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!
Inequalities with Modulus
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- GMATGuruNY
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I believe that Statement 1 has been transcribed incorrectly and that the problem should read as follows:
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.
x² > 5² if x<-5 or x>5.ayushi21 wrote: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!
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.
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- nchaswal
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GMATGuruNY wrote:I believe that Statement 1 has been transcribed incorrectly and that the problem should read as follows:
Dear GMATGuruNYayushi21 wrote: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.
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?
It is GMAT. So what?
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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.
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.
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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.nchaswal wrote: 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.