Data sufficiency

[Rustic Myth]

if x= 3y , is x^2 > y^2 ??

1 ) y+x > y-x

2) x^2 = 9y^2

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

the source is Princeton Problem Solving.

[Guest]

Is the correct answer E?

[Anshul]

given x=3y
Is x^2 > y^2
or x^2-y^2 >0
or 9 y^2 - y^2 > 0
or 8 y ^2 >0
or y^2 > 0
since y^2 >=0 always

therefore, we need to find out if y = 0 or not.

a. y+x > y-x
=> 2x > 0
=> 6y > 0
=> y > 0

SUFFICIENT

b. INSUFFICIENT

[sumit]

q can be rephrased to ask if y=0

1) can be rephrased to give 2y>-y which means that ycannot be 0; hence sufficient

2) says 9y^2= 9y^2 which means y could be any value 0 or 1 or 2....; hence insufficient

[RonPurewal]

substitute 3y for x in the question prompt, since it's always true:
is (3y)^2 > y^2 ?
is 9y^2 > y^2?
subtract y^2 to give:
is 8y^2 > 0?
divide by 8 to give:
is y^2 > 0?

this will always happen unless y is actually 0, as all other squares are positive. therefore, the question can be rephrased as:
is y not equal to 0?
this is awkward - we don't like negative questions as much as we like affirmative questions - so we can just ask the opposite question:
is y = 0 ?

--

statement (1)
subtract y from both sides: x > -x
add x to both sides: 2x > 0
divide by 2: x > 0
but x = 3y, so this means that y is positive.
therefore, y is not 0.
sufficient.

--

statement (2)
this is already implied by the problem statement, so it adds nothing.
insufficient.

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ans = (a)