duartemarchand wrote:Hi guys

While reviewing a CAT exam by Kaplan I faced this question:

What is the value of (x + y)2?

(1) x2 − xy = 28 and 3xy + y2 = 72.

(2) (x + y)4 = 10,000

Statement 1 is clearly enough to solve the issue, however in statement 2 kaplan explanation states that because (x + y)4 is the square of (x + y)2 than the square root of 10,000 will be equal to (x + y)2.

My question is: shouldn't we consider that both 100 and -100 are possible answers to statemenmt 2. Is there anything I'm missing?

Even though (x + y)^4 = 10,000, we cannot say that (x + y)^2 = 100 or -100
The reason for this is that (x+y)^2 must be greater than or equal to zero (since we have something squared)
In other words (x + y)^2 cannot equal -100, which means (x + y)^2 must equal 100

Cheers,
Brent

duartemarchand wrote:
What is the value of (x + y)^2?

(1) x^2 − xy = 28 and 3xy + y^2 = 72.

(2) (x + y)^4 = 10,000

Let's solve this one.

Statement 1
We are given two equations:
x^2 − xy = 28
y^2 + 3xy = 72

If we add the left sides and right sides, we get: x^2 + 2xy + y^2 = 100
Now factor to get: (x+y)^2 = 100
So, statement 1 provides SUFFICIENT information to answer the target question.

Statement 2: (x + y)^4 = 10,000
Normally, we might conclude that, if (x+y)^4 = 10,000, then (x+y)^2 = -100 or 100
However, we can eliminate the possibility that (x+y)^2 = -100, since any number to the power of 2 is always greater than or equal to zero.
So, it MUST be the case that (x+y)^2 = 100
So, statement 2 provides SUFFICIENT information to answer the target question.

The correct answer is D.

Cheers,
Brent