BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Soap alcohol and water

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 2789
Joined: Tue Jul 26, 2011 12:19 am
Location: Chennai, India
Thanked: 206 times
Followed by:43 members
GMAT Score:640

Soap alcohol and water

by GmatKiss » Tue Nov 01, 2011 4:58 am
The ratio, by volume, of soap to alcohol to water in a certain solution is 2:50:100. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved.
If the altered solution will contain 100 cubic centimeters of alcohol, how many cubic centimeters of water will it contain?

A. 50
B. 200
C. 400
D. 625
E. 800

Need a generic method (faster) to solve similar problems.

TIA,
GK
Top
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1239
Joined: Tue Apr 26, 2011 6:25 am
Thanked: 233 times
Followed by:26 members
GMAT Score:680

by sam2304 » Tue Nov 01, 2011 5:12 am
s:a:w = 2:50:100 ----> 1
s:a is doubled = 2*2/50 = 4:50 ----> 2
s:w is halved = 2/100 * 1/2 = 2:200 ----> 3
Express soap value of 3 in terms of 2
s:w = 4: 400

Now 1 becomes 4:50:400

The question asks for 100 cc of alcohol so everything doubles

8:100:800

So E.

The basic concept is similar to addition of fractions where we bring all values to common denominator the similar method should be implemented here keeping the same ratio.
Last edited by sam2304 on Tue Nov 01, 2011 5:13 am, edited 1 time in total.
Getting defeated is just a temporary notion, giving it up is what makes it permanent.
https://gmatandbeyond.blogspot.in/
Top
Legendary Member
Posts: 966
Joined: Sat Jan 02, 2010 8:06 am
Thanked: 230 times
Followed by:21 members

by shankar.ashwin » Tue Nov 01, 2011 5:13 am
S|A|W = 2|50|100

Now altered;

S|A = 4|50 = 8|100
S|W = 1|100 = 8|800

Ratio becomes 8|100|800
E
Top
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

by sanju09 » Tue Nov 01, 2011 5:18 am
GmatKiss wrote:The ratio, by volume, of soap to alcohol to water in a certain solution is 2:50:100. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved.
If the altered solution will contain 100 cubic centimeters of alcohol, how many cubic centimeters of water will it contain?

A. 50
B. 200
C. 400
D. 625
E. 800

Need a generic method (faster) to solve similar problems.

TIA,
GK

OK, so they want to double 2:50 to make the ratio of soap to alcohol in the altered solution to become 4:50 now; and they further want to make half of 2:100 to make the ratio of soap to water in the altered solution to become 1:100 now.

In the altered solution we symbolically have
S:A = 4:50 and S:W = 1:100

And the question cleverly asks us to find A:W first and then answer to the question. See the shortest we can do from here is to divide the two ratios so that the unwanted S cancels out and we have

(S/W)/ (S/A) = A/W

Or A:W in the altered solution = (1/100)/ (4/50) = 1/100 × 50/4 = 1/8 or 1:8.

In other words, in the altered solution, for every 1 cubic centimeters of alcohol, there are 8 cubic centimeters of water contents; likewise for every 100 cubic centimeters of alcohol, there are [spoiler]800 cubic centimeters[/spoiler] of water contents.

[spoiler]E[/spoiler]
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
User avatar
Community Manager
Posts: 1060
Joined: Fri May 13, 2011 6:46 am
Location: Utrecht, The Netherlands
Thanked: 318 times
Followed by:52 members

by neelgandham » Tue Nov 01, 2011 5:20 am
A line-by-line solution:

The ratio, by volume, of soap to alcohol to water in a certain solution is 2:50:100.
S:A:W = 2:50:100

The solution will be altered so that the ratio of soap to alcohol is doubled
S:A:W= 4:50:100

while the ratio of soap to water is halved.
S:A:W= 4:50:400

If the altered solution will contain 100 cubic centimeters of alcohol, how many cubic centimeters of water will it contain?

A = 100
W = ?
a/w = 1/8 => W = 800 Option E

A. 50
B. 200
C. 400
D. 625
E. 800

Need a generic method (faster) to solve similar problems.

TIA,
GK[/quote]
Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
Top
Master | Next Rank: 500 Posts
Posts: 124
Joined: Mon Jun 16, 2008 11:07 am
Thanked: 21 times
Followed by:14 members
GMAT Score:750

by CappyAA » Tue Nov 01, 2011 5:24 am
The only 2 generic ways I know to do this are to set up a table with the 3 parts as the 3 columns. Or to look at the two key ratios that are changing. I'll do it the 2nd way.

Our two key ratios here are:

Soap to alcohol: 2:50 or 1:25
Soap to water: 2:100 or 1:50

We don't need the third ratio of alcohol to water, because it is built into these two relationships.

We want to double the ratio of soap to alchohol, so the new ratio is 2:25 and we want to half the ratio of soap to water so the new ratio is 1:100 or 2:200 (since our first term had 2 parts of soap).

So our new soap:alcohol:water ratio is 2:25:200

So if it contains 100 cm^3 of alcohol, it will contain 200*4 or 800 cm^3 of water.

E
Taking the GMAT Again...PhD this time!

October 2008 Score: GMAT - 750 (50 Q, 41 V) :D

Manhattan GMAT 1 - 11/20/11 - 750 (50 Q, 42 V)
Manhattan GMAT 2 - 12/3/11 - 780 (51 Q, 45 V)
Top
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Sat Jan 29, 2011 8:20 am

by TazDevil » Tue Apr 17, 2012 5:57 pm
S:A:W = 2:50:100

AFTER ALTERED

S/A = 2 (2/50) = 2/25 S/W = 0.5 (2/100) = 1/100

Now, we know altered solution contains 100cc of alcohol

S/A = 2/25
S/100 = 2/25
S= 8

Now solve for W

S/W = 1/100
8/W=1/100
W=800
Top
Post new topic Post Reply
• Page 1 of 1