Data Sufficiency

Hello again! I'm back with another Data Sufficiency question as part of the contest (see main page) in which David, Ashley and I are posting original questions with prizes for the first few correct answers - and remember to show your work! Here goes, and I apologize for the linear fraction format in statement one...


What is the value of x + y?


1) [4x^2 - 4y^2]/[2(x+y)] = 2x - 2y



2) 3x + 2y = 24

What is the value of x + y?


1) [4x^2 - 4y^2]/[2(x+y)] = 2x - 2y



2) 3x + 2y = 24

Considering Statement 1
4 (x^2 - y^2 )/ 2 (x+y) = 2 (x-y)
cross multiplying denominator of Left hand side to Right Hand Side
(x^2 - y^2 ) = (x-y)(x-y)
x2-y2=x2-y2

so this gives us little info about the value of x + y

Statement 2 also doesnt let us know anything about the value of x + y on its own
Even if we combine (1) and (2)
we are not able to know the value .
So Answer is E

Hi,
From(1):
4(x+y)(x-y)/2(x+y) = 2(x-y). This is true for all x, y provided x+y is not equal to zero.
There can be many values for (x+y).
Not sufficient to find unique value of (x+y)

From(2):
3x+2y = 24
x=8, y=0
x=0, y=12
Infinitely many values of x and y satisfy this equation.
We cannot find unique (x+y) from this equation
Not sufficient

Both(1) and (2):
x+y not equal to zero and 3x+2y = 24
Not sufficient

Hence, E

For this
Statement 1 is insufficient
[4x^2 - 4y^2]/[2(x+y)] = 2x - 2y (as a^2 - b^2 = (a+b)(a-b))
therefore, 2x - 2y = 2x -2y, which is true but there is no value for x and y. Hence x+y cannot be determined.

Statement 2 is also insufficient
as it gives the value of 3x+2y=24, but individually we wont be able to calculate x or y

Combining the two statements also yields no solution as statement 1 is an incarnation of a formula and statement 2 not to the point.

Hence the Answer is E

Frankenstein wrote:Hi,
From(1):
4(x+y)(x-y)/2(x+y) = 2(x-y). This is true for all x, y provided x+y is not equal to zero.
There can be many values for (x+y).
Not sufficient to find unique value of (x+y)

From(2):
3x+2y = 24
x=8, y=0
x=0, y=12
Infinitely many values of x and y satisfy this equation.
We cannot find unique (x+y) from this equation
Not sufficient

Both(1) and (2):
x+y not equal to zero and 3x+2y = 24
Not sufficient

Hence, E

I know i got it right when my answer matched yours

mundasingh123 wrote:I know i got it right when my answer matched yours

I hope I don't disappoint you

Frankenstein wrote:

mundasingh123 wrote:I know i got it right when my answer matched yours

I hope I don't disappoint you

Man , You can be sure i wouldnt like it

Considering condition (1)

1) [4x^2 - 4y^2]/[2(x+y)] = 2x - 2y
LHS = [4(x^2 - y^2)]/[2(x+y)]
= [4(x-y)(x+y)]/[2(x+y)]
=2x - 2y
=RHS

This does not get us the answer.

Considering condition (2)

2) 3x + 2y = 24
=> x + 2 (x+y) = 24

This also does not get us the value of x+y.

and combining both the conditions also doesnt get us the value of x+y.

Since we cant get the value of (x+y) through both the conditions 1 and 2 considering them simultaneous hence E is the CORRECT ANSWER.

What is the value of x + y?


1) [4x^2 - 4y^2]/[2(x+y)] = 2x - 2y



2) 3x + 2y = 24

Statement 1 reduces to 2x-2y = 2x-2y once we factorise LHS as 2*(x+y)*2*(x-y)/2(x+y), so we cant determine value of x+y

Statement 2 is an equation that cannot be simplified further and hence cant be used to determine the value of x+y

Even after combining information from both the statements, we cannot get value of x+y, hence Statement 1 and statement 2 are not enough so answer is E

From 1
4x^2-4y^2=2x-2y
2(x+y)

(2x)^2-(2y)^2

(2X+2Y)-(2X-2Y)
2X+2Y

2Y-2X=2X-2Y
Infinite solutions

From 2

3x+2y=24
X=8,Y=0
X=0,Y=12

Not sufficent

Combining both we can't get one solution

Hence E

stmt 1 - solving the eqn v get 4(x^2 - y^2) = 4(x + y)(x-y) which is as good as 1=1
stmt 2- infinite solutions

hence, using both together also we get only infinite solutions

+1 for E . .
But why this question ?

(1) solving 1 gives (x-y)(x+y) = 0
(2) cannot determine x+y value

so the answer is E. Both the satemenets cannot tell the value of x+y

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

Statement 1 factors out so that the numerator becomes (2x + 2y)(2x - 2y), allowing the left hand parentheses to factor with the denominator (both are 2x + 2y), leaving just:

2x - 2y = 2x - 2y

That has infinite solutions, so statement 1 doesn't really say anything at all.

Statement 2 has multiple solutions, as well; it's not horrendously far away from being sufficient (if the coefficients for 3x and 2y were the same, say 2x + 2y = 24, we could solve for x+y) and might convince test-takers that you could do something with it, but as there are indeed multiple solutions (x = 8, y = 0; or y = 12, x = 0, for example) the statement is not sufficient.

And since statement 1 really said nothing at all, there's no hope for using both together, so the correct answer is E.


What I like about this question is that the GMAT can be pretty crafty with statements that may look informational but, when taken a step or two from their given form, can actually add a lot less value than you'd think. If it looks pretty easy to get answer choice C, be very careful - more often than not either one statement is good enough on its own, or as in this case one of the statements may not give you the information you think it does.

E isn't a correct answer choice the GMAT likes to give out lightly - when it's correct you usually have to work to prove it, as in this case.

a comes out to x-y = x-y. hence infinite solutions for x and y. not sufficient.

b x and y may or may not be integers. hence many solution. not sufficient.


a+b many solutions. not sufficient.

E it is.