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mandeepak: Senior | Next Rank: 100 Posts; Posts: 84; Joined: Thu Jan 18, 2007 10:28 pm; Thanked: 2 times

by mandeepak » Sun Oct 28, 2007 1:30 am

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

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

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Source: Beat The GMAT — Data Sufficiency | Sun Oct 28, 2007 1:30 am

jangojess: Master | Next Rank: 500 Posts; Posts: 175; Joined: Mon Jul 02, 2007 12:01 pmFollowed by: 1 member; Thanked: 15 times

by jangojess » Sun Oct 28, 2007 5:42 am

stmt 1 - there can be two solutions for x in this case.
x+1 =2(x-1)...... x= 3.
x+1 =2(1-x)....when modulus is used both conditions of difference need to be considered....In this case x = 1/3.....Since x has two values ...Insuff

stmt 2 - x not equal to 3 is the sol.....Insuff

Both - the only possible sol is x=1/3....Suff ...........So ans is C.

Trying hard!!!

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ri2007: Master | Next Rank: 500 Posts; Posts: 258; Joined: Mon Aug 27, 2007 12:43 pm; Thanked: 15 times

by ri2007 » Sun Oct 28, 2007 9:49 am

can you pls confirm the answer. Thanks

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ri2007: Master | Next Rank: 500 Posts; Posts: 258; Joined: Mon Aug 27, 2007 12:43 pm; Thanked: 15 times

by ri2007 » Sat Nov 17, 2007 10:25 am

Hi

Can some one pls help me whit this one?

This is the way I solved statement 1)

lx+1l = 2lx-1l

so there are two options

Option 1)

(x+1) = 2 (x-1), in which case x = 3

Option 2)

-(x+1) = -2(x-1), in which case X = 3

Both the cases X > 1, so statement 1 is sufficient

However Jess has a diff ans. Can any one confirm the right approach and explain it?

Thanks

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ua: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Sat Nov 18, 2006 3:24 am

by ua » Sun Nov 18, 2007 5:23 pm

Hi ri2007,

Your option 1 is the same as the option 2.

When we have a modulus on a side that means it can have two values +/-. When there is a modulus on both sides that means that both sides will have a +/-

|x+1| = 2|x-1|

+/- (x+1) = +/- (2(x-1))

which leads to the following options:

x+1 = 2(x-1) or -(x+1) = - 2(x-1) (they are same)

AND

-(x+1) = 2(x-1) or x+1 = -2(x-1) (they are same as well)

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ri2007: Master | Next Rank: 500 Posts; Posts: 258; Joined: Mon Aug 27, 2007 12:43 pm; Thanked: 15 times

by ri2007 » Sun Nov 18, 2007 5:30 pm

Thanks so much us. Great explaination

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