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

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For any non-zero a and b that satisfy |ab| = ab and |a| = -a [#permalink]

05 Feb 2012, 20:26

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50% (02:18) correct

50% (01:07) wrong

based on 30 sessions

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

[Reveal] Spoiler: OA

Last edited by Bunuel on 04 Dec 2012, 02:36, edited 1 time in total.

Renamed the topic and edited the question.

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Re: Absolute value question [#permalink]

06 Feb 2012, 01:23

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gmatfrenzy750 wrote:

Can someone please assist me in this questions:

For any non 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

Welcome to GMAT Club. I'll try to help you with this.

Can you please check the question: I guess it should read "for any non zero a and b"

|a|=-a means that a<0 and |ab|=ab means that ab>0, so they have the same sign and since a<0 then b<0 too.

So, we have a<0 and b<0.

Now, b-4=b+(-4)=negative+negative =negative, so |b-4|=-(b-4);
ab-b=positive-negative=positive+positive=positive, so |ab-b|=+(ab-b);

Hence |b-4|+ |ab-b| =-(b-4)+(ab-b)=ab-2b+4.

Answer: D.

For more on this topic check Absolute Value chapter of Math Book: math-absolute-value-modulus-86462.html

Hope it helps.
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Re: For any non-zero a and b that satisfy |ab|=ab and |a|=-a [#permalink]

06 Feb 2012, 01:46

Thanks Bunnel...very good explanation

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Re: For any non-zero a and b that satisfy |ab|=ab and |a|=-a [#permalink]

06 Feb 2012, 07:08

Thanks! It is clear now

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Re: For any non-zero a and b that satisfy |ab|=ab and |a|=-a [#permalink]

04 Dec 2012, 02:30

Given: |ab| = ab and |a| = -a
Question: |b-4| + |ab-b| = ?

**** Looking at |ab| = ab tells us that a and b are either both positive or negative
**** Looking at |a| = -a tells us that a must be negative
**** Combine two observations: a and b are both negative values

Let a=-1 and b=-1
|b-4| + |ab-b| = |-1-4| + |1-(-1)| = 7

Test a) ab-4 = (-1)(-1)-4 = -3
Test b) 2b-ab-4 = (2)(-1) - (1) - 4 = -7
Test c) ab+4 = 1 + 4 = 5
Test d) ab-2b+4 = 1-2(-1)+4=7 BINGO!

Answer: D

Re: For any non-zero a and b that satisfy |ab|=ab and |a|=-a [#permalink] 04 Dec 2012, 02:30

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

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

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