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If the operation * is defined for all integers a and b by

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If the operation * is defined for all integers a and b by [#permalink] New post 06 Jan 2008, 16:34
If the operation * is defined for all integers a and b by a*b=a+b-ab, which of the following statements must be true for all intergers a, b and c?

1 a*b=b*a
II a*0=a
III (a*b)*c=a*(b*c)

a 1 only
b II only
c I and II only
d I and III only
e I, II and III

Any ideas?
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Re: Functions [#permalink] New post 06 Jan 2008, 17:25
Ant wrote:
If the operation * is defined for all integers a and b by a*b=a+b-ab, which of the following statements must be true for all intergers a, b and c?

1 a*b=b*a
II a*0=a
III (a*b)*c=a*(b*c)

a 1 only
b II only
c I and II only
d I and III only
e I, II and III

Any ideas?


I: distributive property: a+b-ab = b+a -ba same thing so I is good.
II a+0-a(0) = a II is good
If both sides cancel then they equal each other:
III: a+b-ab*c = a*b+c-bc --> a+b-ab+c -(a+b-ab)c=b+c-bc+a -(b+c-bc)a -->


a+b-ab+c-ac-bc+abc=b+c-bc+a -ab -ac +abc indeed both sides cancel so III is also sufficient.

E
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Re: Functions [#permalink] New post 06 Jan 2008, 18:12
I finally got E, but it took forever.

This question is a pain in the ass and probably would be tought to do under 2 mins. Where is this question from?
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Re: Functions [#permalink] New post 07 Jan 2008, 19:19
E

the only painful one is the last option
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Re: Functions [#permalink] New post 07 Jan 2008, 19:32
E, All three,
first two are easy, and for the third one I substituted values for a, b and c, that works faster.
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Re: Functions [#permalink] New post 07 Jan 2008, 21:15
This was a test question from the GMAT Test Prep Software.
Re: Functions   [#permalink] 07 Jan 2008, 21:15
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