Is |x^2+y^2| > |x^2-y^2|?
(1) x > y
(2) x > 0
Absolute value inequality
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Hi ollapodrida,
This DS question is perfect for TESTing Values.
We're asked if |x^2 + y^2| > |x^2 - y^2|? This is a YES/NO question. We are told nothing about x and y.
Fact 1: x > y
Let's TEST Values and track the results:
x = 1
y = 0
Is |1| > |1|? The answer to the question is NO.
x = 2
y = 1
Is |5| > |3|? The answer to the question is YES.
Fact 1 is INSUFFICIENT
Fact 2: x > 0
The same two examples from Fact 1 can be applied here.
We have a NO and a YES answer.
Fact 2 is INSUFFICIENT
Combined, we have the same TEST Cases for both Facts.
We have a NO and a YES answer.
Combined, INSUFFICIENT.
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
This DS question is perfect for TESTing Values.
We're asked if |x^2 + y^2| > |x^2 - y^2|? This is a YES/NO question. We are told nothing about x and y.
Fact 1: x > y
Let's TEST Values and track the results:
x = 1
y = 0
Is |1| > |1|? The answer to the question is NO.
x = 2
y = 1
Is |5| > |3|? The answer to the question is YES.
Fact 1 is INSUFFICIENT
Fact 2: x > 0
The same two examples from Fact 1 can be applied here.
We have a NO and a YES answer.
Fact 2 is INSUFFICIENT
Combined, we have the same TEST Cases for both Facts.
We have a NO and a YES answer.
Combined, INSUFFICIENT.
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
- ceilidh.erickson
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Both x^2 and y^2 must be either positive or 0. The absolute value of |pos + pos| will always be greater than |pos - pos|. The only time |x^2 + y^2| will not be greater than |x^2 - y^2| is if either x or y is 0, in which case the quantities will be equal.
Target question: is either x or y equal to 0?
Statement 1: x > y
This tells us nothing about whether either quantity is 0. Insufficient.
Statement 2: x > 0
This tells us that x is not equal to 0, but it doesn't tell us whether y is. Insufficient.
Together: The statements tell us nothing about whether either quantity equals 0. Insufficient.
The answer is E.
Target question: is either x or y equal to 0?
Statement 1: x > y
This tells us nothing about whether either quantity is 0. Insufficient.
Statement 2: x > 0
This tells us that x is not equal to 0, but it doesn't tell us whether y is. Insufficient.
Together: The statements tell us nothing about whether either quantity equals 0. Insufficient.
The answer is E.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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Alternate approach:ollapodrida wrote:Is |x^2+y^2| > |x^2-y^2|?
(1) x > y
(2) x > 0
Let a=x² and b=y².
Substituting a=x² and b=y² into the question stem, we get:
|a+b| > |a-b|?
Since each side has absolute value -- implying that each side is NONNEGATIVE -- we can square both sides:
a² + 2ab + b² > a² - 2ab + b²
4ab > 0
ab > 0.
Substituting a=x² and b=y² into the resulting expression, we can rephrase the question stem as follows:
Is x²y² > 0?
When the statements are combined:
It's possible that x=1 and y=0, in which case x²y² = 0.
It's possible that x=2 and y=1, in which case x²y² > 0.
INSUFFICIENT.
The correct answer is E.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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