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

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Manager
Joined: 23 Jan 2008
Posts: 108
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Kudos [?]: 33 [0], given: 0

If the operation * is defined for all integers a and b by [#permalink]  31 Jan 2008, 18:36
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 ?

1. a*b = b*a
2. a*0 = a
3. (a*b)*c = a*(b*c)

- 1 only
- 2 only
- 1 and 2 only
- 1 and 3 only
- 1,2 and 3
CEO
Joined: 29 Mar 2007
Posts: 2589
Followers: 17

Kudos [?]: 238 [0], given: 0

Re: operation [#permalink]  31 Jan 2008, 18:48
blog 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 ?

1. a*b = b*a
2. a*0 = a
3. (a*b)*c = a*(b*c)

- 1 only
- 2 only
- 1 and 2 only
- 1 and 3 only
- 1,2 and 3

This problem is listed here somewherez.

I: a+b-ab= b+a-ba OK
II: a+0-(a)0=0+a-0(a) OK same thing

III: is def intimidating. just work it like the functions in the MGMAT book if you have that:

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

a+b+c-ab-ac-bc-abc=a+b+c-ab-ac-bc-abc Everything cancels out! So suff.

E
SVP
Joined: 28 Dec 2005
Posts: 1581
Followers: 2

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Re: operation [#permalink]  31 Jan 2008, 20:29
agree with E. The only tough one to work one is option 3, but expand it and youll see theyre the same
Re: operation   [#permalink] 31 Jan 2008, 20:29
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