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

It is currently 21 Jul 2018, 08:43

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 packing for a trip, Sarah puts three pairs of socks - one

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

Hide Tags

7 KUDOS received
Manager
Manager
avatar
Joined: 11 Aug 2011
Posts: 182
Location: United States
Concentration: Economics, Finance
GMAT Date: 10-16-2013
GPA: 3
WE: Analyst (Computer Software)
Reviews Badge
In packing for a trip, Sarah puts three pairs of socks - one  [#permalink]

Show Tags

New post 18 May 2014, 00:27
7
26
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

60% (01:26) correct 40% (01:39) wrong based on 462 sessions

HideShow timer Statistics

In packing for a trip, Sarah puts three pairs of socks - one red, one blue, and one green - into one compartment of her suitcase. If she then pulls four individual socks out of the suitcase, simultaneously and at random, what is the probability that she pulls out exactly two matching pairs?

A. 1/5
B. 1/4
C. 1/3
D. 2/3
E. 4/5

I have not understood how to solve this question properly , can someone help me out here.
Kudos me if you like the post !!!

_________________

Kudos me if you like my post !!!!

Most Helpful Expert Reply
Expert Post
7 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47166
Re: In packing for a trip, Sarah puts three pairs of socks - one  [#permalink]

Show Tags

New post 18 May 2014, 00:46
7
7
akhil911 wrote:
In packing for a trip, Sarah puts three pairs of socks - one red, one blue, and one green - into one compartment of her suitcase. If she then pulls four individual socks out of the suitcase, simultaneously and at random, what is the probability that she pulls out exactly two matching pairs?

A. 1/5
B. 1/4
C. 1/3
D. 2/3
E. 4/5

I have not understood how to solve this question properly , can someone help me out here.
Kudos me if you like the post !!!


\(\frac{C^2_3}{C^2_6}=\frac{3}{15}=\frac{1}{5}\): \(C^2_3\) = picking 2 pairs out of 3 and \(C^2_6\) = picking 2 socks out of 6.

Answer: A.
_________________

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

Most Helpful Community Reply
15 KUDOS received
Intern
Intern
avatar
Joined: 13 May 2014
Posts: 34
Concentration: General Management, Strategy
Re: In packing for a trip, Sarah puts three pairs of socks - one  [#permalink]

Show Tags

New post 18 May 2014, 09:09
15
1
akhil911 wrote:
Hi Brunei,

Can you help in explaining the answer in detail.
I still cant understand how you have plugged in the numbers.

Hi Akhil,

If you look,the successful events are when Sarah pulls 2 matching pair of socks out of 3 matching pairs of socks, which can be done in 3C2 ways as the order is not important
So,3C2 = 3 ways are:
RRBB
RRGG
BBGG

Now,the ways in which 4 socks can be pulled out of 6 socks (3 pairs) = 6C4 = 15
So, probability = 3/15 = 1/5

Kudo if you like my post
General Discussion
Manager
Manager
avatar
Joined: 11 Aug 2011
Posts: 182
Location: United States
Concentration: Economics, Finance
GMAT Date: 10-16-2013
GPA: 3
WE: Analyst (Computer Software)
Reviews Badge
Re: In packing for a trip, Sarah puts three pairs of socks - one  [#permalink]

Show Tags

New post 18 May 2014, 04:55
Hi Brunei,

Can you help in explaining the answer in detail.
I still cant understand how you have plugged in the numbers.
_________________

Kudos me if you like my post !!!!

1 KUDOS received
Intern
Intern
avatar
Joined: 19 Oct 2013
Posts: 17
Location: India
Concentration: General Management, Operations
WE: Engineering (Other)
Re: In packing for a trip, Sarah puts three pairs of socks - one  [#permalink]

Show Tags

New post Updated on: 18 May 2014, 21:53
1
\(1 - P(Exactly 1 Pair)\) \(=1 - ((\frac{2_C_1*2_C_1*2_C_2}{6_C_4})*3)\) \(=1 - (\frac{12}{15})=\) \(\frac{3}{15}\) \(=\frac{1}{5}\)

I know this is a longer approach, but is this right?


NOTE: I understood that this could happen in 3 ways. So, I multiplied by 3.

But I'm never completely sure how to always consider the NUMBER OF ARRANGEMENTS in certain questions.
I get confused when there are different elements to be considered and when there are similar elements.
Can someone help me with this?

Thanks in advance.

Originally posted by shaderon on 18 May 2014, 21:13.
Last edited by shaderon on 18 May 2014, 21:53, edited 1 time in total.
1 KUDOS received
Director
Director
User avatar
Joined: 25 Apr 2012
Posts: 701
Location: India
GPA: 3.21
WE: Business Development (Other)
Premium Member Reviews Badge
Re: In packing for a trip, Sarah puts three pairs of socks - one  [#permalink]

Show Tags

New post 18 May 2014, 21:26
1
shaderon wrote:
akhil911 wrote:
In packing for a trip, Sarah puts three pairs of socks - one red, one blue, and one green - into one compartment of her suitcase. If she then pulls four individual socks out of the suitcase, simultaneously and at random, what is the probability that she pulls out exactly two matching pairs?

A. 1/5
B. 1/4
C. 1/3
D. 2/3
E. 4/5

I have not understood how to solve this question properly , can someone help me out here.
Kudos me if you like the post !!!


Can someone help me with the approach?

1 - P(Exactly 1 Pair) = \(1 - (\frac{2_C_1*2_C_1*2_C_2}{6_C_4})\)

I'm not really sure how to progress after this.
I have to take into account the different ways this could happen, right?
How do I do that?

Is the approach OK?

Thanks in advance.


Hi,

I think \((\frac{2_C_1*2_C_1*2_C_2}{6_C_4})\) represents a case where in 1 type of matching socks are pulled out but there 3 pairs and any one of them can be pulled out so I think it should be

\(1 - 3*(\frac{2_C_1*2_C_1*2_C_2}{6_C_4})\)

1-12/15 or 3/15 or 1/5
_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Expert Post
GMAT Club Legend
GMAT Club Legend
User avatar
P
Joined: 16 Oct 2010
Posts: 8132
Location: Pune, India
Re: In packing for a trip, Sarah puts three pairs of socks - one  [#permalink]

Show Tags

New post 18 May 2014, 22:16
shaderon wrote:
\(1 - P(Exactly 1 Pair)\) \(=1 - ((\frac{2_C_1*2_C_1*2_C_2}{6_C_4})*3)\) \(=1 - (\frac{12}{15})=\) \(\frac{3}{15}\) \(=\frac{1}{5}\)

I know this is a longer approach, but is this right?


NOTE: I understood that this could happen in 3 ways. So, I multiplied by 3.

But I'm never completely sure how to always consider the NUMBER OF ARRANGEMENTS in certain questions.
I get confused when there are different elements to be considered and when there are similar elements.
Can someone help me with this?

Thanks in advance.


Yes, but you need to be more specific about the kind of problems you are talking about. Small things change the entire question in P&C so let me know the exact questions that confuse you.
_________________

Karishma
Private Tutor for GMAT
Contact: bansal.karishma@gmail.com

3 KUDOS received
Intern
Intern
avatar
Joined: 19 Jul 2013
Posts: 44
GMAT ToolKit User
Re: In packing for a trip, Sarah puts three pairs of socks - one  [#permalink]

Show Tags

New post 03 Nov 2014, 09:40
3
akhil911 wrote:
In packing for a trip, Sarah puts three pairs of socks - one red, one blue, and one green - into one compartment of her suitcase. If she then pulls four individual socks out of the suitcase, simultaneously and at random, what is the probability that she pulls out exactly two matching pairs?

A. 1/5
B. 1/4
C. 1/3
D. 2/3
E. 4/5

I have not understood how to solve this question properly , can someone help me out here.
Kudos me if you like the post !!!


easier solution: inverse the problem. Sarah picking up 2 pair of matching socks and keeping one pair in the bag is equivalent to Sarah picking up 1 pair of socks and keeping 2 pairs in the bag. Now let's see what's the probability of that happening when done at random. Sarah picks up the 1st one, can be any color and so probability = 1. Sarah picks up the 2nd one, now for it to be of the same color as the 1st one, she has to pick 1 exact piece out of 5, probability of which is 1/5. So option A.
2 KUDOS received
Manager
Manager
User avatar
Status: A mind once opened never loses..!
Joined: 05 Mar 2015
Posts: 214
Location: India
MISSION : 800
WE: Design (Manufacturing)
GMAT ToolKit User Premium Member
Re: In packing for a trip, Sarah puts three pairs of socks - one  [#permalink]

Show Tags

New post 10 Jun 2015, 06:39
2
Favorable outcomes > selecting 2 pairs out of 3 = 3c2 = 3

Total outcomes > selecting 4 socks randomly = 6c4 = 15

Probability = 3/15 = 1/5
_________________

Thank you

+KUDOS

> I CAN, I WILL <

Manager
Manager
avatar
Joined: 03 May 2013
Posts: 72
Re: In packing for a trip, Sarah puts three pairs of socks - one  [#permalink]

Show Tags

New post 22 Feb 2016, 23:51
experts please tell whats wrong in this

6/6*1/5*4/4*1/3 *6|/2*2 =2/5
Intern
Intern
avatar
Joined: 12 Dec 2015
Posts: 18
GMAT ToolKit User
Re: In packing for a trip, Sarah puts three pairs of socks - one  [#permalink]

Show Tags

New post 09 Mar 2016, 13:43
Hi Guys, can somebody explain what does this C mean? where can I learn the theory? I have never seen this terminology in the books... It is killing me :)

Thanks!
Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47166
Re: In packing for a trip, Sarah puts three pairs of socks - one  [#permalink]

Show Tags

New post 09 Mar 2016, 13:47
1
1
AlexIV wrote:
Hi Guys, can somebody explain what does this C mean? where can I learn the theory? I have never seen this terminology in the books... It is killing me :)

Thanks!


C stands for combinations:

Combinatorics Made Easy!

Theory on Combinations

DS questions on Combinations
PS questions on Combinations

Hope it helps.
_________________

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: 12 Dec 2015
Posts: 18
GMAT ToolKit User
Re: In packing for a trip, Sarah puts three pairs of socks - one  [#permalink]

Show Tags

New post 09 Mar 2016, 16:34
Thank you Bunuel!!!
Intern
Intern
avatar
Joined: 06 Mar 2016
Posts: 1
Re: In packing for a trip, Sarah puts three pairs of socks - one  [#permalink]

Show Tags

New post 28 Mar 2017, 02:10
Can someone please explain in this format? :

[2/6*1/5*2/4*1/3]*3 = 1/30 is my answer...

How can i get a 6 in the numerator so that the answer becomes 1/5? What would the logic be?
Intern
Intern
avatar
B
Joined: 25 Aug 2007
Posts: 38
GMAT ToolKit User Premium Member
In packing for a trip, Sarah puts three pairs of socks - one  [#permalink]

Show Tags

New post 24 Apr 2017, 16:32
Bunuel wrote:
akhil911 wrote:
In packing for a trip, Sarah puts three pairs of socks - one red, one blue, and one green - into one compartment of her suitcase. If she then pulls four individual socks out of the suitcase, simultaneously and at random, what is the probability that she pulls out exactly two matching pairs?

A. 1/5
B. 1/4
C. 1/3
D. 2/3
E. 4/5

I have not understood how to solve this question properly , can someone help me out here.
Kudos me if you like the post !!!


\(\frac{C^2_3}{C^2_6}=\frac{3}{15}=\frac{1}{5}\): \(C^2_3\) = picking 2 pairs out of 3 and \(C^2_6\) = picking 2 socks out of 6.

Answer: A.

Isn't it supposed to be \(C^4_6\) = picking 4 socks out of 6 (i.e 2 pairs)?
Senior Manager
Senior Manager
avatar
G
Joined: 21 Aug 2016
Posts: 281
Location: India
GPA: 3.9
WE: Information Technology (Computer Software)
GMAT ToolKit User Reviews Badge
Re: In packing for a trip, Sarah puts three pairs of socks - one  [#permalink]

Show Tags

New post 07 Jun 2017, 22:54
Hi Bunuel,

Why is the below approach incorrect?

6c1*1*4c1*1/(4!*6c4) Firstly, we are selecting one sock out of 6, then we can select second in just one way as we are assuming that it is the second sock of the pair and so on; since the combination can be any so divide by 4! and total cases are 6c4.
Intern
Intern
avatar
B
Joined: 19 Jul 2014
Posts: 10
Location: United Arab Emirates
GPA: 3.83
Re: In packing for a trip, Sarah puts three pairs of socks - one  [#permalink]

Show Tags

New post 08 Jun 2017, 12:01
i did it using probability directly
(6/6 * 1/5 * 4/4 * 1/3 ) * 3C2 ways = (1/15) * 3 = 1/5

6/6 - we can choose any of the 6 socks in the first one
1/5 - we should pick the exact pair of the first sock picked so only 1 way out of the remaining 5
4/4 - again we can pick any of the remaining 4 socks
1/3 - we have to pick the exact pair of the sock picked.

3C2 - because we could have either red + blue pair or red+ green pair or blue+green pair so 3 ways.
Expert Post
2 KUDOS received
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2679
Re: In packing for a trip, Sarah puts three pairs of socks - one  [#permalink]

Show Tags

New post 10 Jun 2017, 08:12
2
akhil911 wrote:
In packing for a trip, Sarah puts three pairs of socks - one red, one blue, and one green - into one compartment of her suitcase. If she then pulls four individual socks out of the suitcase, simultaneously and at random, what is the probability that she pulls out exactly two matching pairs?

A. 1/5
B. 1/4
C. 1/3
D. 2/3
E. 4/5


We have three scenarios of two matching pairs: 1) a red pair and a blue pair; 2) a red pair and a green pair; 3) a blue pair and a green pair. Let’s start with the probability of selecting a red pair and a blue pair. To select a red pair and a blue pair is to select two red socks and two blue socks. So let’s assume the first two socks are red and the last two socks are blue; the probability of selecting these socks in that order is:

P(R, R, B, B) = 2/6 x 1/5 x 2/4 x 1/3 = 1/6 x 1/5 x 1/3 = 1/90.

However, the two red socks and the two blue socks, in any order, can be selected in 4!/(2! x 2!) = 24/4 = 6 ways. Thus, the probability of two red socks and two blue socks is:

P(2R and 2B) = 1/90 x 6 = 6/90 = 1/15.

Using similar logic, we see that the probability of pulling a red pair and a green pair is 1/15, and so is the probability of pulling a blue pair and a green pair. Thus, the total probability is:

1/15 + 1/15 + 1/15 = 3/15 = 1/5.

Alternate Solution:

From a total of 6 socks, two pairs, i.e., 4 socks, can be pulled in 6C4 = 6!/(4! 2!) = (6 x 5)/2 = 3 x 5 = 15 ways.

Three of these choices contain two matching pairs, namely: 1) a red pair and a blue pair, 2) a blue pair and a green pair; 3) a red pair and a green pair.

Therefore, the probability of pulling two matching pairs is 3/15 = 1/5.

Answer: A
_________________

Jeffery Miller
Head of GMAT Instruction

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

Intern
Intern
avatar
Joined: 14 Oct 2015
Posts: 6
GMAT ToolKit User
Re: In packing for a trip, Sarah puts three pairs of socks - one  [#permalink]

Show Tags

New post 20 Jun 2017, 22:37
Quote:
akhil911 wrote:
In packing for a trip, Sarah puts three pairs of socks - one red, one blue, and one green - into one compartment of her suitcase. If she then pulls four individual socks out of the suitcase, simultaneously and at random, what is the probability that she pulls out exactly two matching pairs?

A. 1/5
B. 1/4
C. 1/3
D. 2/3
E. 4/5



Plz let me know if my approach is wrong-

Total number of socks = 6

Total number of ways Sarah can pick up 4 socks = 6C4 = 15 ways

No. of ways he can pick matching shoes = no.of ways 2 red socks + 2 blue socks + 2 green socks

= 2C2 + 2C2 + 2C2

= 1 + 1 + 1

= 3 ways

Hence

P(Matching socks) =3/15 = 1/15
Senior Manager
Senior Manager
avatar
G
Joined: 21 Aug 2016
Posts: 281
Location: India
GPA: 3.9
WE: Information Technology (Computer Software)
GMAT ToolKit User Reviews Badge
Re: In packing for a trip, Sarah puts three pairs of socks - one  [#permalink]

Show Tags

New post 24 Jun 2017, 09:22
AR15J wrote:
Hi Bunuel,

Why is the below approach incorrect?

6c1*1*4c1*1/(4!*6c4) Firstly, we are selecting one sock out of 6, then we can select second in just one way as we are assuming that it is the second sock of the pair and so on; since the combination can be any so divide by 4! and total cases are 6c4.


Hi JeffTargetTestPrep,


Can you please suggest why my approach is incorrect?
Re: In packing for a trip, Sarah puts three pairs of socks - one &nbs [#permalink] 24 Jun 2017, 09:22

Go to page    1   2    Next  [ 26 posts ] 

Display posts from previous: Sort by

In packing for a trip, Sarah puts three pairs of socks - one

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

Events & Promotions

PREV
NEXT


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®.