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# M24-04

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Math Expert
Joined: 02 Sep 2009
Posts: 44600

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16 Sep 2014, 01:20
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10
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Difficulty:

95% (hard)

Question Stats:

40% (01:21) correct 60% (01:38) wrong based on 123 sessions

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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
[Reveal] Spoiler: OA

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16 Sep 2014, 01:20
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Official Solution:

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, then 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 ($$2x+5y&gt;{9}$$) 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 get that $$y \gt \frac{20}{21}$$. But this is still not sufficient to say whether $$y\leq{1}$$. Not sufficient. Answer: E _________________ Current Student Joined: 12 Aug 2015 Posts: 293 Concentration: General Management, Operations GMAT 1: 640 Q40 V37 GMAT 2: 650 Q43 V36 GMAT 3: 600 Q47 V27 GPA: 3.3 WE: Management Consulting (Consulting) Re: M24-04 [#permalink] ### Show Tags 25 Dec 2015, 01:58 a very GMAT like question _________________ KUDO me plenty Intern Status: in process Joined: 18 Jun 2017 Posts: 30 Location: Uzbekistan Concentration: Operations, Leadership Schools: Babson '21 GMAT 1: 690 Q47 V37 GPA: 4 WE: Education (Education) Re: M24-04 [#permalink] ### Show Tags 03 Jan 2018, 13:15 The price of Mixture A is$2 per gallon and the price of Mixture B is $5 per gallon. Is$9 enough to buy xx gallons of Mixture A and yy gallons of Mixture B?
(1) The ratio of xx to yy is 2 to 1

(2) $10 is NOT enough to buy 2x2x gallons of Mixture A and y2y2 gallons of Mixture B What is the reason this cannot be a C? if the ratio is 2 to 1 (st 1) and that you cannot buy that much for 10 (less than 10$ can be 9) why cannott it be 2*2 + 1*5 = 9?

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Joined: 08 Jun 2015
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GMAT 1: 640 Q48 V29

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11 Apr 2018, 02:54
+1 for option E
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Joined: 08 Jun 2015
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11 Apr 2018, 02:59
BobsterGMAT wrote:
The price of Mixture A is $2 per gallon and the price of Mixture B is$5 per gallon. Is $9 enough to buy xx gallons of Mixture A and yy gallons of Mixture B? (1) The ratio of xx to yy is 2 to 1 (2)$10 is NOT enough to buy 2x2x gallons of Mixture A and y2y2 gallons of Mixture B

What is the reason this cannot be a C?

if the ratio is 2 to 1 (st 1) and that you cannot buy that much for 10 (less than 10\$ can be 9) why cannott it be 2*2 + 1*5 = 9?

What st 2 means is that you can't buy that amount for an amount less than 10. In other words, it will cost you more than 10 and not less than 10 (or 9 as you have assumed)
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Re: M24-04   [#permalink] 11 Apr 2018, 02:59
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# M24-04

Moderators: chetan2u, Bunuel

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