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

It is currently 21 Apr 2019, 19:39

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

Forty slips are placed into a hat, each bearing a number 1, 2, 3, 4, 5

  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: 54401
Forty slips are placed into a hat, each bearing a number 1, 2, 3, 4, 5  [#permalink]

Show Tags

New post 24 Mar 2019, 23:57
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

50% (03:09) correct 50% (03:28) wrong based on 14 sessions

HideShow timer Statistics

Forty slips are placed into a hat, each bearing a number 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10, with each number entered on four slips. Four slips are drawn from the hat at random and without replacement. Let p be the probability that all four slips bear the same number. Let q be the probability that two of the slips bear a number a and the other two bear a number \(b \neq a\). What is the value of q/p?

(A) 162
(B) 180
(C) 324
(D) 360
(E) 720

_________________
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7575
Forty slips are placed into a hat, each bearing a number 1, 2, 3, 4, 5  [#permalink]

Show Tags

New post 25 Mar 2019, 06:14
Bunuel wrote:
Forty slips are placed into a hat, each bearing a number 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10, with each number entered on four slips. Four slips are drawn from the hat at random and without replacement. Let p be the probability that all four slips bear the same number. Let q be the probability that two of the slips bear a number a and the other two bear a number \(b \neq a\). What is the value of q/p?

(A) 162
(B) 180
(C) 324
(D) 360
(E) 720



Since, we have probability out of the same set, and we have probability in both numerator and denominator, the q/p can be taken as (ways of picking two different pairs of number)/(ways of picking all four same). This will save some calculations..

Ways to choose all four - 10 *\(\frac{4!}{4!}\), as all the numbers are similar, so 10 ways
Ways to choose two different pair - 10C2*4C2*4C2, that is (choose two out of 10), then there are 4 of each of these number, so 4C2 ways for each number)

Thus \(\frac{q}{p}=\frac{10C2*4C2*4C2}{10}=\frac{10*9*4*3*4*3}{2*2*2*10}=9*9*2=162\)
A
_________________
GMAT Club Bot
Forty slips are placed into a hat, each bearing a number 1, 2, 3, 4, 5   [#permalink] 25 Mar 2019, 06:14
Display posts from previous: Sort by

Forty slips are placed into a hat, each bearing a number 1, 2, 3, 4, 5

  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®.