GMAT Interact - Session 5, Algebra, Q3 Question!

[DanaG563]

Hi!

In GMAT Interact, I just came to Q3 of Session 5's Algebra lesson and, while the program says Statement 2 is not sufficient, I'm not sure how.. Could you please help me with this?

The question reads:

If x^2 + y^2 = 29, what is the value of (x-y)^2?

(1) xy = 10
(2) x = 5

The program explains how Statement 1 is sufficient

(1) xy = 10
(x-y)^2 => x^2 - 2xy + y^2
And, x^2 + y^2 = 29 => 29 - 2xy = ?
=> 29 - 2(10) = 9

But, I'm just not sure how Statement 2 isn't sufficient. I did the following...

(2) x = 5
x^2 + y^2 = 29
=> 5^2 + y^2 = 29
=> 25 + y^2 = 29
=> y^2 = 4
=> y=2
So x=5 and y=2
...We can now find the value of (x-y)^2... (5-2)(5-2) = 9

Thanks!
Dana

[RonPurewal]

In statement 2, y could also be –2.

[HarrisonI74]

Apologies for bumping an old thread but I am having trouble understanding why statement 2 is insufficient.

Can anyone explain why statement 2 is insufficient if I can plug in the value of X in the same equation used to solve statement 1?

(x-y)^2 => x^2 - 2xy + y^2
And, x^2 + y^2 = 29 => 29 - 2xy

if x = 5 then 29- 2(5)y = 29 - 10y
-10y = 29
y = 29/-10
y = -2.9

Can someone explain why this line of thinking is wrong? Thanks!

[OluwatoyinA64]

Can someone explain

Is |x| < 1 ?

(1) |x + 1| = 2|x – 1|

(2) |x – 3| > 0

[Sage Pearce-Higgins]

Where is this question taken from?

You need to understand the basics of the absolute value function to do this one. Simply put, absolute value removes a negative sign if there is one, so that, for example:
|7| = 7
|-7| = 7

With that in mind you can rephrase the question: Is |x| < 1 ? This is really asking: Is -1 < x < 1? Think about this rephrase before moving on to the next sentence.

(1) |x + 1| = 2|x – 1|
To solve equations with absolute value in them (more about this in chapter 11 of the Algebra strategy guide), we need to consider the positive and negative cases (for example, |y| = 6, then y could be 6 or -6). Here we have two possibilities:
x + 1 = 2(x – 1) and -x - 1 = 2(x – 1)
Solving these equations gives us two solutions: x = 3, and x = 1/3, so not sufficient.

(2) |x – 3| > 0
To deal with absolute value and inequalities check out chapter 13 of the Algebra strategy guide. However, here we have a classic GMAT trap. Look at this inequality and think: "Aren't absolute values always positive?!", so this statement doesn't seem to say anything very interesting. However, note that we could have an absolute value that equals zero, so the small piece of information that we're given here is x does not equal 3. That rules out one of the solutions from our first equation.

Final answer: C