GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Feb 2019, 18:23

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT Algebra Webinar

February 17, 2019

February 17, 2019

07:00 AM PST

09:00 AM PST

Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
• ### Valentine's day SALE is on! 25% off.

February 18, 2019

February 18, 2019

10:00 PM PST

11:00 PM PST

We don’t care what your relationship status this year - we love you just the way you are. AND we want you to crush the GMAT!

# A multiple-choice exam consists of 7 questions and each

Author Message
TAGS:

### Hide Tags

Manager
Joined: 25 Sep 2018
Posts: 187
Location: United States (CA)
Concentration: Finance, Strategy
GMAT 1: 640 Q47 V30
GPA: 3.97
WE: Investment Banking (Investment Banking)
A multiple-choice exam consists of 7 questions and each  [#permalink]

### Show Tags

14 Oct 2018, 00:03
1
5
00:00

Difficulty:

65% (hard)

Question Stats:

44% (02:05) correct 56% (02:10) wrong based on 47 sessions

### HideShow timer Statistics

A multiple-choice exam consists of 7 questions and each question has 3 answer choices. For every question there is exactly one correct answer. If a student randomly guesses at each question, what is the probability that she will correctly answer exactly 4 questions?
A) $$\frac{8}{3^7}$$
B)$$\frac{1}{3^4}$$
C)$$\frac{240}{3^7}$$
D)$$\frac{280}{3^7}$$
E)$$\frac{140}{3^5}$$

_________________

Why do we fall?...So we can learn to pick ourselves up again

If you like the post, give it a KUDOS!

Manager
Joined: 21 Jun 2017
Posts: 234
Concentration: Finance, Economics
WE: Corporate Finance (Commercial Banking)
Re: A multiple-choice exam consists of 7 questions and each  [#permalink]

### Show Tags

14 Oct 2018, 00:22
4
Correct in 1 way. Not correct in two ways.
CCCCNNN
= 7!/4!3! = 35.
Since each not correct can have two possibilities ----> total favourable = 2*2*2*35 = 280
Total outcomes = 3*3*3*3*3*3*3 = 3^7
D
_________________

Even if it takes me 30 attempts, I am determined enough to score 740+ in my 31st attempt. This is it, this is what I have been waiting for, now is the time to get up and fight, for my life is 100% my responsibility.

Dil ye Ziddi hai !!!

Intern
Joined: 19 Sep 2016
Posts: 42
Re: A multiple-choice exam consists of 7 questions and each  [#permalink]

### Show Tags

14 Oct 2018, 13:25
can someone explain in detail ??
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2568
Re: A multiple-choice exam consists of 7 questions and each  [#permalink]

### Show Tags

14 Oct 2018, 16:07

Solution

Given:
• A multiple-choice exam consists of 7 questions

To find:
• Probability that she will correctly answer exactly 4 questions.

Approach and Working:
Probability to correctly answer exactly 4 questions= $$\frac{Total\ ways\ to\ correctly\ answer\ 4\ questions}{Total\ ways\ to\ mark\ 7\ questions}$$.

Total ways to mark 7 questions:

• Each question can be marked in 3 ways.
o Either 1st option or 2nd or 3rd.
• Therefore, ways to answer 7 questions= 3*3*3*3*3*3*3= $$3^7$$.

Ways to mark 4 questions correctly

• Out of 7 questions, we need to select 4 questions whose answers must be correct.
o And, we can select the 4 correct questions in 7c4 ways.
o Now, for each correct question, there can only be one way- Correct option.
o However, for each incorrect question, there can be two ways- 2 incorrect options.
 Hence, total ways to mark 4 questions correct= 7c4* 1*2*2*2= 35*8= 280

Hence, Probability to correctly answer exactly 4 questions= $$\frac{280}{3^7}$$

Hence, the correct answer is option D.

_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Manager
Joined: 24 Jun 2013
Posts: 132
Location: India
Schools: ISB '20
Re: A multiple-choice exam consists of 7 questions and each  [#permalink]

### Show Tags

15 Oct 2018, 07:46
ShankSouljaBoi wrote:
Correct in 1 way. Not correct in two ways.
CCCCNNN
= 7!/4!3! = 35.
Since each not correct can have two possibilities ----> total favourable = 2*2*2*35 = 280
Total outcomes = 3*3*3*3*3*3*3 = 3^7
D

Great explanation, just to tweak a little

desired outcome CCCCWWW :
the probability for correct answer is $$\frac{1}{3}$$ and same for wrong answer is $$\frac{2}{3}$$
we can directly write P(CCCCWWW)= $$\frac{7!}{4!3!}*\frac{1}{3}*\frac{1}{3}*\frac{1}{3}*\frac{1}{3}*\frac{2}{3}*\frac{2}{3}*\frac{2}{3}$$ = $$\frac{280}{3^7}$$
_________________

If this post helped you learn something pls give kudos

Re: A multiple-choice exam consists of 7 questions and each   [#permalink] 15 Oct 2018, 07:46
Display posts from previous: Sort by