Since there are 50 odd numbers and 50 even numbers:
P(odd number) = P(even number) = 1/2.

Ways to get an ODD sum:
3 odd numbers
1 odd number, 2 even numbers

Ways to get an EVEN sum:
3 even numbers
1 even number, 2 odd numbers

Since the probabilities in red are equal and the probabilities in blue are equal, there is a 50% chance that the sum will be ODD and a 50% chance that the sum will be EVEN.

Thus:
P(odd sum) = 1/2.

The correct answer is E.

Alternate approach:

The sum will be odd if all 3 numbers selected are odd or if exactly 1 number selected is odd.
Let O = odd and E = even.
Since there are an equal number of odd numbers and even numbers in the box, P(O) = 1/2 and P(E) = 1/2.

Probability all 3 are odd:
P(OOO) = 1/2 * 1/2 * 1/2 = 1/8

Probability exactly 1 is odd:
P(OEE) = 1/2 * 1/2 * 1/2 = 1/8
Since EOE and EEO are also good outcomes, we multiply this result by 3:
3 * 1/8 = 3/8

Since we'll get a good outcome if all 3 numbers selected are odd OR if exactly 1 number selected is odd, we add the fractions:
1/8 + 3/8 = 4/8 = 1/2.

The correct answer is E.

Hi Rich,

Thank you for responding. yes my target is still 600. I think my problem is when I am practicing. if I miss a hard question, I spent a long long long time trying to figure thing out. I end up running out time. I have not take the CAT. I will take it this weekend. probability is the last concept i need to learn. I thought math was going to be strong for me. verbal is my weakness for sure. I m not doing great in the math concept. I have not studied the verbal section. I have goal to take it in July 2nd because my deadline is July 15 to apply. I will take the whole CAT this weekend and post my score.

Thanks for the feedback.

Another way to think of this: you're equally likely to select an odd or an even each time. Given three numbers, we know

prob(all odd) = prob(all even)
prob(1 odd) = prob(1 even)

and those are the only four cases!

We want (p(all odd) + p(1 odd)) / total

and since we have exactly half the total cases in the numerator, our p = 1/2.