GMAT Changed on April 16th - Read about the latest changes here

 It is currently 22 Apr 2018, 12:52

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In a multiple-choice test, each question is followed by n options.

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44599
In a multiple-choice test, each question is followed by n options. [#permalink]

### Show Tags

17 Jul 2017, 23:17
Expert's post
4
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

47% (01:52) correct 53% (00:55) wrong based on 129 sessions

### HideShow timer Statistics

In a multiple-choice test, each question is followed by n options. What is the value of n?

(1) The test is designed in such a way that if a candidate appearing for the test, decides to mark the options for every question in a random manner, the candidate would expect to receive ‘0’ marks in the test.

(2) For every correct answer, a candidate is awarded 1 mark and for every wrong answer, there are −1/3 marks assigned.
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 5774
Re: In a multiple-choice test, each question is followed by n options. [#permalink]

### Show Tags

18 Jul 2017, 07:09
Expert's post
1
This post was
BOOKMARKED
In a multiple-choice test, each question is followed by n options. What is the value of n?

(1) The test is designed in such a way that if a candidate appearing for the test, decides to mark the options for every question in a random manner, the candidate would expect to receive ‘0’ marks in the test.
We do not know what is the marking system
Insufficient

(2) For every correct answer, a candidate is awarded 1 mark and for every wrong answer, there are −1/3 marks assigned.
We just know marking system. Nothing more
Insufficient

Combined...
I tells us that he clicks option equally as it is random..
II tells us that there is 1 mark for Correct ans and -1/3 for each wrong answer...

Only one option is correct and others(n-1) wrong..
So 1+(n-1)*(-1/3)=0.....1+1/3=n/3.....4/3=n/3....N=4
Sufficient

C
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

GMAT online Tutor

Verbal Forum Moderator
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 1962
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
Re: In a multiple-choice test, each question is followed by n options. [#permalink]

### Show Tags

18 Jul 2017, 23:59
Bunuel wrote:
In a multiple-choice test, each question is followed by n options. What is the value of n?

(1) The test is designed in such a way that if a candidate appearing for the test, decides to mark the options for every question in a random manner, the candidate would expect to receive ‘0’ marks in the test.

(2) For every correct answer, a candidate is awarded 1 mark and for every wrong answer, there are −1/3 marks assigned.

(1) The test is designed in such a way that if a candidate appearing for the test, decides to mark the options for every question in a random manner, the candidate would expect to receive ‘0’ marks in the test. - Insufficient since we do not know the weightage of correct and incorrect answers

(2) For every correct answer, a candidate is awarded 1 mark and for every wrong answer, there are −1/3 marks assigned - Insufficient - now we only the weightage of correct and incorrect answers - marking system

We know the test taker selects options at random and total score when test takers marks answer options in random manner is 0
1 + (n-1)* -1/3 = 0
=>n/3 = 4/3
=> n =4
_________________

When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
+1 Kudos if you find this post helpful

Manager
Joined: 20 Aug 2015
Posts: 72
GMAT 1: 710 Q50 V36
Re: In a multiple-choice test, each question is followed by n options. [#permalink]

### Show Tags

13 Aug 2017, 09:05
Bunuel wrote:
In a multiple-choice test, each question is followed by n options. What is the value of n?

(1) The test is designed in such a way that if a candidate appearing for the test, decides to mark the options for every question in a random manner, the candidate would expect to receive ‘0’ marks in the test.

(2) For every correct answer, a candidate is awarded 1 mark and for every wrong answer, there are −1/3 marks assigned.

1. We cannot infer n since we do not know the marking system.

2. We know the marking system but cannot infer n since we do not know about total marks earned by the candidate.

Combining both the statements, if the candidate randomly marks the options and earns 0 marks in the test,
since one option is correct and rest n-1 options are wrong-

1 + (n-1)*(-1/3) = 0

Sufficient to calculate n.

Hence ans C.
Manager
Joined: 07 Jun 2017
Posts: 103
Re: In a multiple-choice test, each question is followed by n options. [#permalink]

### Show Tags

28 Aug 2017, 20:07
i dont understand.
how do everyone get the formula -- 1 + (n-1)*(-1/3) = 0
does that mean the candidate get 1 correct, and the other one wrong?
the question is asking how many options for the each question, how do you all get this formula?
Manager
Joined: 20 Aug 2015
Posts: 72
GMAT 1: 710 Q50 V36
In a multiple-choice test, each question is followed by n options. [#permalink]

### Show Tags

28 Aug 2017, 21:39
pclawong wrote:
i dont understand.
how do everyone get the formula -- 1 + (n-1)*(-1/3) = 0
does that mean the candidate get 1 correct, and the other one wrong?
the question is asking how many options for the each question, how do you all get this formula?

Hello pclawong,

Let's say, the candidate guesses the 1st question correctly and gets 1 mark. For each question, only one option is correct and rest of the options are wrong.

If there are n options for each question to choose from, he gets 1 for selecting the right option and (n-1)*(-1/3) for choosing the other (n-1) wrong options for the following questions.

So, our equation becomes 1 + (n-1)*(-1/3) = 0. Sufficient to calculate n.

Hence, both A and B are needed to answer the question correctly.

Doubts?
Manager
Joined: 07 Jun 2017
Posts: 103
Re: In a multiple-choice test, each question is followed by n options. [#permalink]

### Show Tags

29 Aug 2017, 00:01
shoumkrish wrote:
pclawong wrote:
i dont understand.
how do everyone get the formula -- 1 + (n-1)*(-1/3) = 0
does that mean the candidate get 1 correct, and the other one wrong?
the question is asking how many options for the each question, how do you all get this formula?

Hello pclawong,

Let's say, the candidate guesses the 1st question correctly and gets 1 mark. For each question, only one option is correct and rest of the options are wrong.

If there are n options for each question to choose from, he gets 1 for selecting the right option and (n-1)*(-1/3) for choosing the other (n-1) wrong options for the following questions.

So, our equation becomes 1 + (n-1)*(-1/3) = 0. Sufficient to calculate n.

Hence, both A and B are needed to answer the question correctly.

Doubts?

Does that mean this person can select all the options?
so he can at least get 1 point?
does that mean he select all the option for each question?
thank you so much.
it just very confusing to me.
the question states that he ramdomly choose an option but didn't say he chooses all the options
Intern
Joined: 08 Jun 2015
Posts: 21
Location: United States
Concentration: Finance, Economics
WE: Engineering (Other)
In a multiple-choice test, each question is followed by n options. [#permalink]

### Show Tags

Updated on: 29 Aug 2017, 03:59
The Probability(correct ans)=1/n and Probability(incorrect ans)= (1-1/n).

Statement 1: It only provides us the information of what would happen if candidate answers the question in a random way. So clearly not sufficient for answer.

Statement 2: It tells us about the marking scheme of the test. So not sufficient for answer.

If we combine 1 & 2 , we get for every correct answer the candidate gets +1 and for incorrect answer -1/3 and by randomly marking answer candidate can get 0 marks.

So 1*(1/n) - 1/3 X (1-1/n) = 0, solving which we get n=4. So IMO answer is C

Originally posted by shivam2506 on 29 Aug 2017, 00:44.
Last edited by shivam2506 on 29 Aug 2017, 03:59, edited 1 time in total.
Manager
Joined: 20 Aug 2015
Posts: 72
GMAT 1: 710 Q50 V36
In a multiple-choice test, each question is followed by n options. [#permalink]

### Show Tags

29 Aug 2017, 02:37
pclawong wrote:
shoumkrish wrote:
pclawong wrote:
i dont understand.
how do everyone get the formula -- 1 + (n-1)*(-1/3) = 0
does that mean the candidate get 1 correct, and the other one wrong?
the question is asking how many options for the each question, how do you all get this formula?

Hello pclawong,

Let's say, the candidate guesses the 1st question correctly and gets 1 mark. For each question, only one option is correct and rest of the options are wrong.

If there are n options for each question to choose from, he gets 1 for selecting the right option and (n-1)*(-1/3) for choosing the other (n-1) wrong options for the following questions.

So, our equation becomes 1 + (n-1)*(-1/3) = 0. Sufficient to calculate n.

Hence, both A and B are needed to answer the question correctly.

Doubts?

Does that mean this person can select all the options?
so he can at least get 1 point?
does that mean he select all the option for each question?
thank you so much.
it just very confusing to me.
the question states that he ramdomly choose an option but didn't say he chooses all the options

Does that mean this person can select all the options? No.
does that mean he select all the option for each question? Also no.

Each question has n options, out of which only one is correct. He chooses only one option per question, which could be either correct or incorrect.

Let's say, he chooses the right option for the first question. His score is 1.
For the next question, he chooses one out of those (n-1) wrong options. He gets -1/3. So his total score now is 1-(1/3) = 2/3.
He continues to do this till his score is 0.

So, the equation is 1+(n-1) * (-1/3) = 0
Senior Manager
Joined: 02 Apr 2014
Posts: 469
In a multiple-choice test, each question is followed by n options. [#permalink]

### Show Tags

20 Nov 2017, 12:56
Statements 1 and 2 are clearly insufficient on their own.

combining,

Let number of correct answers be $$a$$
Let number of incorrect answers be $$b$$

Total marks in random manner = $$a(1) + b(-1/3) = 0$$
=> $$b = 3a$$

=> For every correct question answered, 3 questions will be incorrectly answered
=> for this to happen, there has to be 4 options, so that out of 4 questions attended, 3 will be incorrect and 1 will be correct

so answer is 4 options (C)
In a multiple-choice test, each question is followed by n options.   [#permalink] 20 Nov 2017, 12:56
Display posts from previous: Sort by