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

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Math Expert
Joined: 02 Sep 2009
Posts: 43831
A standardized multiple-choice exam has 60 questions, each with five [#permalink]

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02 Apr 2017, 23:31
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Difficulty:

45% (medium)

Question Stats:

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

_________________
Senior Manager
Joined: 19 Apr 2016
Posts: 275
Location: India
GMAT 1: 570 Q48 V22
GMAT 2: 640 Q49 V28
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WE: Web Development (Computer Software)
A standardized multiple-choice exam has 60 questions, each with five [#permalink]

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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
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Manager
Joined: 18 Oct 2016
Posts: 139
Location: India
WE: Engineering (Energy and Utilities)
Re: A standardized multiple-choice exam has 60 questions, each with five [#permalink]

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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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Posts: 1975
Re: A standardized multiple-choice exam has 60 questions, each with five [#permalink]

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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.

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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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