GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 30 May 2020, 05:26

### 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

# A box contains 10 pairs of shoes (20 shoes in total). If two

Author Message
TAGS:

### Hide Tags

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16746
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: A box contains 10 pairs of shoes (20 shoes in total). If two  [#permalink]

### Show Tags

19 Sep 2015, 16:10
Hi All,

In these types of questions, you'll find that there are usually at least a couple of different ways that you can 'do the math' - however, there's the potential to make everything far more complex than it needs to be. Certain Quant questions are based heavily on logic, so if you can think through the logic involved, then the math itself will be rather minimal (and sometimes quite simple).

Here, we're dealing with 10 pairs of shoes and we're asked for the probability that selecting two random shoes will lead to a matching pair.

Since there are 20 shoes in total, you will end up choosing one of them with the first 'draw.' Whichever one you choose for that first shoe, it will have a match - 1 shoe out of the remaining 19 shoes will match the first one one that you 'drew', so the probability of selecting a matching pair is 1/19.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Intern
Joined: 28 Dec 2015
Posts: 37
Re: A box contains 10 pairs of shoes (20 shoes in total). If two  [#permalink]

### Show Tags

15 Jun 2016, 21:52
No matter what shoes you choose out of the 20 shoes,they will have an equal probability of getting selected.Now,once we have selected 1 shoe,the matching pair would be in the remaining 10 shoes and selecting them is 10c1.
So,Probability(matching shoes)=1*10c1/20c2=1/19
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 6286
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: A box contains 10 pairs of shoes (20 shoes in total). If two  [#permalink]

### Show Tags

04 Mar 2019, 00:42
total pairs = 10
so 1 shoe of a pair ; 1/10
P of getting another matching shoe ; 1/19
total pairs 10
1/10 * 1/19 * 10 = 1/19
IMO C

tejal777 wrote:
A box contains 10 pairs of shoes (20 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?

A. 1/190
B. 1/20
C. 1/19
D. 1/10
E. 1/9

Numerator:
Out of 20 shoes we have to select one shoe first..w/o any restrictions.So that's 20C1 (choosing one out of 20).
Now,the second show has to be the matching shoe.There is only ONE such possible shoe,so the probability of choosing that shoe is 1.

Denominator:
Chosing 2 shoes out of 20.So, 20C2

20C1/20C2 = 2/19

Non-Human User
Joined: 09 Sep 2013
Posts: 15022
Re: A box contains 10 pairs of shoes (20 shoes in total). If two  [#permalink]

### Show Tags

14 Mar 2020, 18:25
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: A box contains 10 pairs of shoes (20 shoes in total). If two   [#permalink] 14 Mar 2020, 18:25

Go to page   Previous    1   2   [ 24 posts ]