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

gmatfrenzy750 · **Posted:** Sun Feb 05, 2012 8:26 pm


		00:00



	GMAT Timer...

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

[Reveal] Spoiler: OA

D

Bunuel · **Posted:** Mon Feb 06, 2012 1:23 am

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.

gamezfreak · **Posted:** Mon Feb 06, 2012 1:46 am

Thanks Bunnel...very good explanation

MSoS · **Posted:** Mon Feb 06, 2012 7:08 am

Thanks! It is clear now

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

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