BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Testprep7

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 468
Joined: Sat Mar 03, 2007 10:17 pm
Thanked: 5 times

Testprep7

by moneyman » Sat Sep 01, 2007 5:56 am
If the operation * is defined for all integers a and b by a*b=a+b-ab,which of the foll 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)
Maxx
Top
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 101
Joined: Tue Aug 07, 2007 1:45 am
Followed by:1 members

by agps » Sat Sep 01, 2007 7:08 am
I is true
a*b = a+b+ab
b*a = b+a+ba (ba= ab)

II is true
a*0 = a+0+0=a (any number multiplied by 0 is 0)

III is true
a*b = a+b+ab
(a*b)*c = a+b+ab+c+ca+cb+cab = a+b+c+ab+ac+bc+abc

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

the answer would be the one that said I,II and III
which one is it??? :D
Top
Master | Next Rank: 500 Posts
Posts: 468
Joined: Sat Mar 03, 2007 10:17 pm
Thanked: 5 times

by moneyman » Sat Sep 01, 2007 11:08 pm
You are right ...The answer is I II and III

But I have a question.The question says that a*b=a+b-ab..but you have mentioned in the answer as a*b=a+b+ab...Why is that??
Maxx
Top
Master | Next Rank: 500 Posts
Posts: 101
Joined: Tue Aug 07, 2007 1:45 am
Followed by:1 members

by agps » Sun Sep 02, 2007 2:09 am
sorry, my mistake, i read a+b+ab instead of a+b-ab
lucky for me the final result still holds true, in the exam this might not be true.

I is true
a*b = a+b-ab
b*a = b+a-ba (ba= ab)

II is true
a*0 = a+0-0=a (any number multiplied by 0 is 0)

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

b*c = b+c-bc
a*(b*c) = a+b-bc+c-a(b+c-bc) = a+b+c-ab-ac-bc+abc
Top
Master | Next Rank: 500 Posts
Posts: 468
Joined: Sat Mar 03, 2007 10:17 pm
Thanked: 5 times

by moneyman » Sun Sep 02, 2007 6:14 am
Thank u
Maxx
Top
Post new topic Post Reply
• Page 1 of 1