Tough DS inequalities

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ssgmatter: Legendary Member; Posts: 549; Joined: Wed Jan 06, 2010 7:00 amFollowed by: 3 members; Thanked: 16 times

by ssgmatter » Wed Jun 23, 2010 9:31 pm

Is |x| < 1?
(1) |x + 1| = 2 |x - 1|
(2) |x - 3| â‰ 0

I understand stmt 2 but could not deduce anything from stmt 1 except that x=3

Any thoughts???

Best-
Amit

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Source: Beat The GMAT — Data Sufficiency | Wed Jun 23, 2010 9:31 pm

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Wed Jun 23, 2010 10:01 pm

Is |x| < 1? means is -1 < x < 1?

(1) From |x + 1| = 2 |x - 1|, we get x = 3 and also -(x+1) = 2(x -1) implies x = 1/3
So, we have 2 values of x from statement (1). Hence, (1) is NOT SUFFICIENT to answer the question.

(2) implies that x is not equal to 3, but this is NOT SUFFICIENT to answer the question.

Combining, we are able to get a unique value for x, which is x = 1/3 as x is not equal to 3 by statement (2) and answer to the main question is "yes"

The correct answer is (C).

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sreak1089: Master | Next Rank: 500 Posts; Posts: 379; Joined: Wed Jun 03, 2009 3:05 amFollowed by: 1 member; Thanked: 19 times; GMAT Score:690

by sreak1089 » Wed Jun 23, 2010 10:22 pm

Stmt # 1: Says |x+1| = 2|x-1|

=> x+1 = 2(x-1) or x+1 = -2(x-1)
=> x = 3 => x = 1/3
=> x = 3 or 1/3

Substitute x=3, we have |x+1| = 4 = 2|x-1| = 2|2| = 4. Hence x = 3 is valid solution.
Substitute x=1/3, we have |x+1| = 4/3 = 2|-2/3| = 4/3. Hence x = 1/3 is also a valid solution.

If x = 3 |x| > 1 and if x = 1/3 |x| < 1. Hence there is ambiguity. NOT SUFFICIENT.

Stmt # 2: Says |x-3| != 0

=> x != 3 (x is NOT EQUAL to 3). However, x can be equal to 1/3 or 2 or 5, or any number other than 3.
Hence there is ambiguity. NOT SUFFICIENT.

Combining 1 and 2, we have x = 1/3. Hence, |x| < 1. Thus SUFFICIENT. Hence C is
the answer.

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