himu wrote:Which of the following CANNOT be a product of two distinct positive integers a and b?

A a
B b
C 3b + 2a
D b - a
E ba

In other words, which of the following CANNOT equal ab?

A. Can ab = a?
Yes. For example, if a=3 and b=1, then ab = a
Eliminate A

B. Can ab = b?
Yes. For example, if a=1 and b=3, then ab = b
Eliminate B

C. Can ab = 3b - 2a?
Yes. For example, if a=2 and b=4, then ab = 3b - 2a
Eliminate C

D. Can ab = b - a?
Rearrange to get,"Can ab + a = b?"
Factor to get,"Can a(b + 1) = b?"
Divide both sides by b+1 to get, "Can a = b/(b+1)?"
No.
If b is a positive integer, then b/(b+1) can never be an integer.
Since we're told that a and b are both positive integers, it's impossible for a to equal b/(b+1)

E. Can ab = ba?
Yes. . . always
Eliminate E

Answer = D

Cheers,
Brent