Last visit was: 09 Jul 2025, 18:59 It is currently 09 Jul 2025, 18:59
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
User avatar
udaymathapati
Joined: 06 Apr 2010
Last visit: 27 Jan 2015
Posts: 91
Own Kudos:
5,397
 [99]
Given Kudos: 15
Products:
Posts: 91
Kudos: 5,397
 [99]
5
Kudos
Add Kudos
93
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
KarishmaB
Joined: 16 Oct 2010
Last visit: 09 Jul 2025
Posts: 16,101
Own Kudos:
74,229
 [78]
Given Kudos: 475
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,101
Kudos: 74,229
 [78]
46
Kudos
Add Kudos
32
Bookmarks
Bookmark this Post
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 09 Jul 2025
Posts: 102,609
Own Kudos:
Given Kudos: 97,813
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,609
Kudos: 739,909
 [22]
10
Kudos
Add Kudos
12
Bookmarks
Bookmark this Post
General Discussion
User avatar
soumanag
Joined: 09 Jun 2010
Last visit: 19 Jul 2012
Posts: 80
Own Kudos:
365
 [16]
Given Kudos: 1
Posts: 80
Kudos: 365
 [16]
13
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
Let the total solution is 150 L with 80 L water & 70 L syrup.

To make 40% syrup solution, the result solution must have 90 L syrup and 60 L syrup.

Therefore we are taking 10 L of syrup from initial solution and replacing with water.

using urinary method:
70 L syrup in 150 L solution
10 L syrup in 21.4 L solution

We started by multiplying 10
Now to get to the result we need to divide by 10 => amount of solution to be replaced with water = (21.4/10) = 2.14.

Correct option : C
avatar
krushna
Joined: 30 Sep 2010
Last visit: 21 Apr 2011
Posts: 35
Own Kudos:
168
 [4]
Posts: 35
Kudos: 168
 [4]
2
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
C it is
total solution 15, Lemonoid = 7
we want to make it 40% lemonoid >> so 6 parts of lemonoid
so we need to remove 1 part of lemonoid
each part of solution has 7/15 lemonoid
that means for 1 part lemonoid will be in 15/7 = 2.14 prt of solution which will be replaced with water
User avatar
Fijisurf
Joined: 10 Sep 2010
Last visit: 26 Nov 2011
Posts: 89
Own Kudos:
Given Kudos: 7
Posts: 89
Kudos: 174
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Does anybody else find the question description ambiguous?

"A solution contains 8 parts for every 7 parts of Lemonade syrup"
Your interpretation is that syrup and water relate as 7 and 8.

However, it can also mean that syrup takes 7 parts out of total of 8 parts of solution.

Does it make sense?
User avatar
KarishmaB
Joined: 16 Oct 2010
Last visit: 09 Jul 2025
Posts: 16,101
Own Kudos:
Given Kudos: 475
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,101
Kudos: 74,229
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Fijisurf
Does anybody else find the question description ambiguous?

"A solution contains 8 parts for every 7 parts of Lemonade syrup"
Your interpretation is that syrup and water relate as 7 and 8.

However, it can also mean that syrup takes 7 parts out of total of 8 parts of solution.

Does it make sense?

Yep. When I read the question, I thought that either the question is worded improperly or the word 'water' after '8 parts' is missing. But I figured that if it is 8 parts solution then the options don't match the answer so it must be 8 parts water. Don't fret!
User avatar
farukqmul
Joined: 15 Apr 2012
Last visit: 09 May 2018
Posts: 76
Own Kudos:
Given Kudos: 134
Location: Bangladesh
Concentration: Technology, Entrepreneurship
GMAT 1: 460 Q38 V17
GPA: 3.56
GMAT 1: 460 Q38 V17
Posts: 76
Kudos: 280
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
udaymathapati
A solution contains 8 parts of water for every 7 parts of Lemonade syrup. How many parts of the solution should be removed and replaced with water so that the solution will now contain 40% lemonade syrup?
A. 1.5
B. 1.75
C. 2.14
D. 2.34
E. 2.64

Please explain.

\(\frac{water}{syrup}=\frac{8}{7}\);

Consider the solution to be 15 liters, so it will contain 8 liters of water and 7 liters syrup. We want to replace \(x\) liters of solution with water so that amount of syrup decreased from 7 liters to 15*0.4=6 liters. So, we should replace (remove) 1 liter of syrup: but with every 1 liter of syrup comes 8/7 liters of water (\(\frac{water}{syrup}=\frac{8}{7}\) --> \(\frac{water}{1}=\frac{8}{7}\) --> \(water=\frac{8}{7}\)) so \(x=1+\frac{8}{7}\approx{2.14}\) liters.

Answer: C.
Can you explain that why the new ration is w/1 = 8/7 ? I thought it be w/6 =8/7..Thanks
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 09 Jul 2025
Posts: 102,609
Own Kudos:
739,909
 [3]
Given Kudos: 97,813
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,609
Kudos: 739,909
 [3]
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
farukqmul
Bunuel
udaymathapati
A solution contains 8 parts of water for every 7 parts of Lemonade syrup. How many parts of the solution should be removed and replaced with water so that the solution will now contain 40% lemonade syrup?
A. 1.5
B. 1.75
C. 2.14
D. 2.34
E. 2.64

Please explain.

\(\frac{water}{syrup}=\frac{8}{7}\);

Consider the solution to be 15 liters, so it will contain 8 liters of water and 7 liters syrup. We want to replace \(x\) liters of solution with water so that amount of syrup decreased from 7 liters to 15*0.4=6 liters. So, we should replace (remove) 1 liter of syrup: but with every 1 liter of syrup comes 8/7 liters of water (\(\frac{water}{syrup}=\frac{8}{7}\) --> \(\frac{water}{1}=\frac{8}{7}\) --> \(water=\frac{8}{7}\)) so \(x=1+\frac{8}{7}\approx{2.14}\) liters.

Answer: C.
Can you explain that why the new ration is w/1 = 8/7 ? I thought it be w/6 =8/7..Thanks

8/7 is not the new ratio. Again: we want to remove 1 liter of syrup, but with every 1 liter of syrup comes 8/7 liters of water (because if s=1 then w from w/s=8/7 becomes 8/7), hence in order to remove 1 liter of syrup we should remove total of 1+8/7 liters of mixture.

Hope it's clear.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 09 Jul 2025
Posts: 102,609
Own Kudos:
Given Kudos: 97,813
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,609
Kudos: 739,909
Kudos
Add Kudos
Bookmarks
Bookmark this Post
From 100 hardest questions
Bumping for review and further discussion.
User avatar
SVaidyaraman
Joined: 17 Dec 2012
Last visit: 05 Jul 2025
Posts: 577
Own Kudos:
Given Kudos: 20
Location: India
Expert
Expert reply
Posts: 577
Kudos: 1,741
Kudos
Add Kudos
Bookmarks
Bookmark this Post
1. Let the number of parts of the original solution be 30.
2.The original solution contains 14 parts lemonade and 16 parts water
3. The new solution contains 12 parts lemonade and 18 parts water
4. Let x parts of solution be replaced. Water replaced is 16x/30
5. x parts of water is added
6. From (2) and (3) we see the net increase in water is 18-16=2 parts
7. From (4) and (5) we see the net increase in water is x-(16x/30) parts
8. Equating (6) and (7) we have x=4.28
9. If we take the total number of parts as 30, the solution removed is 4.28 parts. Therefore for a total of 15 parts, the solution removed is 2.14 parts
User avatar
KarishmaB
Joined: 16 Oct 2010
Last visit: 09 Jul 2025
Posts: 16,101
Own Kudos:
Given Kudos: 475
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,101
Kudos: 74,229
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Quote:
Why we take 2/5 as 40% ..we need to take 40 % of 7/15 ?


The question tells you that in the final solution, lemonade syrup is 40% of the solution i.e. there is 2 parts lemonade syrup for 3 parts of water
It does not imply that the concentration of lemonade syrup is 40% of its initial concentration. The final concentration is actually 40% i.e. 2/5.
avatar
Asifpirlo
Joined: 10 Jul 2013
Last visit: 26 Jan 2014
Posts: 222
Own Kudos:
1,129
 [8]
Given Kudos: 102
Posts: 222
Kudos: 1,129
 [8]
3
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
udaymathapati
A solution contains 8 parts of water for every 7 parts of Lemonade syrup. How many parts of the solution should be removed and replaced with water so that the solution will now contain 40% lemonade syrup?

A. 1.5
B. 1.75
C. 2.14
D. 2.34
E. 2.64
My solution with explanation:
Attachments

Lemonade.png
Lemonade.png [ 36.54 KiB | Viewed 17752 times ]

User avatar
jlgdr
Joined: 06 Sep 2013
Last visit: 24 Jul 2015
Posts: 1,316
Own Kudos:
Given Kudos: 355
Concentration: Finance
Posts: 1,316
Kudos: 2,717
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Alternative approach, give kudos if you like

Let's say total of 15 liters, 8 of water and 7 of lemonade
Therefore, if we need lemonade to be 60% we need the ratio to be 3:2

Thus we have

2(8+x-8/15x) = 3(7-7/15x)

Solving for 'x' we get 15/7=2.14 (C)

Just to elaborate a little more on this. 2:3 are of course the ratios, in some problems we are asked so that there's an equal amount of both, then we don't need to care about the 2 and 3.

Next, we are basically replacing quantities so if we put x we take away x of the solution. But the 'x' liters of the solution contain part of both lemonade and water, therefore, that's why we use the respective ratios.

Hope its clear now

Cheers
J
User avatar
m3equals333
User avatar
Retired Moderator
Joined: 20 Dec 2013
Last visit: 18 Jun 2016
Posts: 141
Own Kudos:
150
 [1]
Given Kudos: 71
Location: United States (NY)
GMAT 1: 640 Q44 V34
GMAT 2: 720 Q49 V40
GMAT 3: 710 Q48 V40
GPA: 3.16
WE:Consulting (Finance: Venture Capital)
Products:
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Def took longer to rationalize than I would have allowed on test day...anyway, here's my take:

Replacing one part of the solution with water will take away 8/15 of water and 7/15 of Lemonade (and replace it with 15/15 water)...essentially just switching out 7/15 of Lemonade with 7/15 Water for every part removed...

So, from a Lemonade composition perspective:

[7 - (7x/15)]/15 = 4/10

x=15/7
avatar
VSabc
Joined: 19 Dec 2013
Last visit: 12 May 2015
Posts: 10
Own Kudos:
Given Kudos: 11
GPA: 4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
It seems I took a completely different tangent here, can someone please help me:
Let there be total 15l of solution implying 8l water and 7l lemonade. Acc. to the problem, let's take off 'w'l from solution and add 'w'l of water implying:
(8+w)/(15-w)=0.6 solving which gives w=0.525
What's wrong here?
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,788
Own Kudos:
12,488
 [1]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,788
Kudos: 12,488
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi VSabc,

This question is a little tougher than a typical "mixture" question. The prompt tells us to REPLACE some of the existing mixture with pure water (with the goal of turning the new mixture into a 40% syrup mix.

To start, we have 15 total liters -->a mixture that is 8 liters water and 7 liters syrup.

If we pour 1 liter of this mixture into a glass, we would have a liquid that is 7/15 syrup (so a little less than half syrup).

For the mixture to be 15 total liters and 40% syrup, we need the mixture to be 9 liters water and 6 liters syrup.

In basic math terms, we need to pour out enough of the mixture that we remove 1 full liter of syrup; when we pour an equivalent amount of water back in, we'll have 15 total liters (and 6 of them will be syrup). Since each liter is 7/15 syrup......

We need to remove 15/7 liters and replace them with 15/7 liters of pure water.

15/7 is a little more than 2 liters (about 2.14 liters)

Final Answer:
GMAT assassins aren't born, they're made,
Rich
User avatar
KarishmaB
Joined: 16 Oct 2010
Last visit: 09 Jul 2025
Posts: 16,101
Own Kudos:
Given Kudos: 475
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,101
Kudos: 74,229
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VSabc
It seems I took a completely different tangent here, can someone please help me:
Let there be total 15l of solution implying 8l water and 7l lemonade. Acc. to the problem, let's take off 'w'l from solution and add 'w'l of water implying:
(8+w)/(15-w)=0.6 solving which gives w=0.525
What's wrong here?

Here is the problem with your equation.

When you took out 'w' lt of solution, the water left is less than 8 lt. So how can total water after replacement be (8 + w) lts? It will 'something less than 8 + w' lts.
Also, the new solution after you replace with water is again 15 lts. So why would you have (15 - w) in the denominator?

Your equation should be

\(\frac{8 - (8/15)*w + w}{15} = 0.6\) (the fraction of water removed will be (8/15) of w)

\(8 + (7/15)*w = 9\)

\(w = 15/7\)
avatar
GauravSolanky
Joined: 12 Oct 2014
Last visit: 20 Jul 2016
Posts: 39
Own Kudos:
Given Kudos: 241
Location: India
Concentration: Finance, General Management
GMAT 1: 550 Q44 V21
WE:Analyst (Finance: Investment Banking)
GMAT 1: 550 Q44 V21
Posts: 39
Kudos: 23
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasPrepKarishma
Though Bunuel and soumanag have already explained the solution well, I will add the method I like the most.

In replacement questions, focus on the thing that decreases. When solution is removed, water decreases but then water is added. While when solution is removed, lemonade decreases and does not get added later. So we will work with lemonade concentration.

The fraction of lemonade in the solution is 7/15
We need to get this fraction down to 2/5 (to make it 40%)
Let us say, we remove a fraction 'f' of the solution.
Then 7/15 - f * (7/15) = 2/5
f = 1/7
So (1/7)th of the solution has to be removed. But we want the answer in terms of parts (how many of the 15 parts have to be removed)
So we need to remove (1/7) * 15 = 2.14 parts



Hi Karishma,

Thanks for explaining it so well. I got it wrong as I thought we have to give answer in terms of lemonade.
So, here can we say that replacing 1 unit of lemonade and 1.14 units of water will serve the purpose ?

Regards,

Gaurav :-D
User avatar
KarishmaB
Joined: 16 Oct 2010
Last visit: 09 Jul 2025
Posts: 16,101
Own Kudos:
74,229
 [1]
Given Kudos: 475
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,101
Kudos: 74,229
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GauravSolanky
VeritasPrepKarishma
Though Bunuel and soumanag have already explained the solution well, I will add the method I like the most.

In replacement questions, focus on the thing that decreases. When solution is removed, water decreases but then water is added. While when solution is removed, lemonade decreases and does not get added later. So we will work with lemonade concentration.

The fraction of lemonade in the solution is 7/15
We need to get this fraction down to 2/5 (to make it 40%)
Let us say, we remove a fraction 'f' of the solution.
Then 7/15 - f * (7/15) = 2/5
f = 1/7
So (1/7)th of the solution has to be removed. But we want the answer in terms of parts (how many of the 15 parts have to be removed)
So we need to remove (1/7) * 15 = 2.14 parts



Hi Karishma,

Thanks for explaining it so well. I got it wrong as I thought we have to give answer in terms of lemonade.
So, here can we say that replacing 1 unit of lemonade and 1.14 units of water will serve the purpose ?

Regards,

Gaurav :-D

Yes, you are removing a total of 2.14 units, of which (7/15)*2.14 = 1 unit is lemonade and rest 1.14 units is water.

Note that saying "replace 1 unit of lemonade and 1.14 units of water" is not very logical since you cannot remove the two separately. They are mixed together so you need to remove the solution only. You cannot remove 1 unit of lemonade alone since water will come along with it. So it will be logical to say that we must remove 2.14 units of solution of which 1 unit will be lemonade and rest will be water since solutions are assumed homogeneous.
 1   2   
Moderators:
Math Expert
102609 posts
PS Forum Moderator
683 posts