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Absolute value

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by alex.gellatly » Tue Jul 17, 2012 8:05 pm
For this question I am going to use ~ as the absolute value sign as I cannot type it.

Is ~x~<1?
1. ~x+1~ = 2~x-1~
2. ~x-3~ does not equal 0

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Source: — Data Sufficiency |

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by Anurag@Gurome » Tue Jul 17, 2012 11:11 pm
alex.gellatly wrote:Is |x| < 1?
1. |x + 1| = 2|x - 1|
2. |x - 3| ≠ 0
Statement 1: This means the distance of x from -1 on the number line is twice the distance of x from 1. Now if you try to draw the scenario on the number line you will see that this is possible in two ways,
  • # x lies between -1 and 1.
    Hence, |x + 1| = (x + 1) and |x - 1| = -(x - 1) = (1 - x)
    Hence, (x + 1) = 2(1 - x) ---> x = 1/3
    Or, |x| < 1

    # x is greater than 1.
    Hence, |x + 1| = (x + 1) and |x - 1| = (x - 1)
    Hence, (x + 1) = 2(x - 1) ---> x = 3
    Or, |x| > 1
Not sufficient

Statement 2: x can be anything except 3.

Not sufficient

1 & 2 Together: x = 1/3 --> |x| < 1

Sufficient

The correct answer is C.
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by Anurag@Gurome » Tue Jul 17, 2012 11:12 pm
For an algebraic approach >> https://www.beatthegmat.com/absolute-ran ... tml#331319
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