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)
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