Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 26 Apr 2015, 02:03

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Is lxl < 1? (1) lx + 1l = 2lx - 1l (2) lx - 3l ≠ 0

Author Message
TAGS:
Manager
Joined: 11 Jan 2007
Posts: 202
Location: Bangkok
Followers: 1

Kudos [?]: 10 [0], given: 0

Is lxl < 1? (1) lx + 1l = 2lx - 1l (2) lx - 3l ≠ 0 [#permalink]  04 Jun 2007, 19:19
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
Q5:
Is lxl < 1?
(1) lx + 1l = 2lx - 1l
(2) lx - 3l ≠ 0

Q16:
If m, p, and t are positive integers and m < p < t, is the product mpt an even integer?
(1) t – p = p - m
(2) t – m = 16
_________________

cool

SVP
Joined: 01 May 2006
Posts: 1805
Followers: 8

Kudos [?]: 98 [0], given: 0

Q5:
Is lxl < 1?
(1) lx + 1l = 2lx - 1l
(2) lx - 3l ≠ 0

(C) for me

lxl < 1 ?
<=> -1 < x < 1 ?

From (1)
lx + 1l = 2lx - 1l, what are the solutions of it?

o If x >=1, then:
lx + 1l = 2lx - 1l
<=> x+1 = 2*(x-1)
<=> x = 3 >>>>> 1 solution as x must be superior or equal to 1

o If -1 > x > 1, then:
lx + 1l = 2lx - 1l
<=> x+1 = 2*[-(x-1)]
<=> x+1 = -2*x + 2
<=> x = 1/3 >>>>> 1 solution as x must be between -1 and 1

Note that it's already insufficient, but let us continue to state later between (C) or (E)...

o If x =< -1, then:
lx + 1l = 2lx - 1l
<=> -(x+1) = 2*[-(x-1)]
<=> x+1 = 2*(x-1)
<=> x = 3 >>>>> no solution as x must be inferior or equal to -1

INSUFF.

From (2)
lx - 3l ≠ 0
<=> x < 3 or x > 3

INSUFF.

From (1) and (2)
With the system of sulution from 1, we have x = 3 or x = 1/3. Then, we have x that must be different from 3.

So, x = 1/3 (-1 < x < 1)

SUFF.
Senior Manager
Joined: 03 Jun 2007
Posts: 384
Followers: 2

Kudos [?]: 10 [0], given: 0

Another method to solve

Stmt 1 lx + 1l = 2lx - 1l
(x + 1) ^2 = 4(x - 1) ^ 2
Solving for x we get 3 and 1/3

Stmt 2

x <> 3

Using 1 and 2 we see x = 1/3
Senior Manager
Joined: 24 Nov 2006
Posts: 351
Followers: 1

Kudos [?]: 14 [0], given: 0

Re: 2 DS - Absolute / Number properties [#permalink]  06 Jun 2007, 15:21
jet1445 wrote:
Q5:
Is lxl < 1?
(1) lx + 1l = 2lx - 1l
(2) lx - 3l ≠ 0

Q16:
If m, p, and t are positive integers and m < p < t, is the product mpt an even integer?
(1) t – p = p - m
(2) t – m = 16

Q5.
(1) Two cases: x+1 =2x-2 OR =-2x+2. In the 1st case, x=3; in the 2nd, x=1/3. Insuff.
(2) x<>3. Insuff.
(1&2) x has to be =1/3. Suff, then C.

Q16.
(1) Insuff. Take m, p, t = 1, 4, 7 and 1, 5, 9. In the 1st case mpt is even, in the 2nd case it´s odd.
(2) Insuff. Simple inspection.
(1&2) Insuff (take a similar example as in (1)), then E.
Senior Manager
Joined: 04 Jun 2007
Posts: 374
Followers: 1

Kudos [?]: 22 [0], given: 0

for the first question, why cant we write:
x+1= 2x-2
x= 3
OR
-x-1=-2x+2
x=3

doesn't |x+1| = x+1 OR -x-1??
i guess i am not understanding how modulus works then.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5078
Location: Singapore
Followers: 22

Kudos [?]: 184 [0], given: 0

Question is really asking whether x a fraction.

St1:
|x+1| = 2|x-1|
If x = 3, |x+1| = 4, and 2|x-1| = 4 and |x| > 1
If x = 1/3, |x+1| = 4/3 and 2|x-1| = 4/3 and |x| < 1.
Insufficient.

St2:
X can be anything apart from 3. Insufficient.

Using st1 and st2:
x must be 1/3. sufficient.

ans C
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5078
Location: Singapore
Followers: 22

Kudos [?]: 184 [0], given: 0

r019h wrote:
for the first question, why cant we write:
x+1= 2x-2
x= 3
OR
-x-1=-2x+2
x=3

doesn't |x+1| = x+1 OR -x-1??
i guess i am not understanding how modulus works then.

No, we only meddle with the signs on the RHS of the equation.
Similar topics Replies Last post
Similar
Topics:
1L to MBA 2 08 Dec 2012, 16:13
57 A container has 3L of pure wine. 1L from the container is 41 03 Nov 2009, 22:04
Is lxl < 1? (1) lx + 1l = 2 lx - 1l (2) lx - 3l 0 A. 1 09 Nov 2008, 17:19
Is lx^3-23x^2+132xl=x^3-23x^2+132x? 1. x>0 2. lx-2l>5 4 29 Dec 2007, 08:58
Is lxl < 1? (1) lx + 1l = 2lx - 1l (2) lx - 3l ≠ 0 8 02 Aug 2007, 09:05
Display posts from previous: Sort by