A = {0, 1, -3, 6, -8} B = {-1, 2, -4, 7} If a is a number t

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A = {0, 1, -3, 6, -8} B = {-1, 2, -4, 7} If a is a number t

by BTGmoderatorAT » Sat Sep 30, 2017 8:33 pm

A = {0, 1, -3, 6, -8}
B = {-1, 2, -4, 7}

If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0?

A. 1/4
B. 1/3
C. 2/5
D. 4/9
E. 1/2

I'm confused how to set up the formulas here. Any experts help?

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Source: Beat The GMAT — Problem Solving | Sat Sep 30, 2017 8:33 pm

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by [email protected] » Sun Oct 01, 2017 10:23 am

Hi ardz24,

A = {0, 1, -3, 6, -8}
B = {-1, 2, -4, 7}

Since Set A has 5 elements and Set B has 4 elements, there are (5)(4) = 20 possible 'pairs.' We're asked for the probability that the (element from A)(element from B) > 0.

For that product to be greater than 0, the elements must either be both positive OR both negative. Those options are:
1 and 2
1 and 7
-3 and -1
-3 and -4
6 and 2
6 and 7
-8 and -1
-8 and -4

8 out of 20 = 8/20 = 2/5

Final Answer: C

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Rich

Contact Rich at [email protected]

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A = {0, 1, -3, 6, -8} B = {-1, 2, -4, 7} If a is a number t

by EconomistGMATTutor » Sun Oct 08, 2017 10:04 am

ardz24 wrote:A = {0, 1, -3, 6, -8}
B = {-1, 2, -4, 7}

If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0?

A. 1/4
B. 1/3
C. 2/5
D. 4/9
E. 1/2

I'm confused how to set up the formulas here. Any experts help?

Hi ardz24,
Let's take a look at your question.

A = {0, 1, -3, 6, -8}
B = {-1, 2, -4, 7}
a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, then we will first check for all the possibilities of ab>0 to find the probability.
Total possibilities of making products of two numbers one from set A and other from set B = (Number of elements in Set A) x (Number of elements in set B)
Total outcomes = 5 x 4 = 20

Now, we will find out all the products that are greater than zero i.e. ab>0
1 x 2 = 2
1 x 7 = 7
-3 x -1 = 3
-3 x - 4 = 12
6 x 2 = 12
6 x 7 = 42
-8 x -1 = 8
-8 x -4 = 32
Hence, there are 8 possibilities out of 20 that results into ab>0.
P(ab>0) = 8/20 = 2/5

Therefore, Option C is true.

I am available if you'd like any followup.

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