Answer to GMAT Question #15

Here is the answer to GMAT Practice Question #15

Answer: D

Explanation:
In this probability question, we are asked to determine the probability of choosing a specific group in which the order doesn’t matter. To do so, we first need to know how many total possible groups there are to choose. To do this:

Step 1: How many spaces are there to fill? We will choose 6 numbers, so there are 6 spaces to fill: __ x __ x __ x __ x __ x __

Step 2: What goes in those spaces? Because we are figuring out how many TOTAL possible groups there are, we will assume at first that anything is possible. So we don’t worry about even and odd numbers, and just pay attention to the 8 total numbers in the mix. So we have: _8_ x _7_ x _6_ x _5_ x _4_ x _3_. Remember, you don’t need to do the math at this point, you will cancel later.

Step 3: Does the order matter? In this case it does not; we are not asked for a particular order of the numbers, so we divide the above by the number of spaces, factorial: (_8_ x _7_ x _6_ x _5_ x _4_ x _3_)/6!. After cancellation, we are left with 4 x 7 = 28

So there are 28 total ways to pull 6 numbers from 8 numbers when the order does not matter.

Now we need to know how many ways we can pull 3 odds and 3 evens from a group of 4 odds and 4 evens. That follows the same process above, for each. Let’s look at just the odds:

Step 1: How many spaces are there to fill? We will choose 3 numbers, so there are 3 spaces to fill: __ x __ x __

Step 2: What goes in those spaces? Now there are only 4 numbers to choose from, because we are focusing on the odds exclusively. So we have: _4_ x _3_ x _2_.

Step 3: Does the order matter? In this case it does not; we are not asked for a particular order of the numbers, so we divide the above by the number of spaces, factorial: (_4_ x _3_ x _2_)/3!. After cancellation, we are left with just 4.

Follow the same process for the even numbers.

Now we just put it all together. There are 4 ways to choose the even numbers and 4 ways to choose the odd numbers, so we multiply to find the number of ways they are combined: 16.

There are 28 total ways to choose 6 numbers.

So the final probability is 16/28, or 4/7.

The answer and explanation to GMAT Practice Question #15 was written by Integrated Learning, a company that provides professional and private one on one tutoring services.