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

Redeem

Finding Mixture Amounts

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 41
Joined: Sat Mar 09, 2013 1:10 pm
Thanked: 1 times

Finding Mixture Amounts

by Rudy414 » Mon Mar 18, 2013 5:15 pm
This problem was from the Princeton Review 1037 Practice Problems Edition 2 book.


At Anjelina Winery, the vintner wants to blend this year's New Sherry with last year's Old Sherry to create next year's Future Sherry. The vintner decides to use a hogshead with a total capacity of 240 liters that is partially full of Old Sherry. If the hogshead is filled up to full capacity with New Sherry, and Future Sherry will have 17% alcohol by volume (a.b.v.), what is the a.b.v. of New Sherry?

1) There will be 40% more New Sherry than Old Sherry in the filled hogshead, and the Old Sherry is 1.72% higher in a.b.v. than the New Sherry.

2) 100 liters of Old Sherry is in the hogshead, at 18% a.b.v.


Thanks.
Top
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 511
Joined: Wed Aug 11, 2010 9:47 am
Location: Delhi, India
Thanked: 344 times
Followed by:86 members

by Anju@Gurome » Mon Mar 18, 2013 7:10 pm
Rudy414 wrote:At Anjelina Winery, the vintner wants to blend this year's New Sherry with last year's Old Sherry to create next year's Future Sherry. The vintner decides to use a hogshead with a total capacity of 240 liters that is partially full of Old Sherry. If the hogshead is filled up to full capacity with New Sherry, and Future Sherry will have 17% alcohol by volume (a.b.v.), what is the a.b.v. of New Sherry?

1) There will be 40% more New Sherry than Old Sherry in the filled hogshead, and the Old Sherry is 1.72% higher in a.b.v. than the New Sherry.

2) 100 liters of Old Sherry is in the hogshead, at 18% a.b.v.
Let us assume, the hogshead has L liters of Old Sherry and a.b.v. of Old Sherry and New Sherry is O% and N%, respectively.
Hence, the amount of New Sherry in the 240 liters of Future Sherry is (240 - L) liters.

Hence, L*O + (240 - L)*N = 240*17
We need to determine N.

Statement 1: (240 - L) is 40% more that L ---> This is sufficient to determine the value of L.
Also, O is 1.72% higher than N ---> This is sufficient to express in terms of N.
Hence, in the original equation we can replace L with a certain value and express O in terms of N. Therefore, we will get an equation only in term of N which will be sufficient to find the value of N.

Sufficient

Statement 2: We know, L and O.
We can easily find N.

Sufficient

The correct answer is D.


Note : If someone is looking for the calculations (which is not necessary at all) to clear things up a bit more, here you go...
For Statement #1 :
### (240 - L) is 40% more than L
--> (240 - L - L) = 40% of L
--> (240 - 2L) = 4L/10
--> (120 - L) = L/5
--> 6L/5 = 120
--> L = 100

### O is 1.72% more than N
--> O = N + 1.72% of N = (1.0172)*N

So, 100*(1.0172)*N + 140*N = 240*17 ---> We can find N

For Statement #2 :
L = 100 and O = 18%

So, 100*18 + 140*N = 240*17 ---> We can find N
Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Tue Mar 19, 2013 1:01 pm
Rudy414 wrote:This problem was from the Princeton Review 1037 Practice Problems Edition 2 book.


At Anjelina Winery, the vintner wants to blend this year's New Sherry with last year's Old Sherry to create next year's Future Sherry. The vintner decides to use a hogshead with a total capacity of 240 liters that is partially full of Old Sherry. If the hogshead is filled up to full capacity with New Sherry, and Future Sherry will have 17% alcohol by volume (a.b.v.), what is the a.b.v. of New Sherry?

1) There will be 40% more New Sherry than Old Sherry in the filled hogshead, and the Old Sherry is 1.72% higher in a.b.v. than the New Sherry.

2) 100 liters of Old Sherry is in the hogshead, at 18% a.b.v.
Statement 1: There will be 40% more New Sherry than Old Sherry in the filled hogshead, and the Old Sherry is 1.72% higher in a.b.v. than the New Sherry.
Let N = New Sherry, O = Old Sherry, and F = Future Sherry.
To determine N's a.b.v., use ALLIGATION:

Step 1: Plot the 3 a.b.v's on a number line, with the ingredients (N and O) on the ends and the mixture (F) in the middle.
N----------F=17%----------O

Step 2: Plot the distances between the percentages.
(distance between N and F) : (distance between F and O) is equal to the RECIPROCAL of the ratio of N to O in the mixture.
Since the amount of N is 40% greater than the amount of O, N:O = 140:100 = 7:5.
Plotting the reciprocal of this ratio on the number line, we get:
N----5x-----F=17%----7x----O

Since the difference between N's a.b.v and O's a.b.v. is 1.72, we get:
5x+7x = 1.72
12x = 1.72
x ≈ .143.

Thus:
N's a.b.v = F's a.b.v - 5x = 17 - 5(.143) ≈ 16.28.
SUFFICIENT.

Statement 2: 100 liters of Old Sherry is in the hogshead, at 18% a.b.v.
Since the amount of O in statement 1 also is 100 liters, let's calculate O's a.b.v. in statement 1:
O's a.b.v = N's a.b.v + 1.72 = 16.28 + 1.72 = 18.

Thus, BOTH STATEMENTS indicate that the mixture contains 100 liters of O with an a.b.v of 18.
Thus, like statement 1, statement 2 implies following mixture:
100 liters of O with an a.b.v of 18.
140 liters of N with an a.b.v. of 16.28.
SUFFICIENT.

The correct answer is D.

For similar problems solved with alligation, check here:

https://www.beatthegmat.com/mixture-prob ... 01619.html
https://www.beatthegmat.com/what-percent ... 53954.html (second post)
https://www.beatthegmat.com/algebra-t195034.html
https://www.beatthegmat.com/mixture-prob ... 90121.html (second post)
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1