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## Kaplan CAT 4 question

tagged by: Brent@GMATPrepNow

This topic has 3 expert replies and 1 member reply
duartemarchand Just gettin' started!
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Kaplan CAT 4 question Tue Mar 20, 2012 4:40 pm
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
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?

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Brent@GMATPrepNow GMAT Instructor
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Tue Mar 20, 2012 6:02 pm
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

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GMATGuruNY GMAT Instructor
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Tue Mar 20, 2012 6:03 pm
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?
Statement 1: x² - xy = 28, 3xy + y² = 72.
Adding the two equations, we get
(x² - xy) + (3xy + y²) = 28+72.
x² + 2xy + y² = 100
(x+y)² = 100.
SUFFICIENT.

Statement 2: (x+y)⁴ = 10,000
Thus, (x+y)² = 100.
SUFFICIENT.

It is not possible that (x+y)² = -100.
The square of a value can never be negative.

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### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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Tue Mar 20, 2012 6:10 pm
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.

Cheers,
Brent

_________________
Brent Hanneson - GMAT Prep Now instructor
- Check out GMAT Prep Now’s online course at http://www.gmatprepnow.com/
- Use our video course in conjunction with
- Watch hours of free videos on DS, RC and AWA
- Our top 3 free videos:
1) The Double Matrix method
3) Managing your time on the GMAT

Study Smart! Use Beat The GMAT’s FREE 60-Day Study Guide in conjunction with GMAT Prep Now’s video course and reach your target score in 2 months! With two money-back guarantees, you can try us out risk-free.
duartemarchand Just gettin' started!
Joined
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Posted:
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Wed Mar 21, 2012 5:08 am
Thanks for both for you answers.

Cheers

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