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16 Sep 2014, 01:20
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The price of Mixture A is $2 per gallon and the price of Mixture B is $5 per gallon. Is $9 enough to buy \(x\) gallons of Mixture A and \(y\) gallons of Mixture B?
(1) The ratio of \(x\) to \(y\) is 2 to 1
(2) $10 is NOT enough to buy \(2x\) gallons of Mixture A and \(\frac{y}{2}\) gallons of Mixture B
(1) The ratio of \(x\) to \(y\) is 2 to 1
(2) $10 is NOT enough to buy \(2x\) gallons of Mixture A and \(\frac{y}{2}\) gallons of Mixture B
16 Sep 2014, 01:20
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Official Solution:
The price of Mixture A is $2 per gallon and the price of Mixture B is $5 per gallon. Is $9 enough to buy \(x\) gallons of Mixture A and \(y\) gallons of Mixture B?
The question asks whether \(2x+5y\leq{9}\).
(1) The ratio of \(x\) to \(y\) is 2 to 1.
This implies that \(\frac{x}{y}=\frac{2}{1}\) or that \(x=2y\). Thus, the question becomes: is \(2(2y)+5y\leq{9}\) or is \(y\leq{1}\). Since we don't know that, this statement is not sufficient.
(2) $10 is NOT enough to buy \(2x\) gallons of Mixture A and \(\frac{y}{2}\) gallons of Mixture B.
So, we are told that \(2*2x+5*\frac{y}{2} \gt 10\), or that \(8x+5y \gt 20\). If \(x=0\) and \(y=5\), then the answer is NO (\(2x+5y > 9\)) but if \(x=3\) and \(y=0\), then the answer is YES (\(2x+5y\leq{9}\)). Not sufficient.
(1)+(2) From (1) we know that \(x=2y\). Substitute this in (2): \(8(2y)+5y \gt 20\), from which we can deduce that \(y \gt \frac{20}{21}\). However, this is still not sufficient to determine whether \(y\leq{1}\). Not sufficient.
Answer: E
The price of Mixture A is $2 per gallon and the price of Mixture B is $5 per gallon. Is $9 enough to buy \(x\) gallons of Mixture A and \(y\) gallons of Mixture B?
The question asks whether \(2x+5y\leq{9}\).
(1) The ratio of \(x\) to \(y\) is 2 to 1.
This implies that \(\frac{x}{y}=\frac{2}{1}\) or that \(x=2y\). Thus, the question becomes: is \(2(2y)+5y\leq{9}\) or is \(y\leq{1}\). Since we don't know that, this statement is not sufficient.
(2) $10 is NOT enough to buy \(2x\) gallons of Mixture A and \(\frac{y}{2}\) gallons of Mixture B.
So, we are told that \(2*2x+5*\frac{y}{2} \gt 10\), or that \(8x+5y \gt 20\). If \(x=0\) and \(y=5\), then the answer is NO (\(2x+5y > 9\)) but if \(x=3\) and \(y=0\), then the answer is YES (\(2x+5y\leq{9}\)). Not sufficient.
(1)+(2) From (1) we know that \(x=2y\). Substitute this in (2): \(8(2y)+5y \gt 20\), from which we can deduce that \(y \gt \frac{20}{21}\). However, this is still not sufficient to determine whether \(y\leq{1}\). Not sufficient.
Answer: E
General Discussion
shasadou
Joined: 12 Aug 2015
Last visit: 24 Nov 2022
Posts: 219
Given Kudos: 1,475
Concentration: General Management, Operations
Schools: Johnson '18 (WL) Duke '18 (M) Tuck '18 (D)
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE:Management Consulting (Consulting)
25 Dec 2015, 01:58
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a very GMAT like question
