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GMATPrep Algebra

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GMATPrep Algebra

by erjamit » Thu Aug 07, 2008 5:58 am
Hi,
Pls help with this.

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 integers, a, b, and c?

I. a (*) b = b (*) a
II. a (*) 0 = a
III. (a*b)*c = a*(b*c)

A) I
B) II
C) I,II
D) I,III
E) I,II,III

I couldn't figure out why III is true. Can someon explain how to derive III.

OA E

Thanks
Amit
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by malolakrupa » Thu Aug 07, 2008 10:23 am
I think the answer is C .
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by erjamit » Thu Aug 07, 2008 10:25 am
As already told OA is E.

Pls explain why the III option is correct.
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by parallel_chase » Thu Aug 07, 2008 10:48 am
III. (a*b)*c = a*(b*c)


Let (a*b) = y = a+b-2ab

y*c = y + c -2yc = a+b-ab +c - 2c(a+b-2ab) = a+b+c-2ab-2ac-2bc+4abc

Let (b*c) = x = b+c-2bc

a*x = a+x-2ax = a+b+c-2bc-2a(b+c-2bc) = a+b+c-2ab-2ac-2bc+4abc


Hence the answer is E.

Hope this helps.
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by erjamit » Thu Aug 07, 2008 10:53 am
(a*b)*c = (a + b - ab)*c
= a + b - ab + c - (a + b - ab)c


a*(b*c) = a*(b+c-bc)
= a + b +c - bc - a(b+c-bc)

What is wrong with my approach?

Thanks
Amit
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by parallel_chase » Thu Aug 07, 2008 11:04 am
erjamit wrote:(a*b)*c = (a + b - ab)*c
= a + b - ab + c - (a + b - ab)c
absolutely nothing is wrong with your approach, If you expand,

a+b-ab+c-ac-bc+abc -------I
a*(b*c) = a*(b+c-bc)
= a + b +c - bc - a(b+c-bc)
a+b+c -bc-ab-ac+abc -------II

If you compare I and II both are equal.

In fact i took the a*b = a+b-2ab instead of a+b-ab

But it doesnt matter as you can see one can still get E as the answer.
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by erjamit » Thu Aug 07, 2008 11:06 am
This is what nerves do to you. :( ......

I just solved till this part and then glanced at both options and eliminated it.

Thanks mate.

Amit
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by aj5105 » Thu Oct 02, 2008 5:53 am
imo, one of better ways to solve these kind of problems is use numbers.
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Very Confused

by olpre4 » Mon Nov 24, 2008 7:56 pm
1) What is being tested in this problem?

2) Operationally, how did you get

From (a*b)*c = (a + b - ab)*c

To = a + b - ab + c - (a + b - ab)c
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by niraj_a » Tue Nov 25, 2008 5:10 pm
you could try picking numbers abd testing this out too....
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