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1 > x > y > 0
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08 Jan 2018, 14:16
08 Jan 2018, 14:16
1
Expert Reply
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Question Stats:
80% (00:34) correct
19% (00:30) wrong based on 106 sessions
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\(1 > x > y > 0\)
Quantity A |
Quantity B |
\(x^2\) |
\(y^2\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Kudo for the right answer and explanation.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: 1 > x > y > 0
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09 Jan 2018, 12:09
09 Jan 2018, 12:09
1
Carcass wrote:
\(1 > x > y > 0\)
Quantity A |
Quantity B |
\(x^2\) |
\(y^2\) |
If 0 < y < x, then y² < x²
Answer: A
Cheers,
Brent
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: 1 > x > y > 0
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09 Jan 2018, 12:14
09 Jan 2018, 12:14
Carcass wrote:
\(1 > x > y > 0\)
Quantity A |
Quantity B |
\(x^2\) |
\(y^2\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Kudo for the right answer and explanation.
Here's another approach:
Given:
Quantity A: x²
Quantity B: y²
Subtract y² from both quantities:
Quantity A: x² - y²
Quantity B: 0
Factor quantity B:
Quantity A: (x + y)(x - y)
Quantity B: 0
Since 0 < y < x, we know that x + y is POSITIVE, and we know that x - y is POSITIVE
So, we get:
Quantity A: (POSITIVE)(POSITIVE)
Quantity B: 0
Since the Quantity A must evaluate to be SOME POSITIVE value, Quantity A must be greater.
Answer: A
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