Hello everyone.
Is y^2 equal to xy?
(1) x^2 - y^2 = (x + 3)(y - 3)
(2) x = y
[spoiler]For some reason I think the anwer is already in the statement, can somone check my logic. y^2=xy => y^2/y = x => y = x. Is this logic correct? [/spoiler]
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Is x^2 equal to xy?
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GMATGuruNY
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Statement 1:RobertP wrote:Hello everyone.
Is y^2 equal to xy?
(1) x^2 - y^2 = (x + 3)(y - 3)
(2) x = y
If we substitute y=3 into x² - y² = (x + 3)(y - 3), we get:
x² - 3² = (x + 3)(3 - 3)
x² - 9 = (x + 3)(0)
x² - 9 = 0
x² = 9
x = ±3.
It's possible that x=3 and y=3.
In this case, y² = xy, and the answer to the question stem is YES.
It's possible that x=-3 and y=3.
In this case, y² ≠xy, and the answer to the question stem is NO.
Since the answer is YES in the first case but NO in the second case, INSUFFICIENT.
Statement 2:
Since y=x, xy = y*y = y².
Thus, y² = xy.
SUFFICIENT.
The correct answer is B.
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Hi RobertP,
When dealing with DS questions, you have to be very careful about differentiating the QUESTION from the FACTS.
This question ASKS if Y^2 = (X)(Y). This is a YES/NO question. Since we don't know ANYTHING about those 2 variables, it's possible that the answer is YES or that it is NO.
For example, if Y=0, then the answer to the question is YES (and the value of X won't matter).
However, If Y=1 and X=2, then the answer to the question is NO.
As such, we need the data in the two Facts to properly sort out whether the answer to the question is Always YES, Always NO or sometimes YES/sometimes NO.
GMAT assassins aren't born, they're made,
Rich
When dealing with DS questions, you have to be very careful about differentiating the QUESTION from the FACTS.
This question ASKS if Y^2 = (X)(Y). This is a YES/NO question. Since we don't know ANYTHING about those 2 variables, it's possible that the answer is YES or that it is NO.
For example, if Y=0, then the answer to the question is YES (and the value of X won't matter).
However, If Y=1 and X=2, then the answer to the question is NO.
As such, we need the data in the two Facts to properly sort out whether the answer to the question is Always YES, Always NO or sometimes YES/sometimes NO.
GMAT assassins aren't born, they're made,
Rich
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Matt@VeritasPrep
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One crucial takeaway here:
Is x² = xy? is a question, not a statement. (It's kind of like asking, "Does Mike live in California?" He might ... but he might live in Fiji, for all we know.)
We can simplify the question as
Is x² - xy = 0 ?
or
Is x * (x - y) = 0 ?
or
Is x = 0 or x = y ?
But we still need some facts to answer it, and that's where the statements come in.
Is x² = xy? is a question, not a statement. (It's kind of like asking, "Does Mike live in California?" He might ... but he might live in Fiji, for all we know.)
We can simplify the question as
Is x² - xy = 0 ?
or
Is x * (x - y) = 0 ?
or
Is x = 0 or x = y ?
But we still need some facts to answer it, and that's where the statements come in.
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Brent@GMATPrepNow
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Doubtful.Matt@VeritasPrep wrote: It's kind of like asking, "Does Mike live in California?" He might ... but he might live in Fiji, for all we know.
I've been to Fiji, and I never met any Mikes!
Brent Hanneson - Creator of GMATPrepNow.com
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Matt@VeritasPrep
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Somewhere on the internet, Mike Gosling from Suva, Fiji, is heartbroken.Brent@GMATPrepNow wrote:Doubtful.Matt@VeritasPrep wrote: It's kind of like asking, "Does Mike live in California?" He might ... but he might live in Fiji, for all we know.
I've been to Fiji, and I never met any Mikes!
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Brent@GMATPrepNow
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I met Mike Gosling in Queensland (where he lives), but he never mentioned where he was born!
Brent Hanneson - Creator of GMATPrepNow.com
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ceilidh.erickson
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Be careful! You're falling for a classic GMAT trap here: you forgot about zero!RobertP wrote: For some reason I think the anwer is already in the statement, can somone check my logic. y^2=xy => y^2/y = x => y = x. Is this logic correct?
You divided both sides by y, but what if y itself is 0? Then it's impossible to divide.
The correct way to translate this statement is: does x = y, or does y = 0 ?
The GMAT test writers know that the human brain is naturally biased towards positives and integers, so they'll try to catch us on those assumptions. When you're translating DS questions, make sure you're thinking about what I call the ZONE-F numbers, too:
Zero
One
Negatives
Exponents
Fractions
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
