May 24 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. May 25 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. May 27 01:00 AM PDT  11:59 PM PDT All GMAT Club Tests are free and open on May 27th for Memorial Day! May 27 10:00 PM PDT  11:00 PM PDT Special savings are here for Magoosh GMAT Prep! Even better  save 20% on the plan of your choice, now through midnight on Tuesday, 5/27 May 30 10:00 PM PDT  11:00 PM PDT Application deadlines are just around the corner, so now’s the time to start studying for the GMAT! Start today and save 25% on your GMAT prep. Valid until May 30th.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 17 Mar 2014
Posts: 68

A spirit and water solution is sold in a market. The cost pe
[#permalink]
Show Tags
17 Mar 2014, 23:01
Question Stats:
32% (01:56) correct 68% (01:44) wrong based on 448 sessions
HideShow timer Statistics
A spirit and water solution is sold in a market. The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. A solution of 1 liter of spirit and 1 liter of water costs 50 cents. How many cents does a solution of 1 liter of spirit and 2 liters of water cost? A. 13 B. 33 C. 50 D. 51 E. 52
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 55267

Re: A spirit and water solution is sold in a market. The cost pe
[#permalink]
Show Tags
03 Apr 2014, 02:34
PiyushK wrote: qlx wrote: A spirit and water solution is sold in a market. The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. A solution of 1 liter of spirit and 1 liter of water costs 50 cents. How many cents does a solution of 1 liter of spirit and 2 liters of water cost?
A. 13 B. 33 C. 50 D. 51 E. 52 I solved it as : Cost = k (Part of spirit) 50cents = k (1/2) (1) k=100 Now part (fraction of spirit in 3 Liters) 1/3 Cost=100(1/3) = 33.33  (B) I am not sure what is wrong with my understanding... 1L spirit + 1L water = 50% concentration 1L spirit + 2L water = 33.33% concentration Logically price should be less for diluted liquid as in 1L solution spirit has reduced in parts per liter. You missed the following part: The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. According to the above the cost of each liter of the solution = \(k*\frac{s}{s+w}\). So, s+w liters of the solution should cost \(k*\frac{s}{s+w}*(s+w)=ks\). So, we can see that the price of the solution is based only the amount of the spirit there (s), which means that both solutions must have the same price because both have 1 liter of spirit. Answer: C.
_________________




Director
Joined: 03 Aug 2012
Posts: 695
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29 GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)

Re: A spirit and water solution is sold in a market. The cost pe
[#permalink]
Show Tags
19 Apr 2014, 03:30
Another Approach, a more mathematical one:
Cost/Ltr @ Concentration
Consider a constant of proportionality as K.
So,
Cost/Ltr = K * Conc.
Scenario 1:
50/2 = K * 1/2 => K=50
Scenario 2:
C/3 = K * 1/3
=> C=K
=>C=50




VP
Joined: 02 Jul 2012
Posts: 1158
Location: India
Concentration: Strategy
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: A spirit and water solution is sold in a market. The cost pe
[#permalink]
Show Tags
17 Mar 2014, 23:36
2 litres of 1/2 concentration spirit costs 50 cents = \(\frac{1}{2}\) dollars 2 litres of 1/3 concentration spirit will cost \(\frac{1}{3}\) dollars 3 litres of 1/3 concentration spirit will cost \(\frac{1}{3}*\frac{3}{2}\) dollars = \(\frac{1}{2}\) dollars = 50 cents Answer is C
_________________



Manager
Joined: 17 Mar 2014
Posts: 68

Re: A spirit and water solution is sold in a market. The cost pe
[#permalink]
Show Tags
18 Mar 2014, 00:17
MacFauz wrote: 2 litres of 1/2 concentration spirit costs 50 cents = \(\frac{1}{2}\) dollars
2 litres of 1/3 concentration spirit will cost \(\frac{1}{3}\) dollars
3 litres of 1/3 concentration spirit will cost \(\frac{1}{3}*\frac{3}{2}\) dollars = \(\frac{1}{2}\) dollars = 50 cents
Answer is C Hi how did you get 2 liters of 1/3 concentration of spirit will cost 1/3 dollars ?



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1812
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: A spirit and water solution is sold in a market. The cost pe
[#permalink]
Show Tags
18 Mar 2014, 00:19
The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. It means there is no effect of change in volume of water to the costing of the solution So a solution of 1 liter of spirit and 2 liters of water will cost 50 cents Answer = c = 50
_________________
Kindly press "+1 Kudos" to appreciate



VP
Joined: 02 Jul 2012
Posts: 1158
Location: India
Concentration: Strategy
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: A spirit and water solution is sold in a market. The cost pe
[#permalink]
Show Tags
18 Mar 2014, 00:21
It is given that the cost is directly proportional to the fraction of the spirit in volume. 50% spirit corresponds to 50 cents So 33.33% spirit will correspond to 33.33 cents qlx wrote: MacFauz wrote: 2 litres of 1/2 concentration spirit costs 50 cents = \(\frac{1}{2}\) dollars
2 litres of 1/3 concentration spirit will cost \(\frac{1}{3}\) dollars
3 litres of 1/3 concentration spirit will cost \(\frac{1}{3}*\frac{3}{2}\) dollars = \(\frac{1}{2}\) dollars = 50 cents
Answer is C Hi how did you get 2 liters of 1/3 concentration of spirit will cost 1/3 dollars ?
_________________



Intern
Joined: 23 Jan 2013
Posts: 5
Concentration: Marketing, Organizational Behavior
GPA: 3.9
WE: Information Technology (Computer Software)

Re: A spirit and water solution is sold in a market. The cost pe
[#permalink]
Show Tags
18 Mar 2014, 23:22
qlx wrote: The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has This statment can also be restated as "The Cost of 1 litre of Spririt is 50 Cents and water is free". If the mixture is changed by adding another litre of water, still the amount of Spirit in the solution is unchanged and you have pay only for the spirit. Hence the price is also unchanged, 50 Cents.



Director
Status: Everyone is a leader. Just stop listening to others.
Joined: 22 Mar 2013
Posts: 749
Location: India
GPA: 3.51
WE: Information Technology (Computer Software)

Re: A spirit and water solution is sold in a market. The cost pe
[#permalink]
Show Tags
02 Apr 2014, 13:06
qlx wrote: A spirit and water solution is sold in a market. The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. A solution of 1 liter of spirit and 1 liter of water costs 50 cents. How many cents does a solution of 1 liter of spirit and 2 liters of water cost?
A. 13 B. 33 C. 50 D. 51 E. 52 I solved it as : Cost = k (Part of spirit) 50cents = k (1/2) (1) k=100 Now part (fraction of spirit in 3 Liters) 1/3 Cost=100(1/3) = 33.33  (B) I am not sure what is wrong with my understanding... 1L spirit + 1L water = 50% concentration 1L spirit + 2L water = 33.33% concentration Logically price should be less for diluted liquid as in 1L solution spirit has reduced in parts per liter.
_________________
Piyush K Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. EdisonDon't forget to press> Kudos My Articles: 1. WOULD: when to use?  2. All GMATPrep RCs (New)Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction".



Director
Status: Everyone is a leader. Just stop listening to others.
Joined: 22 Mar 2013
Posts: 749
Location: India
GPA: 3.51
WE: Information Technology (Computer Software)

Re: A spirit and water solution is sold in a market. The cost pe
[#permalink]
Show Tags
03 Apr 2014, 04:09
Thanks Bunuel, I got it now.. I think I was sleeping while reading this question
_________________
Piyush K Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. EdisonDon't forget to press> Kudos My Articles: 1. WOULD: when to use?  2. All GMATPrep RCs (New)Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction".



Senior Manager
Joined: 28 Feb 2014
Posts: 294
Location: United States
Concentration: Strategy, General Management

Re: A spirit and water solution is sold in a market. The cost pe
[#permalink]
Show Tags
26 Jan 2015, 21:26
qlx wrote: A spirit and water solution is sold in a market. The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. A solution of 1 liter of spirit and 1 liter of water costs 50 cents. How many cents does a solution of 1 liter of spirit and 2 liters of water cost?
A. 13 B. 33 C. 50 D. 51 E. 52 'Tis a tricky question. I had to reread it twice to notice it said "cost per liter of the solution is directly proportional to the part of spirit." That means the cost is still the same since there is 1 liter in both instances. C. 50 cents



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9234
Location: Pune, India

Re: A spirit and water solution is sold in a market. The cost pe
[#permalink]
Show Tags
26 Jan 2015, 21:57
peachfuzz wrote: qlx wrote: A spirit and water solution is sold in a market. The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. A solution of 1 liter of spirit and 1 liter of water costs 50 cents. How many cents does a solution of 1 liter of spirit and 2 liters of water cost?
A. 13 B. 33 C. 50 D. 51 E. 52 'Tis a tricky question. I had to reread it twice to notice it said "cost per liter of the solution is directly proportional to the part of spirit." That means the cost is still the same since there is 1 liter in both instances. C. 50 cents Yes, ensure that you understand the relation thoroughly! Cost per liter = K * Fraction of Spirit 50 cents is the cost of 2 liters of solution (1 part water, 1 part spirit). So cost per liter is 25 cents. Fraction of spirit is 1/2. 25 = K * (1/2) K = 50 Cost per liter = 50 * (1/3) (1 part spirit, 2 parts water) Cost for 3 liters = 50 * (1/3) * 3 = 50 cents
_________________
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 >



VP
Joined: 07 Dec 2014
Posts: 1192

Re: A spirit and water solution is sold in a market. The cost pe
[#permalink]
Show Tags
01 Jul 2016, 15:28
let x=cost of 3 liters of 1:2 solution 50/(2*1/2)=x/(3*1/3) x=50¢



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2823

Re: A spirit and water solution is sold in a market. The cost pe
[#permalink]
Show Tags
12 Jul 2017, 16:24
qlx wrote: A spirit and water solution is sold in a market. The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. A solution of 1 liter of spirit and 1 liter of water costs 50 cents. How many cents does a solution of 1 liter of spirit and 2 liters of water cost?
A. 13 B. 33 C. 50 D. 51 E. 52 When a solution has 1 liter of spirit and 1 liter of water, the solution has 2 liters of liquid with a spirit concentration of 1/2. Since the cost is 50 cents for 2 liters, the cost per liter is 25 cents. Now we can create an equation to find the proportional constant k: (1/2) x k = 25 k = 50 Now we need to determine the cost of a solution that has 1 liter of spirit and 2 liters of water. We see that the solution has 3 liters of liquid with a spirit concentration of 1/3. Let’s first find the cost per liter, c: (1/3) x k = c (1/3) x 50 = c 50/3 = c Since the cost per liter is 50/3 cents and there are 3 liters of solution, the cost of the solution is: 50/3 x 3 = 50 cents Answer: C
_________________
5star 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.



Intern
Joined: 17 Jul 2017
Posts: 1

Re: A spirit and water solution is sold in a market. The cost pe
[#permalink]
Show Tags
18 Jul 2017, 23:07
2 L 50% sol costs=50 cents 1 L 50% sol costs=25 cents 1 L 33.33% sol costs=[25 x 33.33][/50] cents 3 L 33.33% sol costs=[25 x 33.33 x 3][/50] cents
3 L 33.33% sol costs=[25 x 100 x 3][/50 x 3] cents = 50 cents



Manager
Joined: 04 May 2014
Posts: 158
Location: India
WE: Sales (Mutual Funds and Brokerage)

A spirit and water solution is sold in a market. The cost pe
[#permalink]
Show Tags
16 Aug 2017, 00:22
Spirit and solution are sold in the market Solution cost=amount of spirit in the solution ie anything else mixed has no effect on the price of the solution First solution has 1 part spirit and 1 part water and price is=50 cents As stated in 2nd line above the 50cent is the price of spirit. 1 part spirit and 2 part water will have price equal to the price of 1 part spirit which is 50 cents



Intern
Joined: 10 Dec 2015
Posts: 26

Re: A spirit and water solution is sold in a market. The cost pe
[#permalink]
Show Tags
18 Jan 2018, 11:06
2 lts soln. of 1/2 conc. costs 50 cents 1 lts soln. of 1/2 conc. costs 50/2 cents 1 lts soln. of 1 conc. costs (50/2)*2 cents 1 lts soln. of 1/3 conc. costs (50/2)*2*(1/3) cents 3 lts soln. of 1/3 conc. costs (50/2)*2*(1/3)*3 cents = 50 cents. Ans. C P.S. Wrote more steps for clarity. Hope it helps.
_________________
Please give me KUDOS, if my posts help you in anyway. Please PM me any doubts which you might have, and I will do my level best to help.



NonHuman User
Joined: 09 Sep 2013
Posts: 11007

Re: A spirit and water solution is sold in a market. The cost pe
[#permalink]
Show Tags
19 Apr 2019, 04:38
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: A spirit and water solution is sold in a market. The cost pe
[#permalink]
19 Apr 2019, 04:38






