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xy = 2 and x > 0 and y > 0

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xy = 2 and x > 0 and y > 0 [#permalink] New post 08 Mar 2020, 10:42
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Question Stats:

64% (00:31) correct 35% (00:36) wrong based on 62 sessions
\(xy = 2 \)
\(x > 0 \)
\(y > 0 \)


Quantity A
Quantity B
\(x+y\)
\(5\)



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Kudos for the right answer and explanation
[Reveal] Spoiler: OA

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Re: xy = 2 and x > 0 and y > 0 [#permalink] New post 09 Mar 2020, 07:04
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Carcass wrote:
\(xy = 2 \)
\(x > 0 \)
\(y > 0 \)


Quantity A
Quantity B
\(x+y\)
\(5\)



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Kudos for the right answer and explanation


Key concept: If we ASSUME that x and y are integers, we'll incorrectly conclude that quantity B is greater
However, if we realize that x and y can be non-integers, we can quickly see that the correct answer must be D

To show why, let's test some values

case i: Since \(xy = 2 \), one possible pair of values is \(x=1\) and \(y=2\)
We get:
Quantity A: \(x+y=1+2=3\)
Quantity B: \(5\)
In this case, Quantity B is greater

case ii: Since \(xy = 2 \), another possible pair of values is \(x=8\) and \(y=0.25\)
We get:
Quantity A: \(x+y=8+0.25=8.25\)
Quantity B: \(5\)
In this case, Quantity A is greater

Answer: D

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Re: xy = 2 and x > 0 and y > 0 [#permalink] New post 10 Mar 2020, 09:32
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Using AM-GM inequality, we find that (x+y)/2 >= sqrt(xy), which implies x+y >= 2*sqrt(2) = 2.82...., which is less than 5. Also, notice that y=2/x. Hence, we can increase x indefinitely and since y is always positive as long as x is positive, x+y can go up to infinity.
Since x+y can be greater than or less than 5 depending on the values of x and y, the correct option is D.
Re: xy = 2 and x > 0 and y > 0   [#permalink] 10 Mar 2020, 09:32
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