If any number from set A is multiplied by any number from set B, what

Thx a lot.....

But applying your procedure seems taking longer than 2 minutes............

Is there a short cut?

If you follow the steps above it will take 1 min or at most 1.5 minutes.
You dont have to write subjective ans, skip the steps and answer it quickly.

We could have the following three cases:

Case 1:
If a number from set A is not a multiple of 2, then the number from set B must be a multiple of 4 in order for the product to be divisible by 4. The probability of this scenario is 3/5 x 1/5 = 3/25.

Case 2:
If a number from set A is a multiple of 2 but not a multiple of 4, then the number from set B must be a multiple of 2 or 4 for the product to be divisible by 4. The probability of this scenario is 1/5 x 2/5 = 2/25.

Case 3:
If a number from set A is a multiple of 4, then any number from set B will make the product divisible by 4. The probability of this scenario is 1/5 x 5/5 = 5/25.

Thus, the overall probability is 3/25 + 2/25 + 5/25 = 10/25 = 2/5.

Alternate Solution:

The total number of ways to pick one element from set A and one element from set B is 5C1 x 5C1 = 5 x 5 = 25.

The pairs of elements (where the first number comes from set A and the second number comes from set B) where the product is a multiple of 4 are (21, 24), (22, 24), (22, 26), (23, 24), (24, 23), (24, 24), (24, 25), (24, 26), (24, 27), and (25, 24).

Since there are 10 favorable outcomes from a total of 25 outcomes, the probability is 10/25 = 2/5.

The following is the logic I applied. Please let me know why the answer is correct even though I did not consider the case of 22 times 26.

From both the sets (A and B), we can clearly see that only 24 is the number that can break down to give a factor of 4.
Thus, if you pick any number from set A, the number from set B MUST be 24 OR if you pick any number from set B, the number from set A MUST be 24.
Both the sets have 5 numbers each. And Total possibilities of picking the numbers will be 5*5 as no restriction on repetition of the numbers has been given. So, the calculation will be as follows:
[(Any # from A * Only 24 from B)+ (Any # from B * Only 24 from A)] / Total possibilities of picking the numbers

[(5*1) + (5*1)] / 5*5
= [5+5]/25
=10/25
=2/5