If a, b and c are all positive integers, is abc an even number?

Hi All,

This DS question is a great example of how you can TEST VALUES and keep things SIMPLE to quickly get to the solution.

We're told that A, B and C are positive integers. We're asked if (A)(B)(C) is an EVEN number. This is a YES/NO question.

Fact 1: A+B is a PRIME number

IF....
A = 1
B = 1
A+B = 1+1 = 2

IF....
C = 1, then (1)(1)(1) = 1 and the answer to the question is NO
C = 2, then (1)(1)(2) = 2 and the answer to the question is YES
Fact 1 is INSUFFICIENT

Fact 2: B+C is an EVEN number

IF....
B = 1
C = 1
B+C = 1+1 = 2

IF....
A = 1, then (1)(1)(1) = 1 and the answer to the question is NO
A = 2, then (2)(1)(1) = 2 and the answer to the question is YES
Fact 2 is INSUFFICIENT

Combined, we know...
A+B is a PRIME
B+C is EVEN

IF....
A = 1
B = 1
C = 1
Then (1)(1)(1) = 1 and the answer to the question is NO

IF...
A = 2
B = 1
C = 1
Then (2)(1)(1) = 1 and the answer to the question is YES
Combined, INSUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Hi here ‘a or b’ anyone is not necessarily even all the time… So statement 1 is not sufficient:
Statement 1 : Not sufficient:
If a=1 , b=1 and c=3 then a+b is prime but abc is not even. Answer is NO to the question.
If a=2 , b=1 and c=3 then a+b is prime and abc is even. Answer is YES to the Question.
Statement 2 : Not sufficient:
If a=1, b=2 and c=4 then b+c(both even) is even and abc is even. Answer is YES to the question.
If a=1 , b=1 and c=3 then b+c(both odd) is even but abc is not even. Answer is NO to the Question.
So not sufficient.
So together also you can use the same example.
If a=1, b=2 and c=4 then a+b is prime and b+c(both even) is even and abc is even. Answer is YES to the question.
If a=1 , b=1 and c=3 then a+b is prime and b+c(both odd) is even but abc is not even. Answer is NO to the Question.

You can see that even together it is not sufficient.
So answer is E.

Hi Bunuel,

Is it ALWAYS explicitly stated (in GMAT) when variables considered in question are different numbers?

For example, in this question, I am confused whether given variables denote different number or can have same number, since a b & c are different variables. This confusion led me to the wrong answer as I did not consider the case where a can be equal to b.

Regards,
Rishabh

Hi Rishabh,

The answer to your immediate question is NO: if you are dealing with multiple variables, unless the prompt explicitly states that the variables are differenent numbers, then you should NOT assume that they have to be different.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: Rich.C@empowergmat.com
www.empowergmat.com