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| x +5 | = 10

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Source: — Data Sufficiency |
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by shankar.ashwin » Fri Dec 30, 2011 9:35 am
(1) | x-5 | = 10

x = 15 (or) -5

for both |x+5| does not equal 10 - sufficient

(2) | x | -5 = 10

x = -15 (or) 15

for x=15 -> |x+5| = 20

and for x=-15 -> |x+5| = 10 - Insuff

A
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by pemdas » Fri Dec 30, 2011 10:05 am
st(1) x-5=10 or x-5=-10, xE(-5;15) Suff
st(2) x=15 or x=-15, xE(-15;15) Insuff

a
jainrahul1985 wrote:is | x +5 | = 10?
(1) | x-5 | = 10
(2) | x | -5 = 10
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by GMATGuruNY » Fri Dec 30, 2011 10:08 am
jainrahul1985 wrote:is | x +5 | = 10?
(1) | x-5 | = 10
(2) | x | -5 = 10

Shankar's solution is great.

Another approach:
|x-y| = the DISTANCE between x and y.

Question stem rephrased:
Is | x - (-5) | = 10?
Is the distance between x and -5 equal to 10?
In other words:
Does x=-15 or x=5?

Statement 1: |x-5| = 10.
The distance between x and 5 is equal to 10.
Thus, x=-5 or x=15.
Does x=-15 or x=5? NO.
SUFFICIENT.

Statement 2: |x| - 5 = 10.
{x-0| = 15.
The distance between x and 0 is 15.
Thus, x=-15 or x=15.
Does x=-15 or x=5?
If x=-15, YES.
If x=15, NO.
INSUFFICIENT.

The correct answer is A.
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by pemdas » Fri Dec 30, 2011 11:58 am
actually squaring both sides in this case also solves question

(x+5)^2=100, x^2+10x-75=0 and (x+15)(x-5)=0
question rephrased is x(-15;5)?

st(1) (x-5)^2=100, x^2-10x-75=0 and (x-15)(x+5) Suff
st(2) x^2=225 or x^2-225=0, (x-15)(x+15)=0 Insuff

ans. A
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