# is a function such that 1#a=1 and a#b = b#a for all a and b. Which of the following must be true?

I. a#1 = 1
II. (1#b)#c = 1#(b#c)
III.(1#a)/(b#1) = 1

a. I only
b. II only
c. III only
d. I and II only
e. I,II and III

OA is E ???

Given :
eqn 1) 1#a=1
eqn 2) a#b = b#a

Now I. a#1 = 1#a = 1 ( from eqn 2 and eqn 1 above)
=> a#1 = 1 is true

II. (1#b)#c = 1#(b#c)
LHS
1#b = 1 ( from eqn 1) = > (1#b)#c = (1)#c
again 1#c =1
=>(1#b)#c =1

RHS

1#(b#c) = 1 ( from eqn 1 above)

LHS=RHS =1 thus II. is also true.

III. applyin the above logic -> III . also true

And yes .. I guess ppl have got such questions ... If i remember correctly, i got one such q on my GMATPrep Test 1.


Amit

Ya the OA is E. Thanks for the explanation Amit.