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

 It is currently 09 Dec 2019, 06:49 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # A drawer contains 6 socks. If two socks are randomly

Author Message
TAGS:

### Hide Tags

GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4125
A drawer contains 6 socks. If two socks are randomly  [#permalink]

### Show Tags

4
Top Contributor
13 00:00

Difficulty:   95% (hard)

Question Stats: 28% (02:15) correct 72% (01:57) wrong based on 207 sessions

### HideShow timer Statistics

A drawer contains 6 socks. If two socks are randomly selected without replacement, what is the probability that both socks will be black?

(1) The probability is less than 0.3 that the first sock selected will be black.
(2) The probability is greater than 0.4 that both socks will be white.

* Kudos for all correct solutions

_________________ V
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 1045
Location: India
GPA: 3.64
A drawer contains 6 socks. If two socks are randomly  [#permalink]

### Show Tags

6
S1 - Probability of selecting 1 black sock from 6 socks =$$\frac{bC1}{6C1}$$=$$\frac{b}{6}$$<0.3
where b is no. of black socks.
i.e. b<1.8 i.e. b can be 0 or 1.
In either case the probability is 0. So sufficient.

S2 - Probability of both socks white >0.4
i.e.$$\frac{wC2}{6C2}$$ >0.4 where w is no. of white socks
$$\frac{w(w-1)}{30}$$> 0.4
therefore, w>4 i.e. no. of white socks is 5 or 6.
In either case, probability of picking 2 black socks is 0. So, sufficient.

If u find my post useful, please press kudos!
##### General Discussion
Intern  Joined: 18 Sep 2016
Posts: 46
Re: A drawer contains 6 socks. If two socks are randomly  [#permalink]

### Show Tags

1
3
GMATPrepNow wrote:
A drawer contains 6 socks. If two socks are randomly selected without replacement, what is the probability that both socks will be black?

(1) The probability is less than 0.3 that the first sock selected will be black.
(2) The probability is greater than 0.4 that both socks will be white.

* Kudos for all correct solutions

The number of black socks and white socks have to be integers
let's call The number of black socks b and The number of white socks w

(1) The probability is less than 0.3 that the first sock selected will be black.
it means that $$\frac{b}{6}<0.3$$ ===> $$b<1.8$$=====> $$b<=1$$
Thus, there is not possibility to selected without replacement 2 black socks because there is only one of those or none of those.

probability=0 SUFFICIENT

(2) The probability is greater than 0.4 that both socks will be white.
$$\frac{w}{6}*(w-1)/5>0.4$$ w*(w-1)>12 the lowest integer for w is 5

Thus there are 1 or less black socks
again there is not possibility to selected without replacement 2 black socks

probability=0 SUFFICIENT

Current Student B
Status: preparing
Joined: 30 Dec 2013
Posts: 36
Location: United Arab Emirates
Concentration: Technology, Entrepreneurship
GMAT 1: 660 Q45 V35 GMAT 2: 640 Q49 V28 GMAT 3: 640 Q49 V28 GMAT 4: 640 Q49 V28 GMAT 5: 640 Q49 V28 GPA: 2.84
WE: General Management (Consumer Products)
Re: A drawer contains 6 socks. If two socks are randomly  [#permalink]

### Show Tags

[quote="GMATPrepNow"]A drawer contains 6 socks. If two socks are randomly selected without replacement, what is the probability that both socks will be black?

(1) The probability is less than 0.3 that the first sock selected will be black.
(2) The probability is greater than 0.4 that both socks will be white.

* Kudos for all correct solutions

1) P(B)< 0.3
total socks=6
so, 0.3 x 6 = 1.8 ( black is less than this, since p(b) < 0.3)
black =1
1/6 x 0/5 = 0 sufficient

2) p(w and w)> 0.4
0.4x6 = 2.4 ( in total it must be greater than this, so it will be either 3,4,5 or even 6) but there will be only one value that satisfies the equation.
check values :
lets say : p(w and w) =3
3/6 x 2/5 = 1/5 (0.2,not good)
try p(w and w) =4
4/6 x 3/5 = 2/5 (= 0.4) where p (w and w ) must be greater than 0.4. not good
so either w=5 or w=6
both ways p(b and b) =0
sufficient

Ans : D
Intern  B
Joined: 30 Mar 2017
Posts: 36
Location: United States (FL)
Re: A drawer contains 6 socks. If two socks are randomly  [#permalink]

### Show Tags

Bunuel - Shouldn't the answer should be A. We do not have any information as to how many black socks are among the 6 (if any exist at all).
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8642
Location: United States (CA)
Re: A drawer contains 6 socks. If two socks are randomly  [#permalink]

### Show Tags

2
GMATPrepNow wrote:
A drawer contains 6 socks. If two socks are randomly selected without replacement, what is the probability that both socks will be black?

(1) The probability is less than 0.3 that the first sock selected will be black.
(2) The probability is greater than 0.4 that both socks will be white.

We are given that a drawer contains 6 socks. If we let b = the number of black socks, we see that the probability of a black sock on the first pick is b/6. Since there is no replacement, the probability of a black sock on the second pick is (b - 1)/5. We need to determine the product of (b/6) x (b-1)/5.

Statement One Alone:

The probability is less than 0.3 that the first sock selected will be black.

Using the information in statement one, we have:

b/6 < 3/10

10b < 18

b < 1.8

We see that there is at most 1 black sock. Thus, the probability of pulling 2 black socks in two picks is equal to 0. Statement one alone is sufficient to answer the question.

Statement Two Alone:

The probability is greater than 0.4 that both socks will be white.

Suppose that there were exactly 4 white socks in the drawer. In this case, the probability of drawing 2 white socks would be 4/6 x 3/5 = 12/30 = 2/5 = 0.4. Since the probability of getting 2 white socks is greater than 0.4, there must be more than 4 white socks in the drawer; therefore, there can be at most 1 black sock in the drawer. The probability of pulling 2 black socks is 0. Statement two alone is sufficient to answer the question.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

BSchool Moderator P
Joined: 11 Feb 2018
Posts: 312
Location: India
Concentration: General Management, Finance
GMAT 1: 690 Q47 V37 GMAT 2: 710 Q50 V36 GMAT 3: 750 Q50 V42 Re: A drawer contains 6 socks. If two socks are randomly  [#permalink]

### Show Tags

Awesome, awesome question.Will make many a mathematically inclined people just kick themselves after seeing the answer.Not so tough but thoroughly enjoyed this problem....
Non-Human User Joined: 09 Sep 2013
Posts: 13730
Re: A drawer contains 6 socks. If two socks are randomly  [#permalink]

### Show Tags

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 drawer contains 6 socks. If two socks are randomly   [#permalink] 23 Nov 2019, 21:28
Display posts from previous: Sort by

# A drawer contains 6 socks. If two socks are randomly  