Which of the following CANNOT be a product of two distinct positive integers a and b?
C) 3b + 2a
D) b - a
Please help me in understanding this question. I am confused between C and D.
Thanks & Regards
In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with
take a = 1 and b = 2 and work with the options
ab = 2
A) a take a =2, b = 1
B) b take a = 1 b = 2
C) 3b + 2a Seems tricky, lets see other options and then come back to it.
D) b - a take b = 1 and a = 2 --> b - a = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them?
E) ba Always true
You don't even have to worry what C is !
Choosing a specific value for b
for which there is no a
which fulfills the condition is not a proof. There are infinitely many other possible values for b.
The statement is CANNOT be true, not that it MUST be true for any a
You have to prove/justify that there is no pair (a,b)
of positive integers for which the equality holds.
PhD in Applied Mathematics
Love GMAT Quant questions and running.