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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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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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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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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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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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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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by artstudent » Thu Jul 21, 2011 8:21 pm
how did you get -1?
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