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

 It is currently 12 Dec 2019, 01:03

### 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

# Five gallons of a solution of vinegar and water with 8% vinegar is to

Author Message
TAGS:

### Hide Tags

Intern
Joined: 27 Sep 2014
Posts: 12
Location: Singapore
Concentration: Marketing, Entrepreneurship
GPA: 3.5
WE: Design (Other)
Five gallons of a solution of vinegar and water with 8% vinegar is to  [#permalink]

### Show Tags

15 Dec 2014, 02:58
2
10
00:00

Difficulty:

15% (low)

Question Stats:

83% (01:56) correct 17% (02:10) wrong based on 162 sessions

### HideShow timer Statistics

Five gallons of a solution of vinegar and water with 8% vinegar is to be diluted with water to make a 4% vinegar mixture. How many gallons of water should be added?

A. 10
B. 5
C. 4
D. 2
E. 1

This is probably a very easy question but I have an extreme aversion to raitos, so any help is appreciated.

Source: Bell Curves
Intern
Joined: 13 Aug 2014
Posts: 8
Location: United States
Concentration: Technology, Finance
GPA: 3.85
WE: Programming (Computer Software)
Re: Five gallons of a solution of vinegar and water with 8% vinegar is to  [#permalink]

### Show Tags

15 Dec 2014, 04:33
2
4
Its been given that there is 5 gallons of water and Vinegar with 8% of vinegar.
ie 8% of vinegar in 5 gallons is (8/100)*5 = 0.4 gallons of Vinegar and 4.6 gallons of water.

To make it 4% how many gallons of water should be added to the existing solution(5 g)

let us say it is x. i.e current Vinegar solution/(current soln in gallons + water to be added)=0.04
>> 0.4/(5+x)=4%

0.4/(5+x)=0.04 >> 5+x= 0.4/0.04=10

>>x=5

Ans B
##### General Discussion
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15704
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Five gallons of a solution of vinegar and water with 8% vinegar is to  [#permalink]

### Show Tags

23 Dec 2014, 11:32
3
Hi rvc27,

In these types of mixture questions, if the answers are numbers, then it's likely that you can TEST THE ANSWERS to quickly get to the solution. Here's how:

First, we need to know about the original mixture of vinegar and water. We're told that a 5 gallon mixture is 8% vinegar....

(5 gallons)(.08) = 0.4 gallons vinegar
The rest = 4.6 gallons water

We're told to ADD WATER until the mixture goes from 8% vinegar to 4% vinegar.

Since the answer choices are numbers, we know that one of them will lead us to a 4% mix when added to the current mix. Changing 8% to 4% means that we have to add a significant amount of water (relative to what we started with), so I would TEST one of the bigger numbers first.

Let's TEST B

If 5 gallons of water were added, then we'd have....
0.4 gallons vinegar
9.6 gallons of water

0.4/10 = 4% vinegar. This is EXACTLY what we're looking for, so B MUST be the answer.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9871
Location: Pune, India
Re: Five gallons of a solution of vinegar and water with 8% vinegar is to  [#permalink]

### Show Tags

28 Dec 2014, 22:23
3
rvc27 wrote:
Five gallons of a solution of vinegar and water with 8% vinegar is to be diluted with water to make a 4% vinegar mixture. How many gallons of water should be added?

A. 10
B. 5
C. 4
D. 2
E. 1

This is probably a very easy question but I have an extreme aversion to raitos, so any help is appreciated.

Source: Bell Curves

Yes, the question can be very easily solved by considering it a mixture problem where 8% vinegar solution is mixed with 0% vinegar solution (pure water) to make a 4% vinegar solution.
Check out this post on weighted average: http://www.veritasprep.com/blog/2011/03 ... -averages/
The formula given in it will be very helpful to you in your GMAT journey.

w1/w2 = (A2 - Aavg)/(Aavg - A1) = (0 - 4)/(4 - 8) = 1/1
So weights of both solutions should be same. We should put 5 gallons of water in 5 gallons of 8% vinegar solution.
_________________
Karishma
Veritas Prep GMAT Instructor

Senior SC Moderator
Joined: 22 May 2016
Posts: 3742
Five gallons of a solution of vinegar and water with 8% vinegar is to  [#permalink]

### Show Tags

29 Dec 2017, 11:46
1
rvc27 wrote:
Five gallons of a solution of vinegar and water with 8% vinegar is to be diluted with water to make a 4% vinegar mixture. How many gallons of water should be added?

A. 10
B. 5
C. 4
D. 2
E. 1

This is probably a very easy question but I have an extreme aversion to raitos, so any help is appreciated.

Source: Bell Curves

Let x = amount of water to be added
A = solution with 8% vinegar
B = water, which 0.0 percent vinegar

(% A)(Vol A) + (% B)(Vol B) = (% of A+B)(Vol A+B)

You do not need the 0x on LHS. It's a reminder that water IS being added, but that its concentration /percent vinegar has no weight.

$$.08(5) + 0.0(x) = .04(5 + x)$$
$$.40 + 0x = .20 + .04x$$
$$.20 = .04x$$
$$x = \frac{.20}{.04}=\frac{20}{5}=5$$

_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Never doubt that a small group of thoughtful, committed citizens can change the world; indeed, it's the only thing that ever has -- Margaret Mead
Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 402
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: Five gallons of a solution of vinegar and water with 8% vinegar is to  [#permalink]

### Show Tags

25 Dec 2014, 08:49
May I propose another approach here? That, because coming from a psychology background and pretty much learning math through my gmat practice, the more mathematical approaches are still sometimes difficult for me.

So, as we said above, we have 5 gallons of solution, with 0.4 gallons of vinegar (8% of solution) and 4.6 gallons of water (92% of solution). Now, we can say that if the vinegar is the new solution is 4% of the total solution, then water must be 98%.

Then, we can say: 4.6 gallons of water is 92% of the solution - x gallons are 98%? Or..

4.6 ---> 92
x ---> 98

92x=4.6*98
92x=450.8
x=450.8/92
x= 4.9, so rounding up to 5.
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1727
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Five gallons of a solution of vinegar and water with 8% vinegar is to  [#permalink]

### Show Tags

26 Dec 2014, 00:06
Initial .................. Vinegar .................... Water ............... Total

8% Vinegar ............ $$\frac{40}{100}$$ ........................ $$\frac{460}{100}$$ .............. 5

"x" water added .... $$\frac{40}{100}$$ ....................... $$\frac{460}{100} + x$$ ......... 5+x

Given that post addition of water, vinegar concentration should decrease to 4%

$$\frac{4}{100} (5+x) = \frac{40}{100}$$

x = 5

VP
Joined: 07 Dec 2014
Posts: 1217
Five gallons of a solution of vinegar and water with 8% vinegar is to  [#permalink]

### Show Tags

Updated on: 30 Dec 2017, 10:31
rvc27 wrote:
Five gallons of a solution of vinegar and water with 8% vinegar is to be diluted with water to make a 4% vinegar mixture. How many gallons of water should be added?

A. 10
B. 5
C. 4
D. 2
E. 1

let w=gallons of water to be added
.08*5=.04(5+w)
w=5 gallons
B

Originally posted by gracie on 29 Dec 2017, 11:05.
Last edited by gracie on 30 Dec 2017, 10:31, edited 1 time in total.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3158
Re: Five gallons of a solution of vinegar and water with 8% vinegar is to  [#permalink]

### Show Tags

30 Dec 2017, 01:28
rvc27 wrote:
Five gallons of a solution of vinegar and water with 8% vinegar is to be diluted with water to make a 4% vinegar mixture. How many gallons of water should be added?

A. 10
B. 5
C. 4
D. 2
E. 1

This is probably a very easy question but I have an extreme aversion to raitos, so any help is appreciated.

Source: Bell Curves

Initial vinegar content = 8%

Final vinegar content = 4%

Vinegar content in the additional water that is added = 0% (the water is 100% water and 0% vinegar)

Thus the ratio of the initial mixture and water that is added = (4-0) : (8 - 4) = 1 : 1

Thus in the 5 gallons of initial mixture, you will have to add another 5 gallons of water to get a 4% vinegar in the final mixture.

Note: The method that is used here is Alligation, which is similar to weighted averages, but faster to calculate.

Regards,
Saquib
e-GMAT
Quant Expert
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 13744
Re: Five gallons of a solution of vinegar and water with 8% vinegar is to  [#permalink]

### Show Tags

03 Nov 2019, 13:49
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Five gallons of a solution of vinegar and water with 8% vinegar is to   [#permalink] 03 Nov 2019, 13:49
Display posts from previous: Sort by