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

It is currently 15 Jun 2019, 19:47

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

In how many ways can 10 different paintings be distributed between two

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

Hide Tags

 
Senior Manager
Senior Manager
User avatar
D
Joined: 24 Oct 2016
Posts: 461
GMAT 1: 670 Q46 V36
GMAT 2: 690 Q47 V38
In how many ways can 10 different paintings be distributed between two  [#permalink]

Show Tags

New post 23 May 2019, 15:12
3
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

73% (02:20) correct 27% (02:17) wrong based on 15 sessions

HideShow timer Statistics

In how many ways can 10 different paintings be distributed between two collectors – Dave and Mona – if both collectors should get an even number of paintings? (All paintings should be given away.)

A) 128
B) 256
C) 420
D) 512
E) 1024

_________________

Most Comprehensive Article on How to Score a 700+ on the GMAT (NEW)
Verb Tenses Simplified



If you found my post useful,

KUDOS

are much appreciated. Giving Kudos is a great way to thank and motivate contributors, without costing you anything.
Senior Manager
Senior Manager
User avatar
D
Joined: 24 Oct 2016
Posts: 461
GMAT 1: 670 Q46 V36
GMAT 2: 690 Q47 V38
Re: In how many ways can 10 different paintings be distributed between two  [#permalink]

Show Tags

New post 23 May 2019, 15:12
dabaobao wrote:
In how many ways can 10 different paintings be distributed between two collectors – Dave and Mona – if both collectors should get an even number of paintings? (All paintings should be given away.)

A) 128
B) 256
C) 420
D) 512
E) 1024


Official Solution


Credit: Veritas Prep


Paintings can be distributed in the following ways:

0, 10 – One person gets 0 paintings and the other gets 10

2, 8 – One person gets 2 paintings and the other gets 8

4, 6 – One person gets 4 paintings and the other gets 6

You will need to calculate each one of these ways and then add them. Note that the ‘Total – Opposite’ method does not work here because finding the number of ways in which each person gets odd number of paintings is equally daunting.

Case 1: 0, 10

One person gets 0 paintings and the other gets 10. This can be done in 2 ways – either Dave gets all the paintings or Mona gets them.

Case 2: 2, 8

One person gets 2 paintings and the other gets 8. Select 2 paintings out of 10 for Dave in 10C2 = 45 ways. Mona could also get the 2 selected paintings so total number of ways = 45*2 = 90 ways

Case 3: 4, 6

One person gets 4 paintings and the other gets 6. Select 4 paintings out of 10 for Dave in 10C4 = 210 ways. Mona could also get the 4 selected paintings so total number of ways = 210*2 = 420

Total number of ways such that each person gets even number of paintings = 2 + 90 + 420 = 512 ways

But 512 is 2^9 – in form, suspiciously close to 2^10 we used in question 2 above. Is there some logic which leads to the answer 2^(n-1)? There is!

You have 10 different paintings. Each painting can be given to one of the 2 people in 2 ways. You do that with 9 paintings in 2*2*2… = 2^9 ways. When you distribute 9 paintings, one person will have odd number of paintings and one will have even number of paintings (0 + 9 or 1 + 8 or 2 + 7 or 3 + 6 or 4 + 5).

The tenth painting needs to be given to the person who has the odd number of paintings so you give the tenth painting in only one way. This accounts for all cases in which both get even number of paintings.

Total ways = 2^9 * 1 = 512

ANSWER: D
_________________

Most Comprehensive Article on How to Score a 700+ on the GMAT (NEW)
Verb Tenses Simplified



If you found my post useful,

KUDOS

are much appreciated. Giving Kudos is a great way to thank and motivate contributors, without costing you anything.
GMAT Club Bot
Re: In how many ways can 10 different paintings be distributed between two   [#permalink] 23 May 2019, 15:12
Display posts from previous: Sort by

In how many ways can 10 different paintings be distributed between two

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


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