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,
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.