M24-04

Question

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

Bunuel · Accepted Answer

Official Solution:

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? 
 
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, 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 deduce that  y \gt \frac{20}{21} . However, this is still not sufficient to determine whether  y\leq{1} . Not sufficient.

Answer: E

shasadou · Answer

a very GMAT like question

BobsterGMAT · Answer

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

spetznaz · Answer

+1 for option E

spetznaz · Answer

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)

himalayanmonk · Answer

I think this is a  high-quality  question and I agree with explanation.

KarishmaB · Answer

Responding to a pm:

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.

Priti70s · Answer

I think this is a  high-quality  question and I agree with explanation.

axezcole · Answer

The question is -

2x+5y<=9

will be true when x=1,y=1 or x=2,y=1

So real question is

is x=2/1 & y=1 ??

S1 :

x:y=2:1

x & y can be 2,1 or 4,2 or 8,4.
So we are getting yes and no.

S2:

8x+5y>20

x & y can be 2,1 or 3,5 or any bigger value ...
So we are getting yes and no.

S1 + S2:
x=2y
8x+5y>20
so,
y>20/21
x>40/21

still no definite answer.

Hence option E

philippi · Answer

BEWARE: Might be helpful in order to understand the problem and a little trap that is incoorporated in Stmt. 2:

Question basically was: 2x+5y≤9

St. 2: 10 dollars isn´t enough for 2x and y/2. What happened to me was that I forgot to multiply the first part with 2 (dollars from the Q stem) and second part with 5 (from the Q stem). If forgetting to do so, the quation looks like this. 2x+y/5>10. So I reasoned that obviously, 2x+5y has to be greater than 9 too. This of course is flawed without considering to multiply with 2 and 5. Beware!

RenanBragion · Answer

I think this is a  high-quality  question and I agree with explanation.

Anurag111 · Answer

Hi Bunuel,

I am confused with the explanation. Can we do something like this. I am not understanding the mistake in the following approach.

Statement 1-> x/y::1/2
x=2y or y=x/2 Not Sufficient

Statement 2 -> 2x+y/2>10
=> 4x+y>20 Not Sufficient

Combining both of the statement
8y+y>20
=>9y>20
=>y>20/9

Again coming to the equation -->
4x+y>20
=>4x+x/2>20
=> 8x+x>40
=>9x>40
=> x>40/9

Now our question is 2x+5y<=9
=>2*(40/9)+5(20/9)
=>(80/9)+(100/9)
=>180/9
=>20

So 20>9 so answer option c is giving me answer that $9 is not sufficient for by 2x and 5y.

donaldmcdonald · Answer

Beware lads!

The question is not saying anything about whether x and y are  integers . So it would be wise to not to directly assume so.

datemike · Answer

Combining both statements we have the following:
1) x=2y
2) 16y+5y>20 => y>20/21
Thus subs x we get x>40/21
Now 2x>80/21 and 5y>100/21, add the two you get
2x+5y>180/21
180/21 is 8.5. This value could thus be anything more than 8.5(greater than 9 or not). Therefore both statements together are also insufficient. Note that nowhere is it specified that x and y must be integers- number of gallons can be in decimals.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

lotif · Answer

Can this be solved by adding inequalities?

For example, for the 2nd statement, we are given 8x+5y>20. In the Q we are wondering can we determine whether 2x+5y≤9.

If we add these inequalities, we get 11/17<y. Can this question be solved in this manner? It doesn't seem like it, but what is the reason for this?

Bunuel · Answer

You cannot add inequalities with the signs in the opposite directions. You can subtract 2x + 5y ≤ 9 from 8x + 5y > 20, which will give x > 11/6. So, IF 2x + 5y ≤ 9 were true, then together with 8x + 5y > 20, it would give that x > 11/6. Which is not of much use.

Check here  Manipulating Inequalities

pudu · Answer

i have a doubt. in statement 1y<=1. So at the maximum y=1 then x=2 so the cost is 5+4 =9. so we can purchase using 9. so why it is not A? please help me to understand ...

Bunuel · Answer

The ratio of  x  to  y  is 2 to 1 does NOT meant that the least value of y is 1. For instance it can be that x = 4 and y = 2, or x = 10 and y = 5, and so on.

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