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

Redeem

best way to solve this symbolism?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 72
Joined: Sun Nov 03, 2013 9:29 am
Thanked: 1 times

best way to solve this symbolism?

by josh80 » Wed Dec 11, 2013 5:07 pm
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)

- I only
- II only
- I and II only
- I and III only
- I, II and III only
Top
Source: — Problem Solving |
User avatar
Master | Next Rank: 500 Posts
Posts: 283
Joined: Sun Jun 23, 2013 11:56 pm
Location: Bangalore, India
Thanked: 97 times
Followed by:26 members
GMAT Score:750

by ganeshrkamath » Wed Dec 11, 2013 9:34 pm
josh80 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)

- I only
- II only
- I and II only
- I and III only
- I, II and III only
I. a#b = a+b-ab
= b+a-ba
= b#a
TRUE.

II. a#0 = a+0-(a*0)
= a
TRUE.

III. (a#b)#c = (a#b) + c - (a#b)c
= a + b - ab + c - (a+b-ab)c
= a + b - ab + c - ac - bc + abc
= a - ab - ac + abc + b + c - bc
= a - ab - ac + abc + b#c
= a - a(b+c-bc) + b#c
= a - a(b#c) + (b#c)
= a#(b#c)
TRUE.

Choose E

Cheers
Every job is a self-portrait of the person who did it. Autograph your work with excellence.

Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attemp ... tml#688494
Top
Post new topic Post Reply
• Page 1 of 1