Is x + y 0?

Question

Is x + y > 0 ? (1) xy > 0 (2) x^3y^2>0 Answer Choices A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked. C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked. D. EACH statement ALONE is sufficient to answer the question asked. E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed. Thanks, Saquib Quant Expert e-GMAT Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

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EgmatQuantExpert · Answer

The official solution has been posted. Looking forward to a healthy discussion..

quantumliner · Answer

Is x+y>0

(1) xy>0
This statement tells us that a&y are either both negative or both positive. If both are negative then x+y <0. If both are positive then x+y>0. This statement is not sufficient.

(2) x^3 * y^2>0

In this case we see and odd power of x, so for x^3 * y^2>0 to hold good, x must be positive and y can be positive or negative, as y has an even power.

Now that we know x is positive, Lets say if x is 2 and y is -3, than x+y <0. If x is 2 and y is 1, then x+y>0. This statement is not sufficient.

Combining both statements, we know from statement two that x is positive and from statement 1 we know that for xy>0 to hold good, both x&y either should be positive or negative. As x is positive, y is also positive. therefore x+y>0.

Answer is C

amanvermagmat · Answer

Statement 1. Product of x & y > 0 
This means either both x and y are positive (in which case x+y will be positive)
 Or both x and y are negative (in which case x+y will be negative)
So  Insufficient .

Statement 2. y^2 cannot be negative. So this means x^3 is also > 0 OR x >0
But on this basis, we cannot say whether x+y will be >0 or <0. 
So  Insufficient .

Combining the two statements:
From second statement, x >0
Combining with first statement, y is also >0

Thus the sum x+y > 0.  Sufficient 
Hence  C   is the answer

EgmatQuantExpert · Answer

Official Solution

Steps 1 & 2: Understand Question and Draw Inferences

To Find: Is, x+ y > 0?

Step 3: Analyze Statement 1 independently

(1) xy > 0
• Tells us that x and y have the same sign.

Insufficient to answer.

Step 4: Analyze Statement 2 independently

Insufficient to answer.

Step 5: Analyze Both Statements Together (if needed)

Sufficient to answer

Answer: C

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

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bumpbot · Answer

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Is x + y > 0?

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