Question: Is xy > 5?

2. x + y = 5

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: E
Solution and Explanation
Approach Solution (1):

2. x + y = 5

Probably the easiest way to tackle this problem is to pick numbers. Quite easy to get both an YES and a NO answers:
x = 1 and y = 4 --> xy = 4 < 5;
x = 3 and y = 2 ---> xy = 6 > 5

Approach Solution (2):

St (1): Given
Note x and y have any values (not an integer) in this range
So x = 1 and y = 4 the answer to the question NO
But if x = 2 and y = 3 then answer is YES
So A and D ruled out
St (2): x + y = 5 the above values can be used.
So not enough
B ruled out
Let x = 1.1, y = 3.9 then xy is less than 5
But if x = 2 and y = 3 then xy is greater than 5

Approach Solution 3:
For simplification lets work with integer values only
Statement 1 3 * 2 =6 [yes, xy > 5]
But, 2 * 2 = 4 [ No, xy is not greater than 5]
We have two answers to the questions from statement 1. Hence statement 1 is not sufficient.
Options A and D are eliminated.
Statement 2 says x + y = 5
When x = 1, y = 4 xy <5
When x = 2, y = 3 xy >5
Here, again we have two answers to our question. Hence, statement two alone is not sufficient.
Option B is eliminated.
Now, let's combine both the statements and check.
x = 1, y = 4 xy < 5
x = 3, y = 2 xy > 5
We do not have a definite answer. Both the statements together are also not sufficient.

“Is xy > 5?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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