Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 10 Apr 2012
Posts: 269
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)

Onefourth of a solution that was 10% by weight was replaced
[#permalink]
Show Tags
Updated on: 14 Mar 2013, 02:15
Question Stats:
63% (02:24) correct 37% (02:25) wrong based on 590 sessions
HideShow timer Statistics
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% 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 x16% and 6% in the last one
this gives me x16/6= ? "stuck here "
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by guerrero25 on 13 Mar 2013, 13:52.
Last edited by Bunuel on 14 Mar 2013, 02:15, edited 1 time in total.
Edited the question.




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8373
Location: Pune, India

Re: Onefourth of a solution that was 10% by weight was replaced
[#permalink]
Show Tags
13 Mar 2013, 20:52
guerrero25 wrote: Onefourth 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 x16% and 6% in the last one
this gives me x16/6= ? "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
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!




Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 596
Location: India
Concentration: Strategy, General Management
Schools: Olin  Wash U  Class of 2015
WE: Information Technology (Computer Software)

Re: Onefourth of a solution that was 10% by weight was replaced
[#permalink]
Show Tags
13 Mar 2013, 22:22
guerrero25 wrote: Onefourth 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




Intern
Joined: 28 Jan 2013
Posts: 8
Location: United States
Concentration: Strategy, Technology
GMAT Date: 04202013
GPA: 3.2
WE: Analyst (Computer Software)

Re: Onefourth of a solution that was 10% by weight was replaced
[#permalink]
Show Tags
13 Mar 2013, 18:30
guerrero25 wrote: Onefourth 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 x16% and 6% in the last one
this gives me x16/6= ? "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 %



Math Expert
Joined: 02 Sep 2009
Posts: 49858

Re: Onefourth of a solution that was 10% by weight was replaced
[#permalink]
Show Tags
14 Mar 2013, 02:16



Senior Manager
Joined: 10 Apr 2012
Posts: 269
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)

Re: Onefourth of a solution that was 10% by weight was replaced
[#permalink]
Show Tags
14 Mar 2013, 09:51
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
Joined: 10 Sep 2013
Posts: 17
Location: India
Concentration: Strategy
GPA: 3.8
WE: General Management (Energy and Utilities)

Re: Onefourth of a solution that was 10% by weight was replaced
[#permalink]
Show Tags
17 Sep 2013, 05:38
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
Joined: 06 Feb 2012
Posts: 15

Re: Onefourth of a solution that was 10% by weight was replaced
[#permalink]
Show Tags
21 Oct 2013, 03:41
Vips0000 wrote: guerrero25 wrote: Onefourth 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
Joined: 06 Sep 2013
Posts: 1766
Concentration: Finance

Re: Onefourth of a solution that was 10% by weight was replaced
[#permalink]
Show Tags
16 Dec 2013, 16:05
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% 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 x16% and 6% in the last one
this gives me x16/6= ? "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) + (x16) = 0 18 + x 16 = 0 X= 34 Hence (A) is the answer Hope it helps Cheers! J



Director
Joined: 03 Aug 2012
Posts: 756
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29 GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)

Re: Onefourth of a solution that was 10% by weight was replaced
[#permalink]
Show Tags
19 Apr 2014, 06:41
Alligation is the KEY
3/4 of 10%1/4 of X%
16%
(X16)%6%
(X16)/6=3/1
X=34%



Manager
Joined: 22 Feb 2009
Posts: 176

Re: Onefourth of a solution that was 10% by weight was replaced
[#permalink]
Show Tags
04 Aug 2014, 22:46
TGC wrote: Alligation is the KEY
3/4 of 10%1/4 of X%
16%
(X16)%6%
(X16)/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



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8373
Location: Pune, India

Re: Onefourth of a solution that was 10% by weight was replaced
[#permalink]
Show Tags
05 Aug 2014, 00:05
vad3tha wrote: TGC wrote: Alligation is the KEY
3/4 of 10%1/4 of X%
16%
(X16)%6%
(X16)/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
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Director
Joined: 17 Dec 2012
Posts: 629
Location: India

Onefourth of a solution that was 10% by weight was replaced
[#permalink]
Show Tags
05 Aug 2014, 00:50
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= (1x)*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 + (1x)*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 Holistic Solutions http://www.sravnatestprep.com
Holistic and Systematic Approach



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1829
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: Onefourth of a solution that was 10% by weight was replaced
[#permalink]
Show Tags
05 Aug 2014, 03:07
Total Solution ........................ Sugar Concentration 100 ............................................ 10 (Assumed) 25% solution removed 10025 ......................................... \(10\frac{10}{4}\) 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



Director
Joined: 23 Jan 2013
Posts: 576

Onefourth of a solution that was 10% by weight was replaced
[#permalink]
Show Tags
24 Oct 2014, 06:20
Differential method
1016x problem says that 1/4 was replaced by higher concentration solution, meaning that ratio of 10% sol to X% sol was 3:1 1610=6 > 6*3=18 > 16+18=34% needs to be second solution
Checking
101634 6x=18y x/y=18/6=3:1, it is correct
A



Intern
Joined: 04 Jul 2014
Posts: 46

Onefourth of a solution that was 10% by weight was replaced
[#permalink]
Show Tags
25 Oct 2014, 06:45
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% 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 x16% and 6% in the last one
this gives me x16/6= ? "stuck here " [img]10% x% 16% 3/4 1/4 3 1 [/img] The difference 6 obtained by usual cross subtraction is 1 part. So 3 parts is 18 . To get 18, 16 must be subtracted from X. So x is the addition of 16 plus 18 THEREFORE X = 18+16 = 34 %



Manager
Joined: 22 Aug 2014
Posts: 163

Re: Onefourth of a solution that was 10% by weight was replaced
[#permalink]
Show Tags
07 May 2015, 03:23
Vips0000 wrote: guerrero25 wrote: Onefourth 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. Thank you! Your explanation is crisp and clear...kudos to you!



VP
Joined: 07 Dec 2014
Posts: 1102

Onefourth of a solution that was 10% by weight was replaced
[#permalink]
Show Tags
Updated on: 19 Sep 2018, 14:41
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 x=first solution weight y=second solution sugar % 3/4*.1x+1/4*xy=.16x→ .3x+xy=.64x→ y=.34=34% A
Originally posted by gracie on 26 Aug 2015, 16:54.
Last edited by gracie on 19 Sep 2018, 14:41, edited 1 time in total.



SVP
Joined: 26 Mar 2013
Posts: 1837

Re: Onefourth of a solution that was 10% by weight was replaced
[#permalink]
Show Tags
18 Jan 2016, 05:52
This question could be solved with logic and simple calculation.
If we use equal amount of solution with different concentrations, then the resulting concentration is the Mean of concentrations
So, if we apply the same concept above, solution 1 has 10 % and solution 2 need to be 31% to make the resulting concentration 16% ( if both with same amount solutions, for example 75 ml)
To have same resulting concentration 16%, we need to decrease the amount of solution 2 and increase its concentration above 31%.
only 1 answer fits. Answer A



Manager
Joined: 07 May 2015
Posts: 88

Re: Onefourth of a solution that was 10% by weight was replaced
[#permalink]
Show Tags
18 Jan 2016, 16:02
Thank you SO MUCH VeritasPrepKarishma !!! You made this topic look so easy in your blogs below. I am getting all the mixture questions correct now with the help of your blog. VeritasPrepKarishma wrote: guerrero25 wrote: Onefourth 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 x16% and 6% in the last one
this gives me x16/6= ? "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/




Re: Onefourth of a solution that was 10% by weight was replaced &nbs
[#permalink]
18 Jan 2016, 16:02



Go to page
1 2
Next
[ 28 posts ]



