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Math Expert V
Joined: 02 Sep 2009
Posts: 55273
M24-04  [#permalink]

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Difficulty:   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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Math Expert V
Joined: 02 Sep 2009
Posts: 55273
Re M24-04  [#permalink]

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2
1
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 a very GMAT like question _________________ KUDO me plenty Intern  S 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 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
Senior Manager  S
Joined: 08 Jun 2015
Posts: 424
Location: India
GMAT 1: 640 Q48 V29 GMAT 2: 700 Q48 V38 GPA: 3.33
Re: M24-04  [#permalink]

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+1 for option E
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" The few , the fearless "
Senior Manager  S
Joined: 08 Jun 2015
Posts: 424
Location: India
GMAT 1: 640 Q48 V29 GMAT 2: 700 Q48 V38 GPA: 3.33
Re: M24-04  [#permalink]

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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  B Joined: 10 Jun 2017 Posts: 23 Re: M24-04 [#permalink] ### Show Tags 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  B Joined: 11 Apr 2016 Posts: 7 WE: Information Technology (Telecommunications) Re M24-04 [#permalink] ### Show Tags I think this is a high-quality question and I agree with explanation. Veritas Prep GMAT Instructor D Joined: 16 Oct 2010 Posts: 9237 Location: Pune, India Re: M24-04 [#permalink] ### Show Tags 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  B Joined: 29 Oct 2017 Posts: 5 Re M24-04 [#permalink] ### Show Tags I think this is a high-quality question and I agree with explanation. Manager  B Joined: 18 Jul 2018 Posts: 51 Location: United Arab Emirates Re: M24-04 [#permalink] ### Show Tags 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.

Answer: E

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 .

would appreciate your help!
THANKS
Manager  B
Joined: 18 Jul 2018
Posts: 51
Location: United Arab Emirates
Re: M24-04  [#permalink]

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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.

Answer: E

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 .

would appreciate your help!
THANKS Re: M24-04   [#permalink] 02 Apr 2019, 06:37
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