absolute value

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artstudent: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Mon Mar 28, 2011 9:35 pm; Thanked: 4 times

absolute value

by artstudent » Wed Jul 20, 2011 9:48 pm

For any non-zero a and b that satisfy |ab| = ab and |a| = -a
|b - 4| + |ab - b| =

A. ab - 4
B. 2b - ab - 4
C. ab + 4
D. ab - 2b + 4
E. 4 - ab

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Source: Beat The GMAT — Problem Solving | Wed Jul 20, 2011 9:48 pm

winniethepooh: Master | Next Rank: 500 Posts; Posts: 370; Joined: Sat Jun 11, 2011 8:50 pm; Location: Arlington, MA.; Thanked: 27 times; Followed by:2 members

by winniethepooh » Wed Jul 20, 2011 10:21 pm

IMO answer is c
As |ab|= ab and |a|= -a, therefore even |b| should be -b as -a*-b = ab

|b-4|+ |ab-b| = -b +4 + ab - b = 4 + ab - 2b.
Hence, D.

Last edited by winniethepooh on Wed Jul 20, 2011 11:01 pm, edited 1 time in total.

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by Anurag@Gurome » Wed Jul 20, 2011 10:26 pm

artstudent wrote:For any non-zero a and b that satisfy |ab| = ab and |a| = -a
|b - 4| + |ab - b| =

A. ab - 4
B. 2b - ab - 4
C. ab + 4
D. ab - 2b + 4
E. 4 - ab

Solution
labl = ab means ab > 0.
lal = -a means a < 0.
This implies b < 0.
b-4 < 0
lb-4l = 4 - b.
ab - b > 0
lab-bl = ab - b
lb-4l + lab-bl = 4 + ab - 2b.

The correct answer is D.

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winniethepooh: Master | Next Rank: 500 Posts; Posts: 370; Joined: Sat Jun 11, 2011 8:50 pm; Location: Arlington, MA.; Thanked: 27 times; Followed by:2 members

by winniethepooh » Wed Jul 20, 2011 10:35 pm

Sir, any logic behind |b-4|= 4-b? Though I understand that |b|= -b, so b < 0 and b-4 < 0.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Wed Jul 20, 2011 10:40 pm

winniethepooh wrote:Sir, any logic behind |b-4|= 4-b? Though I understand that |b|= -b, so b < 0 and b-4 < 0.

By definition, |x| = -x if x < 0
As (b - 4) < 0, |b - 4| = -(b - 4) = (4 - b)

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winniethepooh: Master | Next Rank: 500 Posts; Posts: 370; Joined: Sat Jun 11, 2011 8:50 pm; Location: Arlington, MA.; Thanked: 27 times; Followed by:2 members

by winniethepooh » Wed Jul 20, 2011 10:49 pm

Thanks for your help. I really appreciate it!
A note in my Points to Remember!

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amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 am; Location: pune; Thanked: 36 times; Followed by:3 members

by amit2k9 » Thu Jul 21, 2011 1:36 am

ab > 0 and a < 0 meaning b <0.

hence let a=b= -1 each. thus the equation provides 7 as its value.

now checking for a,b,c,d and e we find b and d providing -7 and 7 respectively.

thus D it is.

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