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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

If a portion of a half water/half alcohol mix is replaced [#permalink]

Show Tags

02 Sep 2010, 08:24

3

This post received KUDOS

31

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

54% (02:19) correct
46% (01:24) wrong based on 489 sessions

HideShow timer Statistics

If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?

If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?

a 3% b 20% c 66% d 75% e 80%

Question can be solved algebraically or using allegation method.

Algebraic approach:

Initial solution is "half water/half alcohol mix" means it's 50% (0.5) alcohol solution.

Let the portion replaced be \(x\) and the volume of initial solution be 1 unit.

Then the amount of alcohol after removal of a portion will be \(0.5(1-x)\) and the amount of alcohol added will be \(0.25x\), so total amount of alcohol will be \(0.5(1-x)+0.25x\). On the other hand as in the end 30% alcohol solution was obtained then the amount of alcohol in the end was \(0.3*1\).

Re: Mixture problem-Can someone explain this [#permalink]

Show Tags

02 Sep 2010, 10:11

zest4mba wrote:

If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?

a 3% b 20% c 66% d 75% e 80%

I think the answer B can be considered only if the question was rephrased as what percentage of alcohol was replaced in the original solution with water. (20/100*100). Else the answer should be E as explained by other above.

Re: Mixture problem-Can someone explain this [#permalink]

Show Tags

02 Sep 2010, 17:55

1

This post received KUDOS

Yup. It is E indeed. - If V is volume of the mixture then V/2 is alc and V/2 is water. - Take Xml of the solution away (it takes X/2 alc with it). So the alc level now is (V-X)/2. - Add X ml back but this solution only has X/4 alc. So new alc content = (V-X)/2 + X/4 - New alc content = 3V/10 as it is 30%. Solving it gives X as 80%. More or less the same approach that Bunuel took. Thank you, Hemanth

Re: Mixture problem-Can someone explain this [#permalink]

Show Tags

19 Sep 2010, 09:52

Guys,

I'm trying to apply a shortcut provided by KillerSquirrel in this thread mixture-55090.html, but getting a wrong answer Could you please elaborate this Mystery?

I do not know how to solve mixture problems. Please advise

If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?

a 3% b 20% c 66% d 75% e 80%

Question on Mixtures can be easily solved using weighted averages concept discussed here: http://gmatclub.com/forum/tough-ds-105651.html#p828579 I would also recommend that you go through the complete theory from some standard book if you are not comfortable.

This question involves replacement rather than simply mixing two solutions hence it has one extra step at the end which I will discuss later.

First of all consider, you have a solution with 50% alcohol. Part of it is removed and mixed with a 25% alcohol solution. In effect, this is similar to mixing two solutions, one of 25% alcohol and other of 50% alcohol.

Attachment:

Ques1.jpg [ 3.8 KiB | Viewed 15359 times ]

So 25% alcohol solution volume : 50% alcohol solution volume is 20:5 which is 4:1. Since out of 5 parts of 50% alcohol solution, 4 parts were removed to replace them with 4 parts 25% alcohol solution, the portion of 50% alcohol solution replaced was 4/5 = 80%. The question asks: what percentage of original alcohol was replaced? Since the solution is homogenous, it you replace 80% of it, 80% of the original amount of alcohol in the solution will be replaced.

To understand this, lets say I have 100 liters of 50% alcohol solution. When I remove 80% of it, I remove 80 liters solution. In the solution I remove, I have 40 liters alcohol and 40 liters water. In the 20 liters solution that is remaining, 10 liters is alcohol and 10 liters is water. So amount of alcohol removed (and replaced) is 40/50 = 80%
_________________

I do not know how to solve mixture problems. Please advise

If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?

a 3% b 20% c 66% d 75% e 80%

If you need additional instruction on these problem types, refer to the Jeff Sackmann Total Math handout p.158-159. He gives a more detailed explanation of Bunuel's method (which I think is the quickest approach to solving these problem types).

Re: Mixture problem-Can someone explain this [#permalink]

Show Tags

01 Oct 2011, 06:33

am I right? let x be water, y - alcohol. so we have - 0.5x+0.5y -0.25y=0.3x+0.3y x=1/4y x/y=1/4 so in a new solution y 's portion is 4/5 or 80%
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth

I do not know how to solve mixture problems. Please advise

If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?

a 3% b 20% c 66% d 75% e 80%

Question on Mixtures can be easily solved using weighted averages concept discussed here: http://gmatclub.com/forum/tough-ds-105651.html#p828579 I would also recommend that you go through the complete theory from some standard book if you are not comfortable.

This question involves replacement rather than simply mixing two solutions hence it has one extra step at the end which I will discuss later.

First of all consider, you have a solution with 50% alcohol. Part of it is removed and mixed with a 25% alcohol solution. In effect, this is similar to mixing two solutions, one of 25% alcohol and other of 50% alcohol.

Attachment:

Ques1.jpg

So 25% alcohol solution volume : 50% alcohol solution volume is 20:5 which is 4:1. Since out of 5 parts of 50% alcohol solution, 4 parts were removed to replace them with 4 parts 25% alcohol solution, the portion of 50% alcohol solution replaced was 4/5 = 80%. The question asks: what percentage of original alcohol was replaced? Since the solution is homogenous, it you replace 80% of it, 80% of the original amount of alcohol in the solution will be replaced.

To understand this, lets say I have 100 liters of 50% alcohol solution. When I remove 80% of it, I remove 80 liters solution. In the solution I remove, I have 40 liters alcohol and 40 liters water. In the 20 liters solution that is remaining, 10 liters is alcohol and 10 liters is water. So amount of alcohol removed (and replaced) is 40/50 = 80%

How have u used the weighted avg formula?

w1/w2 = (c2-avg) / (avg-c1)

if c1 = 25 and c2=50 and avg = 30 - here how do we calculate w1 and/ or w2? didnot understand this part "Since out of 5 parts of 50% alcohol solution, 4 parts were removed to replace them with 4 parts 25% alcohol solution, the portion of 50% alcohol solution replaced was 4/5 = 80%. "

if c1 = 25 and c2=50 and avg = 30 - here how do we calculate w1 and/ or w2? didnot understand this part "Since out of 5 parts of 50% alcohol solution, 4 parts were removed to replace them with 4 parts 25% alcohol solution, the portion of 50% alcohol solution replaced was 4/5 = 80%. "

if c1 = 25 and c2=50 and avg = 30 - here how do we calculate w1 and/ or w2? didnot understand this part "Since out of 5 parts of 50% alcohol solution, 4 parts were removed to replace them with 4 parts 25% alcohol solution, the portion of 50% alcohol solution replaced was 4/5 = 80%. "

Re: If a portion of a half water/half alcohol mix is replaced [#permalink]

Show Tags

06 Oct 2013, 23:10

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: If a portion of a half water/half alcohol mix is replaced [#permalink]

Show Tags

16 Dec 2013, 06:22

zest4mba wrote:

If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?

A. 3% B. 20% C. 66% D. 75% E. 80%

Quick way

Use Smart Numbers

Give 100 for the initial amount

Then you will have 50-0.25x = 30 x = 80

So % is 80/100 is 80%

Hence E is the answer Hope it helps Cheers! J

gmatclubot

Re: If a portion of a half water/half alcohol mix is replaced
[#permalink]
16 Dec 2013, 06:22

After days of waiting, sharing the tension with other applicants in forums, coming up with different theories about invites patterns, and, overall, refreshing my inbox every five minutes to...

I was totally freaking out. Apparently, most of the HBS invites were already sent and I didn’t get one. However, there are still some to come out on...

There is without a doubt a stereotype for recent MBA grads – folks who are ambitious, smart, hard-working, but oftentimes lack experience or domain knowledge. Looking around and at...