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A standardized multiple-choice exam has 60 questions, each with five

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A standardized multiple-choice exam has 60 questions, each with five [#permalink]

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New post 02 Apr 2017, 23:31
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59% (00:24) correct 41% (00:49) wrong based on 47 sessions

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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
[Reveal] Spoiler: OA

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A standardized multiple-choice exam has 60 questions, each with five [#permalink]

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New post 03 Apr 2017, 01:34
Bunuel 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


Nice Question +1Kudos

We have to answer 60 questions.
For each question, we have 5 possible answer choices.

So,for the 1st question we have 5 options(either A or B or C or D or E) out of which 1 will be correct at a given point of time,
for the 2nd question we have 5 options(either A or B or C or D or E) out of which 1 will be correct at a given point of time
for the 3rd question we have 5 options(either A or B or C or D or E) out of which 1 will be correct at a given point of time .....and
60th question we have 5 options(either A or B or C or D or E) out of which 1 will be correct at a given point of time.

Therefore, different answer keys to this test possible are =5*5*5*5*5*....(up-to 60 times 5) =\(5^{60}\)

Hence option E is correct
Hit Kudos if you liked it 8-)
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Re: A standardized multiple-choice exam has 60 questions, each with five [#permalink]

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New post 03 Apr 2017, 08:57
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Option E

Each question can be answered in 5C1 = 5 ways
Hence, 60 questions can be answered in 5C1*5C1*5C1* . . . 60 times = 5^60 ways.
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Re: A standardized multiple-choice exam has 60 questions, each with five [#permalink]

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New post 06 Apr 2017, 08:34
Bunuel 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


Since there are 60 questions in the exam and each question has five answer choices, the number of different possible answer keys is 5^60.

Answer: E
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Re: A standardized multiple-choice exam has 60 questions, each with five   [#permalink] 06 Apr 2017, 08:34
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