Is x greater than y? GMAT Data Sufficiency

Question: Is x greater than y?
(1) x - y^2 >0
(2) xy < 0

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.        
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.        
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.        
4. EACH statement ALONE is sufficient.        
5. Statements (1) and (2) TOGETHER are not sufficient.

Correct Answer: C

Solution and Explanation:
Approach Solution 1:
The problem statement asks to find out if x > y.
Statement 1: x-\(y^2\)> 0
Or, x>\(y^2\)
The statement is valid under certain conditions such as:
(A) if x=½, y=½. The stem of the question is negative.
(B) if x=3 and y=1. The answer to this question is yes.
There are numerous instances (x will always be positive because x>\(y^2\)), but to demonstrate the insufficiency, we require 1Y & 1N.
Statement 1 is Insufficient.
Statement 2 : xy < 0
x>0 and y<0 are implied, or x<0 and y>0.
Insufficient,

By combining both statements (1)+(2), we get,
The only scenario is that x>0 and y<0.
Thus, x>y.
Therefore, both statements together are Sufficient.

Approach Solution 2:
Does x exceed y?
In statement 1 it is given: x - y^2 >0
or, we can say, x > y^2
x = 2, y = 1 --- YES
x = 1/2, y = 1/2 --- NO
Therefore statement 1 is Insufficient

In statement 2 it is given: xy < 0
Obviously insufficient given that x and y might be positive or negative, respectively.

Therefore, by combining both statements, we get:
x = 2, y = -1 -----YES
x = 1/2, y = -1/2 ------YES
For each pair in x is positive and y is negative, x > y.
Therefore both statements together are Sufficient.

“Is x greater than y?”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This question has been taken from the book “GMAT Official Guide 2019”. The GMAT Quant section consists of an aggregate of 31 questions. GMAT Data Sufficiency questions emerge with a problem statement followed by two factual statements. GMAT data sufficiency incorporates 15 questions which are two-fifths of the total 31 GMAT quant questions.

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