Last visit was: 12 Dec 2024, 01:26 It is currently 12 Dec 2024, 01:26
Home
GMAT
Messages
Tests
Schools
Reviews
Social
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Dec 2024
Posts: 97,827
Own Kudos:
685,202
 [5]
Given Kudos: 88,254
Products:
GMAT Club Tests Forum Quiz
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 97,827
Kudos: 685,202
 [5]
A fast-food company plans to build four new restaurants. If there are 12 Apr 2021, 02:45
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

70% (02:00) correct 30% (01:51) wrong based on 139 sessions

History

Date
Time
Result
Not Attempted Yet
A fast-food company plans to build four new restaurants. If there are six sites A, B, C, D, E and F, that satisfy the company’s criteria for location of the new restaurants, in how many different ways can the company select four sites if the order of selection does not matter, given that both the sites A and B cannot be selected simultaneously?

(A) 4
(B) 5
(C) 6
(D) 9
(E) 15
ShowHide Answer
Official Answer
D
User avatar
sumitkrocks
User avatar
Joined: 02 Jul 2017
Last visit: 22 Aug 2023
Posts: 643
Own Kudos:
849
Given Kudos: 333
Location: India
Concentration: Strategy, Technology
Schools: IIMA PGPX'22 ISB'22 NUS '23 ESADE IESE '24 NTU
GMAT 1: 730 Q50 V39
GMAT 2: 710 Q50 V36
Products:
My Reviews
Schools: IIMA PGPX'22 ISB'22 NUS '23 ESADE IESE '24 NTU
GMAT 2: 710 Q50 V36
Posts: 643
Kudos: 849
A fast-food company plans to build four new restaurants. If there are 12 Apr 2021, 02:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Total ways of selecting 4 cities out of 6=6c2
Ways of selecting A and B and any other two cities= 1*4c2
Ways of selecting 4 cities and excluding selection of A&B together= 6C2- 4C2=9
Option D
avatar
SHEHAB01
avatar
Joined: 24 Oct 2020
Last visit: 13 Dec 2022
Posts: 12
Own Kudos:
7
 [1]
Given Kudos: 26
Posts: 12
Kudos: 7
 [1]
A fast-food company plans to build four new restaurants. If there are 14 Aug 2021, 21:06
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sumitkrocks
Total ways of selecting 4 cities out of 6=6c2
Ways of selecting A and B and any other two cities= 1*4c2
Ways of selecting 4 cities and excluding selection of A&B together= 6C2- 4C2=9
Option D

i can't understand why you write 6c2 else 6c4??

Posted from my mobile device
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,114
Own Kudos:
17,797
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,114
Kudos: 17,797
A fast-food company plans to build four new restaurants. If there are 14 Aug 2021, 21:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Total cities = 6

Select 4 out of 6: \(^6{C_4} = ^6{C_2} = 15\)

There is 1 way to select A and B together and remaining 2 cities will be selected from 4: \(^4{C_2} = 6 = 1 * 6 = 6\)

A and B not together: 15 - 6 = 9

Answer D
User avatar
Crytiocanalyst
User avatar
Joined: 16 Jun 2021
Last visit: 27 May 2023
Posts: 965
Own Kudos:
194
 [2]
Given Kudos: 309
Posts: 965
Kudos: 194
 [2]
A fast-food company plans to build four new restaurants. If there are 15 Aug 2021, 06:42
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
A fast-food company plans to build four new restaurants. If there are six sites A, B, C, D, E and F, that satisfy the company’s criteria for location of the new restaurants, in how many different ways can the company select four sites if the order of selection does not matter, given that both the sites A and B cannot be selected simultaneously?

(A) 4
(B) 5
(C) 6
(D) 9
(E) 15

The total ways of selecting 4 cities = 15 or 6c4

The total ways of chosing with A and B chosen = 1*4c2=6

Therefore total way of chosing without picking Aand B = 15-6 =9

Therefore IMO D
avatar
adhya9
avatar
Joined: 30 Nov 2020
Last visit: 10 Nov 2022
Posts: 11
Own Kudos:
9
 [1]
Given Kudos: 183
Posts: 11
Kudos: 9
 [1]
A fast-food company plans to build four new restaurants. If there are 27 Aug 2021, 23:10
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
A fast-food company plans to build four new restaurants. If there are six sites A, B, C, D, E and F, that satisfy the company’s criteria for location of the new restaurants, in how many different ways can the company select four sites if the order of selection does not matter, given that both the sites A and B cannot be selected simultaneously?

(A) 4
(B) 5
(C) 6
(D) 9
(E) 15

IMO D

Choose 4 sites from the given 6: A,B,C,D,E,F
A & B cannot be together in a chosen set

Option 1: A _ _ _ -> 4C3 ways to fill the remaining spots = 4 ways
Option 2: B _ _ _ -> 4C3 ways to fill the remaining spots = 4 ways
Option 3 (No A & B) : _ _ _ _ -> Only have 1 way (C,D,E,F in any order)

So, 4+4+1 = 9 ways
User avatar
RastogiSarthak99
User avatar
Joined: 20 Mar 2019
Last visit: 10 Aug 2024
Posts: 144
Own Kudos:
18
Given Kudos: 282
Location: India
Posts: 144
Kudos: 18
A fast-food company plans to build four new restaurants. If there are 02 Jun 2022, 08:55
Kudos
Add Kudos
Bookmarks
Bookmark this Post
My 2 cents on this:

Note down every aspect. 6 locations/sites and 4 restaurants. Total? 6c4= 15 (Therefore answer cannot be E ever)

Then, we are given the condition, A&B cannot be together. So if we equate Total - A&B together = A&B Not together.

A&B together is straightforward. Consider AB is a block that cannot be separated. AB | CDEF are the blocks. AB will give us 2 restaurants. 2c2. Then CDEF will give us 4c2 = 6

So 15-6 = 9 is the answer.

Tricky, but I'm trying to implement this more and more.
Moderator:
Bunuel
Math Expert
97825 posts