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

It is currently 15 Oct 2019, 05:13

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

A man 8 friends whom he wants to invite for dinner. The number of ways

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Senior Manager
Senior Manager
User avatar
G
Joined: 02 Mar 2017
Posts: 256
Location: India
Concentration: Finance, Marketing
A man 8 friends whom he wants to invite for dinner. The number of ways  [#permalink]

Show Tags

New post 27 Apr 2017, 06:35
1
8
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

49% (01:41) correct 51% (01:14) wrong based on 130 sessions

HideShow timer Statistics

A man 8 friends whom he wants to invite for dinner. The number of ways in which he can invite at least one of them is

A)8
B)255
C)8!-1
D)256
E)7

Source :Quantpdf

_________________
Kudos-----> If my post was Helpful
Most Helpful Expert Reply
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4000
Location: Canada
Re: A man 8 friends whom he wants to invite for dinner. The number of ways  [#permalink]

Show Tags

New post 27 Apr 2017, 06:46
2
Top Contributor
7
VyshakhR1995 wrote:
A man 8 friends whom he wants to invite for dinner.The number of ways in which he can invite at least one of them is

A) 8
B) 255
C) 8!-1
D) 256
E) 7



Take the task of inviting friends and break it into stages.

ASIDE: Let's let A, B, C, D, E, F, G and H represent the 8 friends

Stage 1: Decide whether or not to invite friend A
You have 2 options: invite friend A or don't invite friend A
So, we can complete stage 1 in 2 ways

Stage 2: Decide whether or not to invite friend B
You have 2 options: invite friend B or don't invite friend B
So, we can complete stage 2 in 2 ways

Stage 3: Decide whether or not to invite friend C
So, we can complete stage 3 in 2 ways
.
.
.
Stage 8: Decide whether or not to invite friend H
So, we can complete stage 8 in 2 ways

By the Fundamental Counting Principle (FCP), we can complete all 8 stages (and create a guest list) in (2)(2)(2)(2)(2)(2)(2)(2) ways (= 256 ways)

NOTE: in these calculations, one of the possible outcomes is that ZERO friends are invited. The question says that AT LEAST ONE friend must come.
So, we must subtract this 1 outcome from our solution.

So, total number of ways to invite friends = 256 - 1 = 255

Answer:

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

RELATED VIDEOS





_________________
Test confidently with gmatprepnow.com
Image
General Discussion
SVP
SVP
User avatar
V
Joined: 26 Mar 2013
Posts: 2345
Reviews Badge CAT Tests
Re: A man 8 friends whom he wants to invite for dinner. The number of ways  [#permalink]

Show Tags

New post 28 Apr 2017, 04:08
GMATPrepNow wrote:
VyshakhR1995 wrote:
A man 8 friends whom he wants to invite for dinner.The number of ways in which he can invite at least one of them is

A) 8
B) 255
C) 8!-1
D) 256
E) 7



Take the task of inviting friends and break it into stages.

ASIDE: Let's let A, B, C, D, E, F, G and H represent the 8 friends

Stage 1: Decide whether or not to invite friend A
You have 2 options: invite friend A or don't invite friend A
So, we can complete stage 1 in 2 ways

Stage 2: Decide whether or not to invite friend B
You have 2 options: invite friend B or don't invite friend B
So, we can complete stage 2 in 2 ways

Stage 3: Decide whether or not to invite friend C
So, we can complete stage 3 in 2 ways
.
.
.
Stage 8: Decide whether or not to invite friend H
So, we can complete stage 8 in 2 ways

By the Fundamental Counting Principle (FCP), we can complete all 8 stages (and create a guest list) in (2)(2)(2)(2)(2)(2)(2)(2) ways (= 256 ways)

NOTE: in these calculations, one of the possible outcomes is that ZERO friends are invited. The question says that AT LEAST ONE friend must come.
So, we must subtract this 1 outcome from our solution.

So, total number of ways to invite friends = 256 - 1 = 255

Answer:



Hi Brent,

Can you show another approach?

What 'at least' mean?
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4000
Location: Canada
Re: A man 8 friends whom he wants to invite for dinner. The number of ways  [#permalink]

Show Tags

New post 28 Apr 2017, 06:03
Top Contributor
Mo2men wrote:

Hi Brent,

Can you show another approach?

What 'at least' mean?


"at least" means "greater than or equal to"

So, if I say that I own at least 3 guitars, then the number of guitars I own = 3 or 4 or 5 or 6....


Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4000
Location: Canada
Re: A man 8 friends whom he wants to invite for dinner. The number of ways  [#permalink]

Show Tags

New post 28 Apr 2017, 06:09
1
Top Contributor
1
VyshakhR1995 wrote:
A man 8 friends whom he wants to invite for dinner.The number of ways in which he can invite at least one of them is

A) 8
B) 255
C) 8!-1
D) 256
E) 7


Another approach (for Mo2men :-D )

Number of ways to invite at least 1 friend = (# of ways to invite exactly 1 friend) + (# of ways to invite exactly 2 friends) + (# of ways to invite exactly 3 friends) + (# of ways to invite exactly 4 friends) + . . . . + (# of ways to invite exactly 8 friends)

Since the order in which we invite the friends does not matter, we can use COMBINATIONS.
For example, the number of ways to invite exactly 2 friends = 8C2
And the number of ways to invite exactly 3 friends = 8C3
etc.

So, the number of ways to invite at least 1 friend = 8C1 + 8C2 + 8C3 + . . . + 8C7 + 8C8
= 8 + 28 + 56 + 70 + 56 + 28 + 8 + 1
= 255

RELATED VIDEO

_________________
Test confidently with gmatprepnow.com
Image
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8043
Location: United States (CA)
Re: A man 8 friends whom he wants to invite for dinner. The number of ways  [#permalink]

Show Tags

New post 02 May 2017, 16:51
1
VyshakhR1995 wrote:
A man 8 friends whom he wants to invite for dinner.The number of ways in which he can invite at least one of them is

A)8
B)255
C)8!-1
D)256
E)7


We can use the following equation:

Total number of ways to invite friends = number of ways to invite at least one friend - number of ways to invite zero friends.

The total number of ways the man can invite his friends is 2^8 since he can or cannot invite each friend. The number of ways to invite no friends is 1. Thus, the number of ways to invite at least one friend is 2^8 - 1 = 256 - 1 = 255.

Answer: B
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Intern
avatar
B
Joined: 05 Mar 2015
Posts: 41
Location: Azerbaijan
GMAT 1: 530 Q42 V21
GMAT 2: 600 Q42 V31
GMAT 3: 700 Q47 V38
Re: A man 8 friends whom he wants to invite for dinner. The number of ways  [#permalink]

Show Tags

New post 11 Aug 2018, 09:13
The question could be interpreted in another way. "If we will flip a coin 8 times what is the number of ways we get at least one tail"

When you flip a coin 8 times there are 2^8 different ways the result may come out. One of the possible results is to get 8 heads - HHHHHHHH. Now you can imagine tail is to invite a friend and head is not to invite. Getting 8 heads means not to invite any of them.

Therefore, all outcomes satisfy us except when we get eight heads. There is only one way to get 8 heads. So we deduct this one outcome from total number of possible outcomes
Manager
Manager
User avatar
S
Joined: 18 Jul 2015
Posts: 71
GMAT 1: 530 Q43 V20
WE: Analyst (Consumer Products)
GMAT ToolKit User
A man 8 friends whom he wants to invite for dinner. The number of ways  [#permalink]

Show Tags

New post 18 Aug 2019, 05:46
VyshakhR1995 wrote:
A man 8 friends whom he wants to invite for dinner. The number of ways in which he can invite at least one of them is

A)8
B)255
C)8!-1
D)256
E)7

Source :Quantpdf


An alternate approach for this question would be to find the subsets of a set with 8 entities.

Lets take a smaller set, say there were only 3 friends (A, B & C) then the ways to invite at least 1 would be A, B, C, AB, AC, BC and ABC (7 ways). This is \(2^n-1\) \([2^3-1 = 7]\) in terms of the formula to find the subset of a set with n entities. We subtracted 1 because \(2^n\) also includes an empty set, whereas we have been provided a constraint of at least 1.

Applying the same to the problem at hand, there are 8 friends, hence \(2^8-1 = 256-1 = 255\) (Ans B)
_________________
Cheers. Wishing Luck to Every GMAT Aspirant!
SVP
SVP
User avatar
P
Joined: 03 Jun 2019
Posts: 1684
Location: India
Premium Member Reviews Badge CAT Tests
A man 8 friends whom he wants to invite for dinner. The number of ways  [#permalink]

Show Tags

New post 18 Aug 2019, 07:33
VyshakhR1995 wrote:
A man 8 friends whom he wants to invite for dinner. The number of ways in which he can invite at least one of them is

A)8
B)255
C)8!-1
D)256
E)7

Source :Quantpdf


Given: A man 8 friends whom he wants to invite for dinner.

Asked: The number of ways in which he can invite at least one of them is

No of ways to invite at least 1 friends = \(^8C_1 + ^8C_2 + ^8C_3 + ^8C_4 + ^8C_5 + ^8C_6 + ^8C_7 + ^8C_8\)

\((1+x)^n = ^nC_0 x^0 + ^nC_1 x + ^nC_2 x^2 + ... + ^nC_r x^r +.... + ^nC_n x^n\)

n =8
\((1+x)^8 = ^8C_0 x^0 + ^8C_1 x + ^8C_2 x^2 + ... + ^8C_r x^r +.... + ^8C_8 x^n\)
When x =1
\(2^8 = 1 + ^8C_1 + ^8C_2 + ^8C_3 + ^8C_4 + ^8C_5 + ^8C_6 + ^8C_7 + ^8C_8\)
\(2^8 -1= ^8C_1 + ^8C_2 + ^8C_3 + ^8C_4 + ^8C_5 + ^8C_6 + ^8C_7 + ^8C_8 = 256-1 =255\)

IMO B
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
GMAT Club Bot
A man 8 friends whom he wants to invite for dinner. The number of ways   [#permalink] 18 Aug 2019, 07:33
Display posts from previous: Sort by

A man 8 friends whom he wants to invite for dinner. The number of ways

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne