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xy = 2 and x > 0 and y > 0
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08 Mar 2020, 10:42
08 Mar 2020, 10:42
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65% (00:50) correct
34% (00:47) wrong based on 241 sessions
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\(xy = 2 \)
\(x > 0 \)
\(y > 0 \)
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
\(x > 0 \)
\(y > 0 \)
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
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
xy = 2 and x > 0 and y > 0
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09 Mar 2020, 07:04
09 Mar 2020, 07:04
1
Carcass wrote:
\(xy = 2 \)
\(x > 0 \)
\(y > 0 \)
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
\(x > 0 \)
\(y > 0 \)
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
RELATED VIDEO
Re: xy = 2 and x > 0 and y > 0
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10 Mar 2020, 09:32
10 Mar 2020, 09:32
4
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.
Since x+y can be greater than or less than 5 depending on the values of x and y, the correct option is D.
