Data Sufficiency

This question requires us to use the probability rule.

In the solution we must find P(both numbers are positive OR both numbers are negative)
This equals P(both numbers are positive) + P(both numbers are negative)

So, we still need to find the probability that the product is positive, but since this requires to find P(event A OR event B), we need to find the sum of the two probabilities to do so.

This is covered in the GMAT Prep Now video #7 - Applying the OR Rule

I hope that helps.

Cheers,
Brent

J N wrote:9/21?

Exacly

Here's the full solution.

P(positive product) = P(both numbers are positive OR both numbers are negative)
P(both numbers are positive) + P(both numbers are negative)

Now we'll calculate each part separately.

P(both numbers are positive)
P(both numbers are positive) = P(1st number is positive AND 2nd number is positive)
= P(1st number is positive) x P(2nd number is positive)
= (3/7) x (2/6)
= 1/7

P(both numbers are negative)
P(both numbers are negative) = P(1st number is negative AND 2nd number is negative)
= P(1st number is negative) x P(2nd number is negative)
= (4/7) x (3/6)
= 2/7

So, P(positive product) = 1/7 + 2/7
= 3/7

Cheers,
Brent

J N wrote:Luck or another way???

overall possible
7!/2!5! = 21

Pick 2 negatives
4!/2!2! = 6

Pick 2 positives
3!/2! = 3

9 possible ways to get positive/21 possible combinations

Great solution - perfect execution of counting techniques.

Cheers,
Brent

That's a good question.

I'd say that using probability rules is typically the faster approach, but there's also a matter of comfort level. If your counting techniques are strong (which they appear to be, judging from your post in this thread), then stick with that.

Cheers,
Brent