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0 < x < y
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02 Apr 2019, 09:31
02 Apr 2019, 09:31
Expert Reply
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Question Stats:
51% (01:00) correct
48% (00:46) wrong based on 31 sessions
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\(0 < x < y\)
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.
Quantity A |
Quantity B |
\(x+\frac{1}{x}\) |
\(y + \frac{1}{y}\) |
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.
Re: 0 < x < y
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03 Apr 2019, 02:37
03 Apr 2019, 02:37
Expert Reply
This is a good one for picking numbers. Particularly, the range of possible values is so large, especially for y, that I'm sure we can get a D answer.
So first, the low hanging fruit. If y = 999, and x = \(\frac{1}{2}\), then quantity A is somewhere around 2, and quantity B is somewhere close to 1000. So clearly quantity B can be greater.
But now let's go to the opposite extreme. Let's say x = 0.001 and y = \(\frac{1}{2}\). In this case, quantity A is somewhere around 1000, while quantity B is stuck around 2. Quantity A, then, can also be greater.
The range of possible values here is far too great, so choice D is our answer.
So first, the low hanging fruit. If y = 999, and x = \(\frac{1}{2}\), then quantity A is somewhere around 2, and quantity B is somewhere close to 1000. So clearly quantity B can be greater.
But now let's go to the opposite extreme. Let's say x = 0.001 and y = \(\frac{1}{2}\). In this case, quantity A is somewhere around 1000, while quantity B is stuck around 2. Quantity A, then, can also be greater.
The range of possible values here is far too great, so choice D is our answer.
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0 < x < y
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03 Apr 2019, 07:24
03 Apr 2019, 07:24
1
Carcass wrote:
\(0 < x < y\)
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.
Quantity A |
Quantity B |
\(x+\frac{1}{x}\) |
\(y + \frac{1}{y}\) |
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.
Notice that x and 1/x are reciprocals of each other.
Likewise, y and 1/y are reciprocals of each other.
This helps is choose some numbers to test.
Case i: x = 1/2 and y = 2 (notice that I chose two values that are reciprocals of each other)
We get:
QUANTITY A: x + 1/x = 1/2 + 1/(1/2) = 1/2 + 2 = 2.5
QUANTITY B: y + 1/y = 2 + 1/2 = 2.5
In this cases, the two quantities are equal
For the next case, choose ANY two values that satisfy the given condition 0 < x < y
Case ii: x = 1 and y = 2
We get:
QUANTITY A: x + 1/x = 1/1 + 1/1 = 1 + 1 = 2
QUANTITY B: y + 1/y = 2 + 1/2 = 2.5
In this cases, Quantity B is greater
Answer: D
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