GMAT Data Sufficiency- If xy = - 6, What is the Value of xy(x + y)?

Question: If xy = - 6, what is the value of xy(x + y)?

1. x−y = 5
2.  xy2 =18

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.

“If xy = - 6, what is the value of xy(x + y)?”- 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 sufficiencycomprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:

There is only one approach to solve the problem

It is known from the problem statement that xy=-6
The value of xy(x+y) is unknown.

Considering statement 1) x-y=5; ;
we know that xy=-6, ;
we can substitute x=-(6/y) in the given equation, which becomes
-(6/y)-y=5; ;
y^2+5y+6=0; ;
(y+3)(y+2)=0; ;
hence y=-3 or y=-2,
when y=-3, x=2, we get x+y=-1 and xy(x+y)=-(6)(-1)=6
when x=-2, y=3, we get x+y=1 and xy(x+y)= (-6)(1)= -6 hence 1 is not sufficient

Let us consider statement 2) ;
xy^2=18; can be written as xy(y)=18,
-6y=18;
y=-3; ;
Also we know from the question statement that xy=-6; thus x=2 ;
Hence x+y=2-3=-1, hence xy(x+y) = -6(-1)= 6.

This is sufficient. 

Correct Answer: B

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