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

It is currently 21 Mar 2019, 00:49

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

Robin and Terry want to invite 5 of their friends to their wedding. Ro

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53748
Robin and Terry want to invite 5 of their friends to their wedding. Ro  [#permalink]

Show Tags

New post 27 Feb 2019, 23:29
1
3
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

64% (03:13) correct 36% (02:46) wrong based on 25 sessions

HideShow timer Statistics

Robin and Terry want to invite 5 of their friends to their wedding. Robin has 7 friends, Terry has 6, and Robin and Terry have no friends in common. If at least 1 of Robin’s friends and at least 1 of Terry’s friends must be invited, how many different groups of friends could Robin and Terry invite to their wedding?

A. 462
B. 924
C. 1,260
D. 2,520
E. 151,200

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

SVP
SVP
User avatar
P
Joined: 18 Aug 2017
Posts: 2408
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: Robin and Terry want to invite 5 of their friends to their wedding. Ro  [#permalink]

Show Tags

New post 28 Feb 2019, 04:45
Bunuel wrote:
Robin and Terry want to invite 5 of their friends to their wedding. Robin has 7 friends, Terry has 6, and Robin and Terry have no friends in common. If at least 1 of Robin’s friends and at least 1 of Terry’s friends must be invited, how many different groups of friends could Robin and Terry invite to their wedding?

A. 462
B. 924
C. 1,260
D. 2,520
E. 151,200



total friends = 13
so 13*12*11*10*9 / 5! ; 1287 groups possible
now since question has asked at least 1 friend each of tony & robin
Robin 7*6*5*4*3/5! = 21
and Terry ; 6*5*4*3*2/5! = 6
total Robin & Terry = 27
subtract it from 1287 -27 = 1260 groups can be invited
_________________

If you liked my solution then please give Kudos. Kudos encourage active discussions.

Manager
Manager
avatar
G
Joined: 01 Feb 2017
Posts: 201
Re: Robin and Terry want to invite 5 of their friends to their wedding. Ro  [#permalink]

Show Tags

New post 28 Feb 2019, 14:08
1
Without restriction: 13C5= 1287
Only Robin's: 7C5= 21
Only Terry's: 6C5= 6

Remaining options: 1287-21-6= 1260

Ans C

Posted from my mobile device
Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 5380
Location: United States (CA)
Re: Robin and Terry want to invite 5 of their friends to their wedding. Ro  [#permalink]

Show Tags

New post 04 Mar 2019, 20:08
Bunuel wrote:
Robin and Terry want to invite 5 of their friends to their wedding. Robin has 7 friends, Terry has 6, and Robin and Terry have no friends in common. If at least 1 of Robin’s friends and at least 1 of Terry’s friends must be invited, how many different groups of friends could Robin and Terry invite to their wedding?

A. 462
B. 924
C. 1,260
D. 2,520
E. 151,200


We see that there are 4 cases possible: Robin invites 1, 2, 3 or 4 friends (notice that Robin can’t invite 0 friend since she has to invite at least 1 friend, and she can’t invite 5 friends since Terry has to invite at least 1 friend).

1) If Robin invites 1 friend, then Terry invites 4, and there are 7C1 x 6C4 = 7 x 15 = 105 ways to invite 5 of their friends.

2) If Robin invites 2 friends, then Terry invites 3, and there are 7C2 x 6C3 = 21 x 20 = 420 ways to invite 5 of their friends.

3) If Robin invites 3 friends, then Terry invites 2, and there are 7C3 x 6C2 = 35 x 15 = 525 ways to invite 5 of their friends.

4) If Robin invites 4 friends, then Terry invites 1, and there are 7C4 x 6C1 = 35 x 6 = 210 ways to invite 5 of their friends.

Therefore, the total number of ways to invite 5 of their friends is 105 + 420 + 525 + 210 = 1,260.

Alternate Solution:

If there were no restrictions, 5 people among a total of 6 + 7 = 13 people could have been chosen in 13C5 = 13!/(5!*8!) = (13 x 12 x 11 x 10 x 9)/(5 x 4 x 3 x 2) = 13 x 11 x 9 = 1287 ways.

From these 1287, we must subtract the sum of the number of ways in which Robin invites 5 friends and Terry invites 5 friends.

Since Robin has 7 friends, she can choose 5 friends in 7C5 = 21 ways. Similarly, since Terry has 6 friends, he can choose 5 friends in 6C5 = 6 ways. Therefore, 21 + 6 = 27 of the 1287 choices are those in which either party invites no friends. Thus, 5 friends can be invited in 1287 - 27 = 1260 ways such that either party invites at least one friend.

Answer: C
_________________

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

GMAT Club Bot
Re: Robin and Terry want to invite 5 of their friends to their wedding. Ro   [#permalink] 04 Mar 2019, 20:08
Display posts from previous: Sort by

Robin and Terry want to invite 5 of their friends to their wedding. Ro

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.