A standardized multiple-choice exam has 60 questions

This answer choice is formed by multiplying by 5 for every new question. We can think about it like this:

For question 1, we have 5 choices — let's say A, B, C, D, and E. So we have 5 possible answer keys so far.

For question 2, we have 5 more choices. So if A is in the answer key for question 1, we can have A, B, C, D, or E for question 2. That's 5 options. If B is in the answer key for question 2, we can again have A, B, C, D, or E for question 3. That's 5 more options. The same is true for C, D, and E for question 1 — 5 more options for each. So for each possible answer key that we had before question 2, we got 5 more options. We have 5 possible answer keys, so know we have 5 * 5 = 25.

For question 3, we have 5 more choices. We already have 25 possible answer keys, so we get 5 more options for each of those: 25 * 5 = 125.

So each question multiplies our number of possible answer keys by 5. We have 60 questions, so we have 5 * 5 * 5 ... 60 times, or 5^60.

This principle is also known as the rule of product, or the multiplication principle. It's pretty commonly tested, so being comfortable with using it will help you out a lot on test day.

M7MBA wrote:A standardized multiple-choice exam has 60 questions, each with five answer choices. How many different answer keys to this test are possible?

A. 1
B. 5(60)
C. 5^30
D. 60^5
E. 5^60

Take the task of completing the test and break it into stages.

Stage 1: Answer question #1
Since their are 5 answer choices, we can complete stage 1 in 5 ways

Stage 2: Answer question #2
Since their are 5 answer choices, we can complete stage 2 in 5 ways

Stage 3: Answer question #3
Since their are 5 answer choices, we can complete this stage in 5 ways
.
.
.
Stage 59: Answer question #59
Since their are 5 answer choices, we can complete this stage in 5 ways

Stage 60: Answer question #60
Since their are 5 answer choices, we can complete this stage in 5 ways

By the Fundamental Counting Principle (FCP), we can complete all 60 stages (and thus complete the test) in (5)(5)(5)....(5)(5) ways (= 5^60 ways)

Answer: E
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Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat- ... /video/775

You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat ... /video/776

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
- https://www.beatthegmat.com/counting-pro ... 44302.html
- https://www.beatthegmat.com/picking-a-5- ... 73110.html
- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html


MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
- https://www.beatthegmat.com/arabian-hors ... 50703.html
- https://www.beatthegmat.com/sub-sets-pro ... 73337.html
- https://www.beatthegmat.com/combinatoric ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
- https://www.beatthegmat.com/combinatoric ... 67079.html


DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
- https://www.beatthegmat.com/permutation- ... 73915.html
- https://www.beatthegmat.com/permutation-t122873.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/combinations-t123249.html


Cheers,
Brent