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Challenge#1 (Modulus/Absolute Value)

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by aneesh.kg » Tue Jan 29, 2013 8:51 am
Hi people,
Here's a tricky problem on modulus. I gave this problem to my students in my class today and everybody made mistakes in their first attempt.

Lets see if you guys can get it right in the first attempt.

C#1:

Is x positive?
(1) |x^2| = 3
(2) |6 - 5y| = x

OA after some time.
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Source: — Data Sufficiency |
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by hemanthkumarmn » Wed Jan 30, 2013 5:24 am
Is x positive?
(1) |x^2| = 3

For sake of simplifying the calculation let us re frame the above eqn as |x^2|=4 ( it doesn't change the purpose )

The above eqn is true for both x= -2 and x=2

Hence Insufficient.

(2) |6 - 5y| = x

Since x is equated to modulus the value of x remains positive irrespective to the value of y.

Thus sufficient.

Option : B
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by aneesh.kg » Wed Jan 30, 2013 9:50 am
Hemanth, good try! But [spoiler][/spoiler] is not the correct answer.

Lets modify the problem slightly to make two new problems.

Modification 1:
Is x non-negative?
(1) |x^2| = 3
(2) |6 - 5y| = x

Modification 2:
If y is an integer, is x positive?
(1) |x^2| = 3
(2) |6 - 5y| = x

If you solve these, you'd know why [spoiler][/spoiler] is not the correct answer to the original problem.
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by hemanthkumarmn » Thu Jan 31, 2013 3:28 am
aneesh.kg.. I'm struck man.. My wild guess (which is the only option, i'll have if this prob appears during my actual GMAT) will be E..

Do explain me your answer.. And if possible some basics of the above function..

Hemanth.
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by truplayer256 » Thu Jan 31, 2013 8:50 pm
The correct answer is C. Note that the question implying that x is positive means x must always be greater than 0.

Statement 1 is insufficient since x^2 = 3 => x = sqrt(3) or -sqrt(3)

Statement 2 is insufficient because note that since we're not told y has to be an integer, y can take on the value 6 - 5y = 0 => y = 6/5. If this was the case, then x = 0 (Not positive).

Combining both statements, we can see that x can only take on the value x = sqrt(3) since a modulus is always positive.
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by aneesh.kg » Thu Jan 31, 2013 10:35 pm
Statement 1:
x = (3)^0.3 or - (3)^0.5
INSUFFICIENT

Statement 2:
x = Modulus of something
Therefore x must be 0 or greater than zero
INSUFFICIENT

Combining the two, x = (3)^0.5, which is positive.

Therefore, [spoiler][C][/spoiler] is correct.
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by Tommy Wallach » Fri Feb 01, 2013 12:11 pm
Hey Guys,

Just wanna give Aneet a shout-out here. This is a great question, absolutely realistic. What everyone should notice (particularly you, Hemanth!), is that if a GMAT question looks too good to be true, it probably is! In other words, if you solve this without noticing something a little tricky/clever going on, make sure you look a little more closely before confirming that answer! This question perfectly simulates that level of trickiness that the GMAT loves.

-t
Tommy Wallach, Company Expert
ManhattanGMAT

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