Data Sufficiency

As advertised on the main page of Beat the GMAT, Ashley, David, and I will be posting some original questions today and tomorrow with prizes for the first five students to respond with correct answers that show your work!

Here's a Data Sufficiency question to kick things off. I love multiple variables and exponents...



What is the value of x - y?


1) (x + y)^2 = 4xy


2) x^2 - y^2 = 0




(For more information on the contest, please visit https://www.beatthegmat.com/mba/2011/07/ ... g-tomorrow, and note that the "tomorrow" in the URL was posted yesterday, making the date in question "today"!)

Hi,
From(1):
x^2+y^2+2xy = 4xy
So, x^2+y^2-2xy = 0
So, (x-y)^2 =0 =>x-y = 0
Sufficient

From(2):
(x+y)(x-y) = 0
So, either x+y = 0 or x-y =0 or both are equal to zero
Not sufficient to find the value of (x-y)

Hence, A

Ans A)

a)
(x+y)^2 = 4xy
=>(x--y)^2 = 0
=> x-y = 0
Sufficient

b) x^2-y^2 = 0
=> (x-y)(x+y)=0
NOT SUFFICIENT

(x+y)^2 -4xy = (x-y)^2
=> from statement 1

(x+y)^2 = 4xy
we get (x-y)^2 =0
so x-y = 0

=> Statement 2
x^2- y^2 =
(x+y)(x-y) = 0
so either x+y = 0 or x-y =0
so this is insufficient

SO A should be correct

A is the answer

Statement 1 --> (x-y)^2=0
(x-y)=0 Sufficient

What is the value of x - y?

1) (x + y)^2 = 4xy

2) x^2 - y^2 = 0

Answer: (A)

Statement 1:

(x+y)^2 = 4xy

--> x^2 + 2xy + y^2 = 4xy
--> x^2 + y^2 = 2xy
--> x^2 - 2xy +y^2 = 0
--> (x-y)^2 = 0
--> (x-y) = 0
Stmnt 1: Sufficient

Statement 2:

x^2 - y^2 = 0
--> (x+y)*(x-y) = 0
--> Either term could be equal to zero.
Stmnt 2: Insufficient

Answer is A
What is the value of x - y?

1) (x + y)^2 = 4xy

2) x^2 - y^2 = 0
x2 + y2 + 2xy=4xy
x2 + y2 -2xy=0
(x-y)2=0
x-y=0
2)Insufficient
x2-y2=0
x-y)(x+y)=0
x+y could be 0 .In this case x-y=-2y=2x or x-y could be 0 thus Insufficient
So A Alone is sufficient

What is the value of x - y?


1) (x + y)^2 = 4xy


2) x^2 - y^2 = 0

Statement 1) gives x^2+y^2+2xy-4xy=0
or, (x-y)^2=0
Hence, x-y can only be zero and hence sufficient

Statement 2) gives (x-y)*(x+y)=0
implying either x-y=0 or x+y=0
So,x-y cant be determined
Insufficient
Answer A

A is the correct answer

I know its very easy but explanation is same as mentioned above.

A for me as well

What is the value of x - y?


1) (x + y)^2 = 4xy


2) x^2 - y^2 = 0


we are asked to find the difference between x and y. To find the diff., we do not necessarily need to know the individual values of x and y.

Statement 1: (x + y)^2 = 4xy, by expanding the equation, we get

x^2 + y^2 + 2xy = 4xy, taking 4xy to left hand side,

x^2 + y^2 - 2xy = 0

(x - y)^2 = 0

x - y = 0

Statement 1 is sufficient. eliminate B, C and E. The correct answer answer choice is A or D.

Statement 2 x^2 - y^2 = 0 can be rewritten as (x + y)(x - y) = 0, however we can't simplify the equation further to get the unique value of x - y as either x + y can be zero or x - y can be zero. Therefore, Statement 2 alone is NOT sufficient.

Answer Choice A is correct.

From Statement (1) we have:
(x+y)^2 = 4xy
So, x^2+y^2+2xy = 4xy
So, x^2+y^2-2xy = 0
So, (x-y)^2 =0 =>x-y = 0
So, Statement 1 is Sufficient

From Statement (2) we have:
(x^2 - y^2)=0
So,(x+y)(x-y) = 0
So, Either x+y = 0 or x-y =0 or both are equal to zero
So, Not sufficient to find the value of (x-y)

Hence, the answer is A

a x^2-2xy+y^2 = 0
means (x-y)^2 = 0 or x-y = 0 meaning x=y.

b either x+y or x-y = 0. not sufficient.

hence A it is.

Great work, everyone - the correct answer is, indeed, A.

Statement 1, when you break out the parentheses, looks like:

x^2 + 2xy + y^2 = 4xy

And can be reset into the ax^2 + bx + c quadratic form by subtracting 4xy from both sides to get:

x^2 - 2xy + y^2 = 0

You should recognize this as a fairly common algebraic equation - it's the same as:

(x - y)^2 = 0

Which means that x - y = 0 --> the statement is sufficient as it gives us a definite answer to the question.


Statement 2 gets us a step closer if we apply the Difference of Squares factor:

(x + y)(x - y) = 0

We know that either x + y = 0 or x - y = 0, but we don't know which one, so statement 2 is not sufficient, and the correct answer is A.


I like this question because statement 1 rewards you for recognizing the common algebraic transformations between the factored (x+y)^2 and expanded (x^2 + 2xy + y^2) displays of the same equation. Data Sufficiency questions that employ algebra often reward you for changing the view of the same statement - I call this "an inconvenient truth", in which the test gives you a statement in an inconvenient form, and you need to transform it to look more like what the question is asking.

This question also has some further discussion that can make it more valuable. Can anyone think of a restriction that we could put on x and/or y that would make statement 2 sufficient?

How about x+y != 0?