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

It is currently 23 Jun 2018, 12:46

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

D01-39

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

Hide Tags

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46297
D01-39 [#permalink]

Show Tags

New post 16 Sep 2014, 00:13
2
9
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

66% (01:20) correct 34% (01:59) wrong based on 179 sessions

HideShow timer Statistics

Romi has a collection of 10 distinct books out of which 8 are small and 2 are large. In how many ways can he select 5 books to take with him on a trip if he can take at most 1 large book?

A. 56
B. 126
C. 152
D. 196
E. 252

_________________

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

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46297
Re D01-39 [#permalink]

Show Tags

New post 16 Sep 2014, 00:13
2
2
Official Solution:

Romi has a collection of 10 distinct books out of which 8 are small and 2 are large. In how many ways can he select 5 books to take with him on a trip if he can take at most 1 large book?

A. 56
B. 126
C. 152
D. 196
E. 252

Since Romi can take at most 1 large book then he can take with him either 5 small books or 4 small books and 1 large book: \(C^5_8+C^4_8*C^1_2=56+140=196\).

Answer: D
_________________

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

Intern
Intern
avatar
Joined: 11 Jan 2015
Posts: 3
GPA: 3.3
Re: D01-39 [#permalink]

Show Tags

New post 13 Jan 2015, 11:12
Could you pls explain this math in other way except

Since Romi can take at most 1 large book then he can take with him either 5 small books or 4 small books and 1 large book: C^5_8+C^4_8*C^1_2=56+140=196.
Intern
Intern
avatar
Joined: 13 Nov 2011
Posts: 18
Re: D01-39 [#permalink]

Show Tags

New post 14 Dec 2015, 07:07
"C^5_8 = 56" how is this derived?
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46297
Re: D01-39 [#permalink]

Show Tags

New post 17 Dec 2015, 09:23
Intern
Intern
avatar
Joined: 08 Nov 2015
Posts: 2
Re: D01-39 [#permalink]

Show Tags

New post 17 Dec 2015, 19:08
Can you explain what the C^5/8 means. How do I get to 56 from this?
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46297
Re: D01-39 [#permalink]

Show Tags

New post 20 Dec 2015, 11:35
Intern
Intern
avatar
Joined: 31 Oct 2015
Posts: 9
Concentration: Real Estate, Social Entrepreneurship
GMAT 1: 720 Q48 V42
WE: Engineering (Other)
Re: D01-39 [#permalink]

Show Tags

New post 06 May 2016, 16:21
Based on the combinatorics post Cn_k = n!/(k!(n-k)?)

Shouldn't the solution read C^8_5+C^8_4*C^2_1=56+140=196

Doesn't the solution provided switch the n and the k? Just learning this so maybe I am mistaken. Thanks!
2 KUDOS received
Intern
Intern
avatar
Joined: 23 Apr 2016
Posts: 14
Re: D01-39 [#permalink]

Show Tags

New post 09 Jul 2016, 12:24
2
See example in the ebook from Magoosh team under Combinations: http://magoosh.resources.s3.amazonaws.c ... _eBook.pdf

C 5 over 8 = 8!/5!(8-5)! = 8*7*6*5*4*3*2*1/(5*4*3*2*1)*(3*2*1)
Simplify and you get 8*7*6/3*2*1
Simplify more and you get 4*7*2 = 8*7 = 56

You do the same with the other part of the equation.
So this for the first part. Hope this helps everyone!
1 KUDOS received
Intern
Intern
avatar
Joined: 09 May 2016
Posts: 2
Re: D01-39 [#permalink]

Show Tags

New post 15 Oct 2016, 11:00
1
Alternative solution
Since Romi can take at most 1 large book then he can take with him : All possible ways - (2 Large books and 3 books from 5 possible) =(5 small books from 10) - (3 small books from 8)=C510-C38=196
Current Student
avatar
Joined: 23 Jan 2016
Posts: 12
GMAT 1: 640 Q36 V40
GMAT 2: 650 Q41 V38
GMAT 3: 710 Q47 V41
Re: D01-39 [#permalink]

Show Tags

New post 05 Nov 2016, 22:42
Nawfal wrote:
Alternative solution
Since Romi can take at most 1 large book then he can take with him : All possible ways - (2 Large books and 3 books from 5 possible) =(5 small books from 10) - (3 small books from 8)=C510-C38=196


Thanks Nawfal, that was the way I went about solving as well!
Intern
Intern
avatar
Joined: 08 Mar 2016
Posts: 1
Re: D01-39 [#permalink]

Show Tags

New post 06 Mar 2017, 21:23
1
I have a question, for the second combination C^4_8, I get 70 not 140.
C^4_8 = 8*7*6*5 / 4*3*2*1 = 2*7*5 = 70
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46297
Re: D01-39 [#permalink]

Show Tags

New post 07 Mar 2017, 02:30
Intern
Intern
avatar
B
Joined: 07 Feb 2016
Posts: 21
GMAT 1: 650 Q47 V34
GMAT 2: 710 Q48 V39
Re: D01-39 [#permalink]

Show Tags

New post 01 May 2017, 23:07
Although it is more slowly (as it aims for probability and not for combinations), I want to add a different approach.

\(P(at least one large book)=1-P(two large books)\)

\(P(two large books)=\frac{2}{10}*\frac{1}{9}*C^2_5=\frac{1}{45}*10=\frac{2}{9}\)

\(P(at least one large book)=1-P(two large books)=\frac{7}{9}\)

\(Combinations=P(at least one large book)*C^5_10=\frac{7}{9}*252=196\)
Intern
Intern
avatar
B
Joined: 06 Aug 2017
Posts: 1
Re D01-39 [#permalink]

Show Tags

New post 11 Aug 2017, 12:17
I think this is a poor-quality question and I don't agree with the explanation. The answer seems to be wrongly calculated.
PS Forum Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1143
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge
D01-39 [#permalink]

Show Tags

New post 11 Aug 2017, 12:51
Victor__ wrote:
I think this is a poor-quality question and I don't agree with the explanation. The answer seems to be wrongly calculated.


Hi Victor__

it would be great if you could explain what exactly is wrong with the official solution?

As per the question there are two possibilities -

A. take \(1\) large book \(AND\) \(4\) small books. Mathematically this can be represented as -
\(1\) large book can be selected from \(2\) large books in \(2_C_1\) and remaining \(4\) small books can be selected from \(8\) small books in \(8_C_4\)
therefore total number of ways = \(2_C_1\) \(*\) \(8_C_4 = 140\)

\(OR\)

B. take \(5\) small books and no large books. Mathematically it can be represented as -
\(5\) small books can be selected from \(8\) books in \(8_C_5 = 56\)

Therefore total number of ways = \(140+56 = 196\)
Intern
Intern
avatar
B
Joined: 22 Jan 2018
Posts: 2
Re: D01-39 [#permalink]

Show Tags

New post 04 Feb 2018, 14:52
Since we can choose 1 Large book or 0 Large book then:

L-S-S-S-S/4! + S-S-S-S-S/5! (we divide for n! each sub set, n=number of positions)

(2/1!) * (8*7*6*5/4!) + (8*7*6*5*4/5!) = 196
Intern
Intern
avatar
B
Joined: 09 Sep 2015
Posts: 25
Re: D01-39 [#permalink]

Show Tags

New post 01 Apr 2018, 07:04
Hi Guys

What if the question asks for "at least 1 large book" then in how many ways Romi can select 5 books ?

Any Help is appreciated

Thanks
PS Forum Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1143
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge
D01-39 [#permalink]

Show Tags

New post 01 Apr 2018, 09:06
amargad0391 wrote:
Hi Guys

What if the question asks for "at least 1 large book" then in how many ways Romi can select 5 books ?

Any Help is appreciated

Thanks


Hi amargad0391

At least 1 large book will mean that there will be two scenarios -

Scenario 1: 1 Large book and 4 Small Books =\(2_C_1 * 8_C_4\) OR

Scenario 2: 2 Large books and 3 Small Books =\(2_C_2*8_C_3\)

So the final answer will be the sum of these two scenarios
Intern
Intern
avatar
B
Joined: 09 Sep 2015
Posts: 25
Re: D01-39 [#permalink]

Show Tags

New post 01 Apr 2018, 21:07
niks18 wrote:
amargad0391 wrote:
Hi Guys

What if the question asks for "at least 1 large book" then in how many ways Romi can select 5 books ?

Any Help is appreciated

Thanks


Hi amargad0391

At least 1 large book will mean that there will be two scenarios -

Scenario 1: 1 Large book and 4 Small Books =\(2_C_1 * 8_C_4\) OR

Scenario 2: 2 Large books and 3 Small Books =\(2_C_2*8_C_3\)

So the final answer will be the sum of these two scenarios




Thanks niks18 :-) :thumbup:
Re: D01-39   [#permalink] 01 Apr 2018, 21:07

Go to page    1   2    Next  [ 23 posts ] 

Display posts from previous: Sort by

D01-39

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

Moderators: chetan2u, Bunuel



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®.