Inequalities with Modulus

[ayushi21]

Could someone please help me with this :the absolute value baffles me .

Is X^2 > 5^2 ?

1) |X − 5| = 3 |X + 5|

2) |X| > 3

Thanks in advance!

[GMATGuruNY]

I believe that Statement 1 has been transcribed incorrectly and that the problem should read as follows:

Could someone please help me with this :the absolute value baffles me .

Is X^2 > 5^2 ?

1) |X + 5| = 3 |X - 5|

2) |X| > 3

Thanks in advance!

x² > 5² if x<-5 or x>5.
Thus:
x ≤ 5² if -5≤x≤5.
Question stem, rephrased:
Is -5≤x≤5?

Statement 1:
Case 1: signs unchanged
x+5 = 3(x-5)
x+5 = 3x - 15
20 = 2x
x = 10.
In this case, the answer to the rephrased question stem is NO.

Case 2: signs changed in ONE of the absolute values
-x-5 = 3(x-5)
-x-5 = 3x - 15
10 = 4x
x = 10/4 = 5/2.
In this case, the answer to the rephrased question stem is YES.

Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.

Statement 2:
If x=4, then the answer to the rephrased question stem is YES.
If x=10, then the answer to the rephrased question stem is NO.
INSUFFICIENT.

Statements combined:
Of the two values for x in Statement 1, only x=10 also satisfies Statement 2.
Since x=10 is greater than 5, the answer to the rephrased question stem is NO.
SUFFICIENT.

The correct answer is C.

[nchaswal]

I believe that Statement 1 has been transcribed incorrectly and that the problem should read as follows:

Could someone please help me with this :the absolute value baffles me .

Is X^2 > 5^2 ?

1) |X + 5| = 3 |X - 5|

SUFFICIENT.

The correct answer is C.

Dear GMATGuruNY

Is it not that the question posted in its original form is also solvable with this same method?

I also tried and the answer was C itself.

Statement 1: Gives X=-10 or -2.5

Since it gives a YES or NO answer for the question stem. INSUFFICIENT

Statement 2: Gives X>3 & X<-3

Any number between 3 and 5 (both excluding) will give NO for the question stem's answer.

Any number above 5 and less than -5 in this range will give a YES answer.

Hence INSUFFICIENT.

When Combined: For the range in Statement 2, only X=-10 satisfies this condition |X|^2 >5^2

Hence C

Ayushi21 hope this clarifies?

[Matt@VeritasPrep]

Working with the original post, we'd have

Is x² > 5²

Is |x| > 5 ?

S1::

|x - 5| = 3 * |x + 5|
|x - 5| = 3 * |x - (-5)|

so x is THREE TIMES as far from 5 as it is from -5. This means x = -10 or x = -2.5; NOT SUFFICIENT.

S2::

|x| > 3

also NOT SUFFICIENT, since we could have x = 4 or x = 6 (among other contradictory solutions).

Together, only x = -10 satisfies both statements, so yes, C.

[Matt@VeritasPrep]

Is it not that the question posted in its original form is also solvable with this same method?

I also tried and the answer was C itself.

I'd guess the Guru has seen the original somewhere before, and knows how it reads, but yeah, you're right that it's immaterial here.