Data Sufficiency

Is xy > x^2y^2?
(1) 14x^2 = 3
(2) y^2 = 1

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.

I reckon the answer should be C. However in QA they have posted the answer as E. Please help

Is xy > x^2y^2?
(1) 14x^2 = 3
(2) y^2 = 1

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.

I reckon the answer should be C. However in QA they have posted the answer as E. Please help

The answer is E.

If you look at the stem, you can simplify this with the following steps:

y>xy^2
1 > xy

Statement 1 says that effectively x = +- √3/14.
Statement 2 says that y=+- 1

Since you cannot tell whether the signs are both positive or negative you cannot tell whether xy<1 or xy > 1

E is correct.

A couple things you should take away from a problem like this:

1) When a Data Sufficiency question involves inequalities and variables, there's at least a 50% chance you'll have to consider whether any of those variables could be negative.

2) When a Data Sufficiency question involves a variable-squared (or taken to any even exponent), there's a very high likelihood that you'll have to consider whether the variable could be negative.


This question hits both of those points - by test day, that "what about negative" bell should ring automatically in your head when you see variables and exponents or variables and inequalities in any Data Sufficiency question.

rintoo22 wrote:Is xy > x^2y^2?
(1) 14x^2 = 3
(2) y^2 = 1

xy > x²y² only if xy>0.
Thus, we can safely divide each side of the question stem by xy:
xy/xy > x²y²/xy
1 > xy.

Question rephrased: Is 0<xy< 1?

Statement 1, simplified:: x = ±√(3/14).
Statement 2, simplified: y = ±1.

Clearly, neither statement is sufficient on its own.
Statements combined:
It's possible that xy= √(3/14) * 1 = √(3/14).
In this case, 0<xy<1.
It's possible that xy = -√(3/14) * 1 = -√(3/14)
In this case, xy<0.
INSUFFICIENT.

The correct answer is E.