Math; Number Properties Problem (Easy)

bkk_marc 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

Answer :D

I am confuse why answer choice C. I understand the Answer, but I don't understand the answer C.

Answer choice D: ab = b-a
Since a and b are positive integers, their product must be greater than their difference.
Thus, answer choice D is not possible.

The correct answer is D.

Another approach is to show that the other four answer choices ARE possible.

Let a=1 and b=2.
Then ab = 1*2 = 2.
Eliminate any answer choice that is equal to 2.
Eliminate B (since b=2) and E (since ba = 2*1 = 2).

Let a=2 and b=1.
Then ab = 2*1 = 2.
Eliminate any remaining answer choice that is equal to 2.
Eliminate A (since a=2).

Answer choice C: ab = 3b+2a.
ab - 2a = 3b
a(b-2) = 3b
a = 3b/(b-2).

Plug in a value for b and solve for a.
Let b=3.
Then a= (3*3)/(3-2) = 9.
Thus, if a=9 and b=3, then ab = 3b+2a:
9*3 = 3*3 + 2*9.
27 = 27.
Eliminate C.

bkk_marc 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

Answer :D

I am confuse why answer choice C. I understand the Answer, but I don't understand the answer C.

Thanks Mitch, Your explanations are always self explanatory!
Hi bkk_marc, I hope you were able to eliminate option A,B,& E very quickly. Now, Quickest way to solve this question is to choose numbers to eliminate the option.

Let's start with option C.

If this were to be right, the equation will look like this-

3b+2a=ab
divide both sides by a. the equation will become

3b/a= b-2

Let b=3 & a= 9

Clearly this satisfies the given equation. Hence, we can safely eliminate this choice.

We are left with only option and that is D

PS: Logically, if you look at the option D - the value of the expression will always be less that A & B (given = A and B are positive integer). Since, this is not possible... we can directly choose this option.