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B
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Difficulty:
35%
(medium)
Question Stats:
72% (01:39) correct
28%
(01:46)
wrong
based on 2716
sessions
History
Date
Time
Result
Not Attempted Yet
16 Dec 2009, 06:39
Kudos
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Is x^2 equal to xy?
Question: is \(x^2=xy\)? --> \(x(x-y)=0\) --> Equation holds true if \(x=0\) or/and \(x=y\).
So, basically question asks: Is \(x=0\) or/and \(x=y\) true?
Obviously statement (2) is sufficient, as it gives directly that \(x=y\).
(1) x^2 – y^2 = (x + 5)(y - 5) --> \((x+y)(x-y)=(x + 5)(y-5)\)
If \(y=5\) --> \((x+5)(x-5)=(x+5)(5-5)\) --> \((x+5)(x-5)=0\) --> Either \(x=5=y\) and in this case answer to the question is YES OR \(x=-5\), hence \(x\) is not equal to \(y\) (nor to zero) and in this case answer to the question is NO. So two different answers.
Not sufficient.
Answer: B.
Question: is \(x^2=xy\)? --> \(x(x-y)=0\) --> Equation holds true if \(x=0\) or/and \(x=y\).
So, basically question asks: Is \(x=0\) or/and \(x=y\) true?
Obviously statement (2) is sufficient, as it gives directly that \(x=y\).
(1) x^2 – y^2 = (x + 5)(y - 5) --> \((x+y)(x-y)=(x + 5)(y-5)\)
If \(y=5\) --> \((x+5)(x-5)=(x+5)(5-5)\) --> \((x+5)(x-5)=0\) --> Either \(x=5=y\) and in this case answer to the question is YES OR \(x=-5\), hence \(x\) is not equal to \(y\) (nor to zero) and in this case answer to the question is NO. So two different answers.
Not sufficient.
Answer: B.
17 Dec 2019, 20:53
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dobinnoli
Statement One Only:
x^2 – y^2 = (x + 5)(y - 5)
If y = 5, we have:
x^2 - 25 = (x + 5)(0)
x^2 - 25 = 0
(x + 5)(x - 5) = 0
x = 5 or x = -5
If x = 5, then x^2 and xy will be equal since both are 25. However, if x = -5, then x^2 and xy will not be equal since the former is 25 and the latter is -25. Statement one alone is not sufficient.
Statement Two Only:
x = y
Since x = y, if we multiply both sides by x, we have:
x * x = y * x
x^2 = xy
Statement two alone is sufficient.
Answer: B
