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

 It is currently 18 Feb 2019, 06:22

### 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

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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Valentine's day SALE is on! 25% off.

February 18, 2019

February 18, 2019

10:00 PM PST

11:00 PM PST

We don’t care what your relationship status this year - we love you just the way you are. AND we want you to crush the GMAT!
• ### Get FREE Daily Quiz for 2 months

February 18, 2019

February 18, 2019

10:00 PM PST

11:00 PM PST

Buy "All-In-One Standard ($149)", get free Daily quiz (2 mon). Coupon code : SPECIAL # On a shelf there are 6 hardback books and 2 paperback book.  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Intern Joined: 30 Jun 2012 Posts: 7 On a shelf there are 6 hardback books and 2 paperback book. [#permalink] ### Show Tags Updated on: 30 Jun 2012, 06:52 1 3 00:00 Difficulty: 25% (medium) Question Stats: 72% (02:04) correct 28% (02:18) wrong based on 219 sessions ### HideShow timer Statistics On a shelf there are 6 hardback books and 2 paperback book. If we pick up 4 books at random, what is the probability that we pick up at least one paperback book? A. 11/14 B. 5/7 C. 2/7 D. 3/14 E. 1/7 Originally posted by ferrarih on 30 Jun 2012, 06:18. Last edited by ferrarih on 30 Jun 2012, 06:52, edited 1 time in total. Math Expert Joined: 02 Sep 2009 Posts: 52935 Re: On a shelf there are 6 hardback books and 2 paperback..... [#permalink] ### Show Tags 30 Jun 2012, 06:35 2 2 On a shelf there are 6 hardback books and 2 paperback book. If we pick up 4 books at random, what is the probability that we pick up at least one paperback book? A. 11/14 B. 5/7 C. 2/7 D. 3/14 E. 1/7 Let's find the probability of the opposite event and subtract this value from 1. The opposite event would be if out of 4 books we pick all ll will be hardback: $$P(H=4)=\frac{C^4_6}{C^4_8}=\frac{15}{70}=\frac{3}{14}$$. Hence, $$P(P\geq{1})=1-\frac{3}{14}=\frac{11}{14}$$. Answer: A. _________________ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13546 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: On a shelf there are 6 hardback books and 2 paperback book. [#permalink] ### Show Tags 22 Apr 2017, 15:18 1 1 Hi All, The 'math' behind this question can be approached in a couple of different ways - and you can actually avoid using the Combination Formula altogether. The prompt tells us that there are 6 hardcover books and 2 paperback books. We're asked for the probability of selecting AT LEAST one paperback book when we randomly select 4 books from the overall group of 8 books. Since the question focuses on getting AT LEAST one paperback book, we can determine what we DON'T want (meaning 0 paperback books) and subtract that result from 1 (to determine what we DO want). Working one book at a time, the probability of NOT getting a paperback book is.... 1st book = 6/8 chance of NOT getting a paperback 2nd book = 5/7 chance of NOT getting a paperback 3rd book = 4/6 chance of NOT getting a paperback 4th book = 3/5 chance of NOT getting a paperback Thus, the probability of NOT getting a paperback book for the first 4 books is (6/8)(5/7)(4/6)(3/5). You should notice that the 6s and 5s 'cancel out', leaving us with... (4)(3)/(8)(7) = 12/56 = 3/14 Thus, the probability of getting AT LEAST one paperback would be 1 - 3/14 = 11/14 Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Senior Manager
Joined: 22 Feb 2018
Posts: 420
On a shelf there are 6 hardback books and 2 paperback book.  [#permalink]

### Show Tags

22 Oct 2018, 09:03
ferrarih wrote:
On a shelf there are 6 hardback books and 2 paperback book. If we pick up 4 books at random, what is the probability that we pick up at least one paperback book?

A. 11/14
B. 5/7
C. 2/7
D. 3/14
E. 1/7

OA:A

The probability of picking up at least one paperback book $$= 1 -$$ The probability of picking up no paperback book $$= 1- \frac{C(6,4)}{C(8,4)}= 1-\frac{3}{14}=\frac{11}{14}$$
_________________

Good, good Let the kudos flow through you

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4920
Location: United States (CA)
Re: On a shelf there are 6 hardback books and 2 paperback book.  [#permalink]

### Show Tags

23 Oct 2018, 18:24
ferrarih wrote:
On a shelf there are 6 hardback books and 2 paperback book. If we pick up 4 books at random, what is the probability that we pick up at least one paperback book?

A. 11/14
B. 5/7
C. 2/7
D. 3/14
E. 1/7

The phrase “at least one paperback” means “one or more paperbacks.” Thus, the only way we would NOT pick up at least one paperback would be if all 4 books were hardbacks. Thus, we can use the formula:

P(at least one paperback) = 1 - P(all hardbacks)

The number of ways to select all hardbacks is 6C4:

6! / (4! x 2!) = (6 x 5) / (2 x 1) = 15

The number of ways to select 4 books from 8 is 8C4:

8! / (4! x 4!) = (8 x 7 x 6 x 5) / (4 x 3 x 2 x 1) = 7 x 2 x 5 = 70

The probability of all hardbacks is 15/70 = 3/14 and thus P(at least on paperback) = 1 - 3/14 = 11/14.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: On a shelf there are 6 hardback books and 2 paperback book.   [#permalink] 23 Oct 2018, 18:24
Display posts from previous: Sort by