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M24-04

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M24-04  [#permalink]

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New post 16 Sep 2014, 01:20
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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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New post 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 (\(2x+5y>{9}\)) 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
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Re: M24-04  [#permalink]

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New post 25 Dec 2015, 01:58
a very GMAT like question
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Re: M24-04  [#permalink]

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New post 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?

please help me understand
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Re: M24-04  [#permalink]

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New post 11 Apr 2018, 02:54
+1 for option E
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Re: M24-04  [#permalink]

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New post 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)
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Re: M24-04  [#permalink]

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New post 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
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Re M24-04  [#permalink]

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New post 29 Apr 2018, 21:30
I think this is a high-quality question and I agree with explanation.
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Re: M24-04  [#permalink]

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New post 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  [#permalink]

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New post 17 Mar 2019, 23:39
I think this is a high-quality question and I agree with explanation.
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Re: M24-04  [#permalink]

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New post 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.


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
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Re: M24-04  [#permalink]

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New post 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.


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