If a, b, and c are integers and ab^2/c is a positive even integer, which of the following must be true?
I. ab is even
II. ab > 0
III. c is even
A. I only
B. II only
C. I and II
D. I and III
E. I, II, and III
The OA is A.
Experts, may you give me some help here please? It is a hard PS question to me.
Hi VJesus12,
Let's take a look at your question.
The question says,
$$\frac{ab^2}{c}>0$$
and
$$\frac{ab^2}{c}=even$$
$$ab^2=c\times even$$
When any number is multiplied by an even number, it will result into an even number as well. Therefore,
$$ab^2=even$$
ab^2 can be even if a or b or both a and b are even.
Hence, ab will be even.
Therefore, I is true.
Let's check if II is true or not.
The question says that,
$$\frac{ab^2}{c}>0$$
Which can be true even b is negative, therefore, ab > 0 will not be true for b < 0.
Hence, II is not true.
Let's check if III is true or not.
c can not be even in all cases because the given statement can be true for c = 1 and i is not even.
Hence, III is not true.
It means only I is true.
Therefore, Option
A is correct.
Hope that makes sense.
I am available if you'd like any follow up.
