how you get this formula, check: http://www.veritasprep.com/blog/2011/03 ... -averages/
For more on mixtures and replacement, check:
http://www.veritasprep.com/blog/2011/04 ... -mixtures/
http://www.veritasprep.com/blog/2012/01 ... -mixtures/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

3 KUDOS received
Current Student
User avatar
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 648
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
Followers: 35

Kudos [?]: 364 [3] , given: 23

GMAT ToolKit User Premium Member
Re: One-fourth of a solution that was 10% by weight was replaced [#permalink] New post 13 Mar 2013, 21:22
3
This post received
KUDOS
guerrero25 wrote:
One-fourth of a solution that was 10% by weight was replaced by a second solution resulting in a solution that was 16% sugar by weight. The second solution was what percent sugar by weight.
34%
24%
22%
18%
8.5%

I am trying to solve it using Allegation method , but not quit sure how to get the end result , Please help . Also, elaborate the steps so that I can understand the approach .
many thanks !


Instead of using complex calculations and remembering formulae, why dont u directly get to weighted average.

3 parts of 10% + 1 part of x (unknown) % = 4 parts of 16%
=> x% = 64%-30% = 34%

ans A it is.
_________________

Lets Kudos!!! ;-)
Black Friday Debrief

Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29671
Followers: 3495

Kudos [?]: 26308 [2] , given: 2709

Re: One-fourth of a solution that was 10% by weight was replaced [#permalink] New post 14 Mar 2013, 01:16
2
This post received
KUDOS
Expert's post
One fourth of a solution that was 10% sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight?

A. 34%
B. 24%
C. 22%
D. 18%
E. 8.5%

This is a weighted average question.

Say the second solution (which was 1/4 th of total) was x% sugar, then 3/4*0.1+1/4*x=1*0.16 --> x=0.34. Alternately you can consider total solution to be 100 liters and in this case you'll have: 75*0.1+25*x=100*0.16 --> x=0.34.

Answer: A.

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
avatar
Joined: 10 Apr 2012
Posts: 279
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
Followers: 2

Kudos [?]: 115 [0], given: 323

GMAT ToolKit User Premium Member CAT Tests
Re: One-fourth of a solution that was 10% by weight was replaced [#permalink] New post 14 Mar 2013, 08:51
Thank you all for helping me understand the problem . Now I am getting a good grip on the concepts .The members /experts here 're truly amazing !

Kudos all

Regards!
Intern
Intern
avatar
Joined: 10 Sep 2013
Posts: 17
Location: India
Concentration: Strategy
GMAT 1: 700 Q50 V34
GPA: 3.8
WE: General Management (Energy and Utilities)
Followers: 0

Kudos [?]: 7 [0], given: 0

Re: One-fourth of a solution that was 10% by weight was replaced [#permalink] New post 17 Sep 2013, 04:38
One fourth of a solution that was 10% sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight?

A. 34%
B. 24%
C. 22%
D. 18%
E. 8.5%

let the volume of the original solution be X and p be the percentage of sugar in the solution which is replaced.
then

10*3x/4 + p*1x/4 = 16*x
=> 30 + p = 64
=> p =
A
Intern
Intern
avatar
Joined: 06 Feb 2012
Posts: 16
Followers: 0

Kudos [?]: 14 [0], given: 7

Re: One-fourth of a solution that was 10% by weight was replaced [#permalink] New post 21 Oct 2013, 02:41
Vips0000 wrote:
guerrero25 wrote:
One-fourth of a solution that was 10% by weight was replaced by a second solution resulting in a solution that was 16% sugar by weight. The second solution was what percent sugar by weight.
34%
24%
22%
18%
8.5%

I am trying to solve it using Allegation method , but not quit sure how to get the end result , Please help . Also, elaborate the steps so that I can understand the approach .
many thanks !


Instead of using complex calculations and remembering formulae, why dont u directly get to weighted average.

3 parts of 10% + 1 part of x (unknown) % = 4 parts of 16%
=> x% = 64%-30% = 34%

ans A it is.


thanks m8 that really helped. clear and easy
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1664
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 12

Kudos [?]: 164 [0], given: 268

GMAT ToolKit User
Re: One-fourth of a solution that was 10% by weight was replaced [#permalink] New post 16 Dec 2013, 15:05
guerrero25 wrote:
One fourth of a solution that was 10% sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight?

A. 34%
B. 24%
C. 22%
D. 18%
E. 8.5%

[Reveal] Spoiler:
I am trying to solve it using Allegation method , but not quit sure how to get the end result , Please help . Also, elaborate the steps so that I can understand the approach .
many thanks !



I started with 10% ------------ x% in the first row

16% in the second row

and x-16% and 6% in the last one

this gives me x-16/6= ? "stuck here "


By differentials too

So basically we need to find the % of sugar by weight of the second solution. We have this for the first solution 10% and we have the ratio of both and that the final solution was 16%.

So then since only 25% (1/4) is being replace the unknown percentage has a weight of 1 while the original amount remains with a weight of 3 (Thus the ratio 3:1). So by applying the differences between the result of 16% and each point value we can solve for ‘x’, in this case the percentage of sugar in the second solution

3(-6) + (x-16) = 0

-18 + x -16 = 0

X= 34

Hence (A) is the answer

Hope it helps
Cheers!
J :)
Director
Director
avatar
Joined: 03 Aug 2012
Posts: 905
Concentration: General Management, General Management
Schools: ISB '16
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
Followers: 12

Kudos [?]: 204 [0], given: 312

Premium Member CAT Tests
Re: One-fourth of a solution that was 10% by weight was replaced [#permalink] New post 19 Apr 2014, 05:41
Alligation is the KEY

3/4 of 10%------------------------------1/4 of X%

-------------------16%----------------------------


(X-16)%------------------------------------------6%

(X-16)/6=3/1

X=34%
_________________

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

Manager
Manager
User avatar
Joined: 22 Feb 2009
Posts: 229
Followers: 5

Kudos [?]: 33 [0], given: 132

GMAT ToolKit User CAT Tests
Re: One-fourth of a solution that was 10% by weight was replaced [#permalink] New post 04 Aug 2014, 21:46
TGC wrote:
Alligation is the KEY

3/4 of 10%------------------------------1/4 of X%

-------------------16%----------------------------


(X-16)%------------------------------------------6%

(X-16)/6=3/1

X=34%


Is it called cross method? I think it is the fastest solution :)
_________________

.........................................................................
+1 Kudos please, if you like my post

Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4772
Location: Pune, India
Followers: 1111

Kudos [?]: 5044 [0], given: 164

Re: One-fourth of a solution that was 10% by weight was replaced [#permalink] New post 04 Aug 2014, 23:05
Expert's post
vad3tha wrote:
TGC wrote:
Alligation is the KEY

3/4 of 10%------------------------------1/4 of X%

-------------------16%----------------------------


(X-16)%------------------------------------------6%

(X-16)/6=3/1

X=34%


Is it called cross method? I think it is the fastest solution :)


This is called Alligation or the scale method (a variant). Read more about this method here: http://www.veritasprep.com/blog/2011/03 ... -averages/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Senior Manager
Senior Manager
User avatar
Joined: 17 Dec 2012
Posts: 395
Location: India
Followers: 13

Kudos [?]: 180 [0], given: 10

One-fourth of a solution that was 10% by weight was replaced [#permalink] New post 04 Aug 2014, 23:50
guerrero25 wrote:
One fourth of a solution that was 10% sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight?

A. 34%
B. 24%
C. 22%
D. 18%
E. 8.5%


Original - sugar=0.1*s1, other = 0.9*s1
Removed - sugar= -0.1 * s1/4, other= - 0.9*s1/4
Added - sugar= x * s1/4, other= (1-x)*s1/4
Resultant sugar= 0.16*s1, other=0.84*s1

(0.1*s1 - 0.1*s1/4 + x*s1/4) / (0.9*s1 - 0.9*s1/4 + (1-x)*s1/4) = 16/84
x=0.34 or percent sugar by weight is 34%

The advantage with this approach is that you can use it for any mixture problem.
_________________

Srinivasan Vaidyaraman
Sravna Test Prep
http://www.sravna.com/courses.php

Classroom Courses in Chennai
Online and Correspondence Courses

Director
Director
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 925
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 6

Kudos [?]: 236 [0], given: 167

Re: One-fourth of a solution that was 10% by weight was replaced [#permalink] New post 05 Aug 2014, 02:07
Total Solution ........................ Sugar Concentration

100 ............................................ 10
(Assumed)

25% solution removed

100-25 ......................................... 10-\frac{10}{4}


75 ................................................... \frac{30}{4}

Same quantity has been replaced. Say the new solution sugar weight = x%

75 + 25 ......................................... \frac{30}{4} + \frac{25x}{100}

Given that the resultant solution has sugar concentration of 16%

So equating the above

\frac{30}{4} + \frac{25x}{100} = 16

x = 34%

Answer = A
_________________

Kindly press "+1 Kudos" to appreciate :)

Re: One-fourth of a solution that was 10% by weight was replaced   [#permalink] 05 Aug 2014, 02:07
    Similar topics Author Replies Last post
Similar
Topics:
one-fourth of a solution that was 10 percent sugar by weight fozzzy 0 17 Sep 2013, 01:27
3 One fourth of a solution that was 10 percent sugar by weight raghavs 6 21 Dec 2009, 05:17
5 One-fourth of a solution that was 10% by weight was replaced ast 9 04 Oct 2008, 02:53
One fourth of a solution that was 10 percent sugar by weight bmwhype2 4 17 Oct 2007, 12:19
21 Experts publish their posts in the topic One fourth of a solution that was 10 percent sugar by weight mbassmbass04 11 18 Oct 2004, 07:31
Display posts from previous: Sort by

One-fourth of a solution that was 10% by weight was replaced

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.