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x < 0 and y > 0
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27 Feb 2019, 03:21
27 Feb 2019, 03:21
Expert Reply
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Question Stats:
45% (00:23) correct
54% (00:26) wrong based on 22 sessions
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\(x < 0\) and \(y > 0\)
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.
Quantity A |
Quantity B |
\(\sqrt{x^2y^2}\) |
\(xy\) |
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.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: x < 0 and y > 0
[#permalink]
01 Mar 2019, 11:58
01 Mar 2019, 11:58
Carcass wrote:
\(x < 0\) and \(y > 0\)
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.
Quantity A |
Quantity B |
\(\sqrt{x^2y^2}\) |
\(xy\) |
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.
KEY CONCEPT: The √ notation tell us to take the POSITIVE square root of a value.
For example √25 = 5 and √49 = 7
Also recognize that √0 = 0
In general, we can say: If k ≥ 0, then √k ≥ 0
We have:
QUANTITY A: √(x²y²)
QUANTITY B: xy
QUANTITY A
We know that x² ≥ 0 for ALL values of x
And y² ≥ 0 for ALL values of y
So, x²y² ≥ 0
When we apply the above rule, we can conclude that √(x²y²) ≥ 0
In other words, √(x²y²) = some number that's greater than or equal to zero.
QUANTITY B
We're told that x is NEGATIVE, and that y is POSITIVE
So, xy = (NEGATIVE)(POSITIVE) = some NEGATIVE number.
We get:
QUANTITY A: some number that's greater than or equal to zero.
QUANTITY B: some NEGATIVE number.
Answer: A
Cheers,
Brent
gmatclubot
Re: x < 0 and y > 0 [#permalink]
01 Mar 2019, 11:58
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