Source: Official Guide for the GMAT 13th Ed. Problem Solving; #68 Official Guide for the GMAT 2015 14th Ed. Problem Solving; #68

1

Two integers will be randomly selected from

Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability that the sum of two integers will equal 9?

2 Explanations

1

Probability: Number of desired / possible outcomes

desired: 4 operations (2+7, 3+6, 4+5, 5+4)
outcomes: elements in A * elements in B = 4 * 5 possible operations.

P = desired / outcomes: 4 / 20 = 2/10 = 0.2

Jan 25, 2015 • Comment

Maria Chernaya

I also did it this way. I calculated the total number of possibilities using combinations. For set A there are 4 ways to choose 1 out of 4. For set B there are 5 ways to choose 1 out of 5. In total, there are 4 * 5 or 20 total possible choices.

Nov 24, 2015 • Reply

Cydney Seigerman, Magoosh Tutor

That's a perfectly valid way to approach this question :-) Since, as Jose noted, probability can be expressed as the number of desired outcomes over the total number of possible outcomes, we can solve this problem by determine how many ways we can have a sum of 9 and divide this value by the total number of combinations. Well done!

Nov 29, 2015 • Reply

Imtisal A Siddiqui

How did we get 20 total outcomes?

Feb 5, 2018 • Reply

David Recine, Magoosh Tutor

Basically, we want to see how many possible pairings there are *total* between set A and set B, including pairings that do NOT add up to 9. Without this number of outcomes, we won't be able to understand the odds of getting a pair from the subset of pairings that DO add up to 9.

To calculate the total number of pairs between two sets, we multiply the total number of individual figures in one set by the total number of individual figures in the second set.

Set A has 4 numbers. Set B has 5 numbers. 4*5 = 20, so there are 20 possible pairings of elements from set A and set B. Does that make sense? Certainly let me know if you have additional questions, Siddiqui. :)

Feb 6, 2018 • Reply

3

Gravatar Mike McGarry, Magoosh Tutor

Dec 27, 2013 • Comment

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