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# M24-04

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Math Expert
Joined: 02 Sep 2009
Posts: 55273

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16 Sep 2014, 01:20
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95% (hard)

Question Stats:

35% (02:25) correct 65% (02:22) wrong based on 118 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
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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 _________________ Senior Manager Joined: 12 Aug 2015 Posts: 284 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
GMAT 2: 700 Q48 V38
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11 Apr 2018, 02:54
+1 for option E
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Senior Manager
Joined: 08 Jun 2015
Posts: 424
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38
GPA: 3.33

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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: 9237 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. _________________ Karishma Veritas Prep GMAT Instructor Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Intern Joined: 29 Oct 2017 Posts: 5 Re M24-04 [#permalink] ### Show Tags 17 Mar 2019, 23:39 I think this is a high-quality question and I agree with explanation. Manager Joined: 18 Jul 2018 Posts: 51 Location: United Arab Emirates Re: M24-04 [#permalink] ### Show Tags 01 Apr 2019, 10:45 Bunuel wrote: 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 ($$2x+5y>{9}$$) 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.

Hi Bunuel

COMBINED y > 20/21. This implies y can have any integer value > 20/21.
If y = 1 then x = 2
and 2x + 5y ≤ 9 , Answer is YES 4 + 5 ≤ 9

But if y = 2, then x = 4 , Answer is NO.

Since, we don't know the value of y. This is Not Sufficient.

What i don't understand is the last line part below:-
But this is still not sufficient to say whether y≤1 .

THANKS
Manager
Joined: 18 Jul 2018
Posts: 51
Location: United Arab Emirates

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02 Apr 2019, 06:37
JIAA wrote:
Bunuel wrote:
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 ($$2x+5y>{9}$$) 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.

HI Bunuel

COMBINED y > 20/21. This implies y can have any integer value > 20/21.
If y = 1 then x = 2
and 2x + 5y ≤ 9 , Answer is YES 4 + 5 ≤ 9

But if y = 2, then x = 4 , Answer is NO.

Since, we don't know the value of y. This is Not Sufficient.

What i don't understand is the last line part below:-
But this is still not sufficient to say whether y≤1 .

THANKS
Re: M24-04   [#permalink] 02 Apr 2019, 06:37
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# M24-04

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