If XY Does Not Equal Zero, What is the Value of XY? GMAT Data Sufficiency

Question: If XY does not equal zero, what is the value of XY?

(1) 2/x + 2/y = 3
(2) x^3 – (2/y)^3 = 0

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.

“If XY does not equal zero, what is the value of XY?” - is a topic that belongs to the GMAT Quantitative reasoning section of GMAT. The question is borrowed from the book “GMAT Quantitative Review”. The GMAT Quant section mainly comprises a set of 31 questions that need to be answered logically. GMAT Data Sufficiency questions include a problem statement that is heeded by two factual arguments. GMAT data sufficiency consists of 15 questions which are two-fifths of the entire sum of 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:

In this question, x and y are two numbers. Also, it is given that x*y is not equal to zero. The product of two numbers is not zero implying that any of the two numbers cannot be zero. Mathematically can be written as,

Xy\(\neq\) 0
x \(\neq\)0 , y \(\neq\) 0
Now let us check the given statements,
the First statement is,
2/x + 2/y = 3
=> (2y + 2x)/XY = 3
=> (2y + 2x) = 3xy
=> but we know that xy \(\neq\)0
X cannot be zero and y cannot be zero.
But this equation alone is not sufficient to find the value of the variables.
In statement 2 it is given that,
x^3 - (2/y)^3 = 0
=> x^3*y^3 - 2^3 = 0
=> (xy)^3 - 8 = 0
=> (xy)^3 = 8
=> xy = 2
We got the value of xy to be 2
Hence, it proves that the product of x and y is not zero.
Thus this statement is sufficient to get the answer.

Correct Answer: B

Approach Solution 2:

In this question, x and y are two numbers. Also, it is given that x*y is not equal to zero. The product of two numbers is not zero implying that any of the two numbers cannot be zero. Mathematically can be written as,
Xy\(\neq\) 0
x \(\neq\)0 , y\(\neq\) 0
Now let us check the given statements,
the First statement is,
2/x + 2/y = 3
=> (2y + 2x)/XY = 3
=> (2y + 2x) = 3xy
=> 3xy - 2y = 2x
=> y(3x-2) = 2x
=> y = 2x/(3x-2)
We got y in terms of x.
It doesn’t mention whether the product of x and y is 0.
Hence it is not sufficient to get the answer.
In statement 2 it is given that,
x^3 - (2/y)^3 = 0
=> x^3 = (2/y)^3
=> x^3 = (2^3) / (y^3)
=> (xy)^3 = 8
=> xy = \(\pm\)2
We got the value of xy to be 2 and -2.
Hence, it proves that the product of x and y is not zero.
Thus this statement is sufficient to get the answer.

Correct Answer: B

Suggested GMAT Data Sufficiency Questions:

• If x is an integer is an x/12 integer? GMAT Data Sufficiency
• Is 7^7 / 7^x an integer? GMAT Data Sufficiency
• The length of the median BD in a triangle ABC is 12 centimeters, what is the length of the side AC? GMAT Data Sufficiency
• Is the area of the triangle ABC greater than the area of the triangle DEF? GMAT Data Sufficiency
• There is atleast one viper and atleast one cobra in Pandora’s Box GMAT data sufficiency
• If L not equals to 0, is 18K/L an Integer? GMAT Data Sufficiency
• If a, b, and c are positive and a^2 + c^2 = 202, what is the value of b – a – c? GMAT Data Sufficiency
• If x and y are positive integers, is x odd? GMAT Data Sufficiency
• If 0 < x < 53, what is the value of integer x? GMAT Data Sufficiency
• What is the value of 6x^2 + 9y^2 =? GMAT Data Sufficiency
• If x and y are integers and, is x=(y/5 +2) even? GMAT Data Sufficiency
• If m is a positive integer, is √m>25? GMAT Data Sufficiency
• If there are 78 people working at an office, how many of them are women older than 40? GMAT Data Sufficiency
• If ab = ac is b = 2? GMAT Data Sufficiency
• If x is a positive integer, what is the value of x? GMAT Data Sufficiency
• If 53 students are enrolled in both the CS103 (Algorithms and Data Structures) And M101 (Mathematics for Computer Science) classes, how many of the CS103 students are no enrolled in M101? GMAT Data Sufficiency
• Buster leaves the trailer at noon and walks towards the studio at a constant rate of B miles per hour. 20 minutes later, Charlie leaves the same studio and walks towards the same trailer at a constant rate of C miles per hour along the same route as Buster. Will Buster be closer to the trailer than to the studio when he passes Charlie? GMAT Data Sufficiency
• If sq rt{3+sq rt(x-1)} = 4, what is the value of x? GMAT Data Sufficiency
• What is the sum of a, b, and c? GMAT Data Sufficiency
• What is the probability of getting a jack from a 52-card deck on both the first and second draw if the cards are not replaced? GMAT Data Sufficiency