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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]

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01 Oct 2007, 15:04
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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)

OPEN DISCUSSION OF THIS QUESTION IS HERE: gmat-prep-question-101282.html
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Re: GMATPrep#1 Question: If the operation (*) is defined for [#permalink]

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01 Oct 2007, 15:23
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slsu 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 integers, a, b, and c?

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

Here was a question that I was wondering if anyone could offer a simpler method for calculating out option III?

hmm.

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

cannont work out anything else. the same abc on each sides the same order. thus should be true def.
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Re: GMATPrep#1 Question: If the operation (*) is defined for [#permalink]

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01 Nov 2007, 20:51
slsu 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 integers, a, b, and c?

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

Here was a question that I was wondering if anyone could offer a simpler method for calculating out option III?

resurrecting this thread.. anyone have the OA for this?
I and II clearly true but unsure about the third still, thanks.
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Re: GMATPrep#1 Question: If the operation (*) is defined for [#permalink]

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01 Nov 2007, 22:54
I. is not possible because the integers can be negative. ( see is a=1, b= -2 )

II. is definitely true for positive or negative integers.

III. is also true, irrespective of positive or negative integers.

See the III. is

LHS

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

RHS

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

Therefore the answer should be II and III.
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Re: GMATPrep#1 Question: If the operation (*) is defined for... [#permalink]

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19 Feb 2008, 08:19
look at the function. its addition and multiplication. they are simply testing assoc and distrib properties. all 3 must be true.
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Re: GMATPrep#1 Question: If the operation (*) is defined for... [#permalink]

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27 Feb 2013, 02:44
How do you solve option 3?
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Re: GMATPrep#1 Question: If the operation (*) is defined for... [#permalink]

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27 Feb 2013, 02:46
fozzzy wrote:
How do you solve option 3?

Check here: gmat-prep-question-101282.html
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Re: GMATPrep#1 Question: If the operation (*) is defined for...   [#permalink] 27 Feb 2013, 02:46
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