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

It is currently 19 Oct 2019, 12:46

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.

Close

Request Expert Reply

Confirm Cancel

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

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

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
Joined: 25 Aug 2004
Posts: 146
Location: MONTREAL
One-fourth of a solution that was 10% by weight was replaced  [#permalink]

Show Tags

New post 18 Oct 2004, 08:31
4
10
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

63% (02:23) correct 37% (02:26) wrong based on 474 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 x-16% and 6% in the last one

this gives me x-16/6= ? "stuck here "
Most Helpful Expert Reply
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India
Re: One-fourth of a solution that was 10% by weight was replaced  [#permalink]

Show Tags

New post 13 Mar 2013, 20:52
14
13
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

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Most Helpful Community Reply
Intern
Intern
avatar
Joined: 11 Aug 2004
Posts: 10
Location: Prague (I am American)
Re: One-fourth of a solution that was 10% by weight was replaced  [#permalink]

Show Tags

New post 18 Oct 2004, 10:53
11
1
I am awful at these but here is what I got

75(0.1) + 25(x) = 100(0.16)
7.5 + 25x = 16
x = 8.5/25 = 0.34

34% it is
General Discussion
Manager
Manager
User avatar
Joined: 25 Aug 2009
Posts: 111
Location: Streamwood IL
Schools: Kellogg(Evening),Booth (Evening)
WE 1: 5 Years
Re: One-fourth of a solution that was 10% by weight was replaced  [#permalink]

Show Tags

New post 21 Dec 2009, 13:41
2
1
1
Let the original solution be 100ml
It had 10ml of sugar
1/4 of this solution is removed
sugar remaining = 7.5 ML
25 ml of x% solution is added.
New volume of sugar = 7.5+25*x/100
Since resulting solution is 16% sugar by weight, volume of sugar = 16ml

equating the 2

x=(16-7.5)*4
=34

A
_________________
Rock On
Intern
Intern
avatar
Joined: 23 Nov 2009
Posts: 31
Re: One-fourth of a solution that was 10% by weight was replaced  [#permalink]

Show Tags

New post 21 Dec 2009, 17:52
2
Answer A: 34%

Simply,
.75*.1+.25*y = .16
Solving for y would give the value 34%

Explanation:
.75% is still 10% solution
.25% is the y% solution

16% solution is 100%
_________________
A kudos would greatly help :)

Tuhin
Intern
Intern
User avatar
Joined: 17 Dec 2009
Posts: 33
Re: One-fourth of a solution that was 10% by weight was replaced  [#permalink]

Show Tags

New post 22 Dec 2009, 06:59
1
3/4 * 10 + 1/4 * x = 16
x = 16*4 - (30/4)*4
x = 64 - 30
x = 34

Therefore the answer is A
Intern
Intern
avatar
Joined: 04 Jul 2011
Posts: 2
Re: One-fourth of a solution that was 10% by weight was replaced  [#permalink]

Show Tags

New post 19 Jul 2011, 17:55
2
Ok here goes my first gmat club post! After spending a good 6 mins on this problem I can provide some good insight :)

So the total is 10 kg. We are told to remove from the mixture and replace with pure sand. This means that the total is still 10 kg.

Now, let X be the amount of pure sand that is added. This is what we are solving for.

Now the sand in the mixture is going to be (10-X)*0.3 + X. The first part is the sand that is in the mixture now WITHOUT the addition of the additional sand. To make this more clear, (10-X) is the amount of sand and clay mixture with the subtraction of the pure sand that will be added. Multiplying it by 0.3 gives us the amount of sand in this part of the whole mixture. the second part is the additional amount of pure sand that is added. Note that we do not multiply this by any percent number because it is pure sand!

So now the whole equation will look like this:

(10-X)*0.3+X/((10-X)+X) = 0.5.

The numerator is the amount of sand in the mixture. (10-X)*0.3 = amount of sand that is not pure in the mixture. X is the amount of pure sand.

(10-X)*0.3 + X = 5.
3-0.3X+X = 5.
0.7X = 2.
X = 20/7.
Manager
Manager
User avatar
Status: mba here i come!
Joined: 07 Aug 2011
Posts: 191
GMAT ToolKit User
Re: One-fourth of a solution that was 10% by weight was replaced  [#permalink]

Show Tags

New post 13 Sep 2011, 06:16
8
let 100 be the total volume.
total salt = 10
salt taken out = 10/4 = 2.5

to make solution 16%, total salt = 16
salt added = 16-7.5 = 8.5

solution had = 8.5/25*100 = 34% sugar
_________________
press +1 Kudos to appreciate posts
Download Valuable Collection of Percentage Questions (PS/DS)
Intern
Intern
avatar
Status: Mission MBA
Joined: 02 Jul 2010
Posts: 21
Location: Hyderabad, India
Schools: ISB, IIMs
Re: One-fourth of a solution that was 10% by weight was replaced  [#permalink]

Show Tags

New post Updated on: 14 Sep 2011, 23:11
6
Here is another method:

Consider that solution is made of sugar and water:
Solution A: Total 1000gm (10% sugar)
1000= 900 (water) + 100 (Sugar)

Expected Solutin B: Total 1000gm (16% sugar)
1000= 840 (water) + 160 (Sugar)

Now, as said in the question 25% of the solution A is replaced with another solution, which means:
75% of the solution A in untouched and only 25% of the solution (250gm) is touched

Total Sugar in Solution B= 160 = (75% of sugar in solution A) + (sugar replaced in 25% of Solution A with a new solution)

Sugar replaced in 25% Solution A with a new solution = 160- 75 =85

Sugar in new solution: 85/250 = 340/1000 = 34% (Answer) :)
_________________
If you find my posts useful, Appreciate me with the kudos!! +1

Originally posted by chawlavinu on 14 Sep 2011, 18:48.
Last edited by chawlavinu on 14 Sep 2011, 23:11, edited 1 time in total.
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)
Re: One-fourth of a solution that was 10% by weight was replaced  [#permalink]

Show Tags

New post 13 Mar 2013, 18:30
5
2
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 %
Director
Director
User avatar
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 563
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
GMAT ToolKit User Reviews Badge
Re: One-fourth of a solution that was 10% by weight was replaced  [#permalink]

Show Tags

New post 13 Mar 2013, 22:22
8
2
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
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58445
Re: One-fourth of a solution that was 10% by weight was replaced  [#permalink]

Show Tags

New post 14 Mar 2013, 02:16
5
3
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.
_________________
Director
Director
avatar
Joined: 03 Aug 2012
Posts: 660
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)
Re: One-fourth of a solution that was 10% by weight was replaced  [#permalink]

Show Tags

New post 19 Apr 2014, 06:41
2
1
Alligation is the KEY

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

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


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

(X-16)/6=3/1

X=34%
Manager
Manager
User avatar
Joined: 22 Feb 2009
Posts: 156
GMAT ToolKit User
Re: One-fourth of a solution that was 10% by weight was replaced  [#permalink]

Show Tags

New post 04 Aug 2014, 22:46
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
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India
Re: One-fourth of a solution that was 10% by weight was replaced  [#permalink]

Show Tags

New post 05 Aug 2014, 00:05
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

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Director
Director
User avatar
S
Joined: 17 Dec 2012
Posts: 626
Location: India
Re: One-fourth of a solution that was 10% by weight was replaced  [#permalink]

Show Tags

New post 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= (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.sravnatestprep.com

Holistic and Systematic Approach
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1749
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: One-fourth of a solution that was 10% by weight was replaced  [#permalink]

Show Tags

New post 05 Aug 2014, 03:07
2
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 :)
Manager
Manager
avatar
B
Joined: 07 May 2015
Posts: 74
GMAT ToolKit User
Re: One-fourth of a solution that was 10% by weight was replaced  [#permalink]

Show Tags

New post 18 Jan 2016, 16:02
1
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:
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/
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India
Re: One-fourth of a solution that was 10% by weight was replaced  [#permalink]

Show Tags

New post 18 Jan 2016, 22:33
neeraj609 wrote:
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.


Great! Keep practicing!
_________________
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 >
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8109
Location: United States (CA)
Re: One-fourth of a solution that was 10% by weight was replaced  [#permalink]

Show Tags

New post 30 Jan 2017, 17:45
1
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%



Let’s let x = the amount of solution, which initially contains 10% sugar. We remove one-fourth of that solution (.25x), which has 10% sugar. Then we replace that .25x with a solution of unknown percentage (p) of sugar. These actions result in our still having x amount of solution, but now with 16% sugar. We can summarize this in the following equation:

x(0.10) - (0.25x)(0.10) + (0.25x)(p) = x(0.16)

0.10x - 0.025x + 0.25xp = 0.16x

100x - 25x + 250xp = 160x

250xp = 85x

p = 85/250 = .34

Thus, the second solution was 34% sugar by weight.

Answer: A
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: One-fourth of a solution that was 10% by weight was replaced   [#permalink] 30 Jan 2017, 17:45

Go to page    1   2    Next  [ 26 posts ] 

Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne