198 Level 700+ questions

[prachich1987]

If # is defined by a # b = a + b - ab, then which is true?
a # b = b # a
a # 0 = a
(a # b) # c = a # (b # c)

a. I
b. II
c. I & II
d. I & III
e. I, II & III

This is from the document "198 Level 700+ questions from GMAT Prep I which I downloaded from BTG.
But the answer given is E
According to me the answer should be C

[Anurag@Gurome]

If # is defined by a # b = a + b - ab, then which is true?
a # b = b # a
a # 0 = a
(a # b) # c = a # (b # c)

a. I
b. II
c. I & II
d. I & III
e. I, II & III

Let's check all the relations individually.
a # b = b # a

• a # b = (a + b - ab)
  b # a = (b + a - ba) = (a + b - ab) = a # b
  True

a # 0 = a

• a # 0 = (a + 0 - 0) = a

(a # b) # c = a # (b # c)

• (a # b) # c = (a + b - ab) # c = [(a + b - ab) + c - (a + b - ab)c] = (a + b + c - ab - ac - bc + abc)
  a # (b # c) = a # (b + c - bc) = [a + (b + c - bc) - a(b + c - bc)] = (a + b + c - ab - ac - bc + abc)
  True

Thus all of them are true.

The correct answer is E.