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# M24-04

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Math Expert
Joined: 02 Sep 2009
Posts: 49206

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16 Sep 2014, 01:20
1
8
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Difficulty:

95% (hard)

Question Stats:

39% (01:25) correct 61% (01:34) wrong based on 157 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

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16 Sep 2014, 01:20
2
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: 287 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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11 Apr 2018, 02:54
+1 for option E
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Director
Joined: 08 Jun 2015
Posts: 510
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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? please help me understand 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) _________________ " The few , the fearless " Intern Joined: 10 Jun 2017 Posts: 23 Re: M24-04 [#permalink] ### Show Tags 27 Apr 2018, 04:51 Hi guys, Statement 2 says: 4x + 5/2y >10 divide by 2 2x + 5/4y > 10 or 2x + 1,25y > 10 Now the question is: is 2x + 5y <= 9 ? since x and y >= 0, can't we confidently say that since 2x + 1,25y > 10 , then 2x + 5y cannot be <= 9? Thanks Intern Joined: 11 Apr 2016 Posts: 7 WE: Information Technology (Telecommunications) Re M24-04 [#permalink] ### Show Tags 29 Apr 2018, 21:30 I think this is a high-quality question and I agree with explanation. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8278 Location: Pune, India Re: M24-04 [#permalink] ### Show Tags 20 Aug 2018, 08:32 Bunuel 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 $$x$$ 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

Responding to a pm:
Quote:
Can we solve it using weighted averages?

Average Price of the mix has no role to play here since the question focusses on the total cost. Even if we do use average price, we will still need to do the analysis done by Bunuel above.
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Re: M24-04 &nbs [#permalink] 20 Aug 2018, 08:32
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# M24-04

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