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Updated on: 25 Apr 2019, 20:46
Originally posted by GMATinsight on 17 Feb 2018, 05:32.
Last edited by GMATinsight on 25 Apr 2019, 20:46, edited 1 time in total.
Last edited by GMATinsight on 25 Apr 2019, 20:46, edited 1 time in total.
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
64% (02:20) correct
36%
(02:18)
wrong
based on 554
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\(x\) gallon 40% alcohol solution is mixed with another \(y\) gallon\(10\)% alcohol solution to result is \(z\) gallon \(p\)% alcohol solution. Is \(p>25\)?
1) \(x^2>y^2\)
2) \(z > p\)
Source: https://www.GMATinsight.com[/m]
1) \(x^2>y^2\)
2) \(z > p\)
Source: https://www.GMATinsight.com[/m]
17 Feb 2018, 09:11
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GMATinsight
Once we know the ratio between x:y we can calculate the exact value of p.
We'll look for an answer that gives us this information, a Logical approach.
1) this tells us that the ratio of x:y is greater than 1:1 meaning that p is closer to x than to y.
That is, p is closer to 40 than to 10 so it is larger than their midpoint - (40+10)/2 = 25.
Sufficient.
2) This does not give us the information we need and is insufficient.
Insufficient.
(A) is our answer.
General Discussion
17 Feb 2018, 06:52
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GMATinsight
1. For x^2 > y^2, the necessary condition is that x>y.
If x is greater than y, there will be more gallons of 40% alcohol solution than 10% alcohol solution.
Case 1: x = 20, y = 10
First solution will have 8 gallons of alcohol and the second solution will have 1 gallon of alcohol.
When we mix these solutions, we will get 9 gallons of alcohol out of 30 gallons solution. p = 30%
Case 2: x = 1.1, y = 1
First solution will have 0.44 gallons of alcohol and second solution will have 0.1 gallons. On mixing
these solutions, we would have 0.54 gallons of 2.1 gallons which is slightly over 25%
In both these cases, the percentage of alcohol is greater than 25%(Sufficient)
2. z > p
Case 1: x = 10, y = 20
First solution will have 4 gallons of alcohol and the second solution will have 2 gallon of alcohol.
When we mix these solutions, we will get 6 gallons of alcohol out of the 30 gallons, which is 20%
Here z=30 and p=20% (z > p and p is not greater than 25%)
Case 2: x = 50, y = 10
First solution will have 20 gallons of alcohol and the second solution will have 1 gallon of alcohol.
When we mix these solutions, we would have 21 gallons of alcohol out of 60 gallons which is 35%.
Here z=60 and p=35(a > p and p is greater than 25%)
Since we have contradicting cases for p>25%, this statement is not sufficient. (Insufficient) (Option A)
