Is x^2 < y^2 ?

[gmattesttaker2]

Hello,

Can you please tell me if my solution is correct here:

Is x^2 < y^2 ?

1) x < y
2) -y < x

Answer I am getting is E


Original question:

Is x^2 < y^2?

i.e. Is sq. root (x^2 ) < sq. root (^2) ?
i.e. Is |x| < |y| ?

1) x < y
x = 2, y = 3 => |x| < |y|
x = -15, y = 3 => |x| not less than |y|

In-suff.

2) -y < x
=> x + y > 0
x = 2, y = 3 => |x| < |y|
x = 3, y = 2 => |x| not less than |y|

In-suff.


1 and 2:

x < y
-y < x

Adding both the above,
x - y < x + y

=> -y < y
=> -y + y < y + y
=> 0 < 2y
=> 0 < y
i.e. y > 0

We also know that x < y

Let y = 4 and x = 2 => |x| < |y|
Let y = 4 and x = -20 = > |x| is not less than |y|

Hence, answer is E

[[email protected]]

Hi Sri,

Since you just posted this, I'm going to point out an error in your thinking so that you can go back and reattempt this question (before I explain the correct answer).

While I agree that both Fact 1 and Fact 2 are INSUFFICIENT, your examples at the end include a mistake

Y = 4, X = -20 is NOT a match for the information in Fact 2, so it is not correct....

GMAT assassins aren't born, they're made,
Rich

[gmattesttaker2]

Hi Sri,

Since you just posted this, I'm going to point out an error in your thinking so that you can go back and reattempt this question (before I explain the correct answer).

While I agree that both Fact 1 and Fact 2 are INSUFFICIENT, your examples at the end include a mistake

Y = 4, X = -20 is NOT a match for the information in Fact 2, so it is not correct....

GMAT assassins aren't born, they're made,
Rich

Hello Rich,

Thanks for the tip. I totally forgot about checking the values for Statement 2. After adding both 1 and 2 and plugging in the values I thought that it was sufficient to just look at Statement 1. Thanks again for correcting me.

Now from 1 and 2 we have, y > 0

Let y = 4 and x = 2 ( x < y - Hence satisfies 1. -y < x - Hence satisfies 2 )
=> |x| < |y| ? - Yes

Let y = 14 and x = -13 ( x < y - Hence satisfies 1. -y < x - Hence satisfies 2 )
=> |x| < |y| ? - Yes

Let y = 6 and x = -5 ( x < y - Hence satisfies 1. -y < x - Hence satisfies 2 )
=> |x| < |y| ? - Yes

Hence, is the answer C?

Thanks a lot for your help.

Best Regards,
Sri

[GMATGuruNY]

Is x^2 < y^2 ?

1) x < y
2) -y < x

Question stem:
x² < y²?
x² - y² < 0?
(x+y)(x-y) < 0?

Question stem, rephrased: Are (x+y) and (x-y) different signs?

Statement 1: x < y
x-y < 0.
No information about x+y.
INSUFFICIENT.

Statement 2: -y < x
0 < x+y
x+y > 0.
No information about x-y.
INSUFFICIENT.

Statements combined:
Since x-y<0 and x+y>0, (x+y) and (x-y) are different signs.
SUFFICIENT.

The correct answer is C.

[[email protected]]

Hi Sri,

Your updated answer IS correct. Nice "repair work" to find the correct answer. Going forward, you have to remember that DS questions are usually not going to involve tough math concepts (because that's NOT the skill set the DS questions test). DS is about organization, accuracy, thoroughness, attention to detail, being able to prove that you're correct, etc. These are the skills to focus on when you're working on a DS question. Since DS questions have no "safety net", there's no way to catch a minor mistake if you make one - you'll just end up choosing the wrong answer without knowing it. A higher level of note-taking and diligence is a must on DS questions, so just do the work that is required and you'll have the correct answer.

GMAT assassins aren't born, they're made,
Rich