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

It is currently 19 Sep 2018, 22:11

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

If 40 percent of all students at college X have brown hair a

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

Hide Tags

Manager
Manager
User avatar
Joined: 11 Feb 2011
Posts: 120
If 40 percent of all students at college X have brown hair a  [#permalink]

Show Tags

New post 09 Mar 2011, 23:09
3
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

75% (01:14) correct 25% (01:32) wrong based on 147 sessions

HideShow timer Statistics

If 40 percent of all students at college X have brown hair and 70 percent of all students at college X have blue eyes what is the difference between the minimum and maximum probability of picking a student from college X who has neither brown hair nor blue eyes?

A. 0.2
B. 0.3
C. 0.4
D. 0.6
E. 0.7

_________________

target:-810 out of 800!

Most Helpful Community Reply
Retired Moderator
avatar
Joined: 20 Dec 2010
Posts: 1868
Re: Simple but difficult !  [#permalink]

Show Tags

New post 09 Mar 2011, 23:30
4
1
If 40 percent of all students at college X have brown hair and 70 percent of all students at college X have blue eyes what is the difference between the minimum and maximum probability of picking a student from college X who has neither brown hair nor blue eyes?

Let's say there are 100 students.

40 Students BROWN hair
70 Students BLUE eyes
y Students have both brown hair and blue eyes
x Students neither Brown hair nor blue eyes

\(n(Total) = n(A)+n(B)-n(A\cap B)+n(Neither)\)
n(Total Students) = n(Brown Hair)+ n(Blue eyes) - n(Brown hair and Blue eyes) + n(Neither)
100 = 40+70-y+x
x = y-10

x will be maximum when y is maximum. What is the maximum value for
Max value for y = minimum of (40,70).
Because the number of students with brown hair is 40, the maximum number of students to have both brown hair and blue eyes can only be 40.

When y=40
x=30

Probability of selecting 30 students out of 100 students = 30/100 = 0.3

x will be minimum when y is minimum.

The minimum possible value for y=10
x = y-10
x=0

Because if "y" gets less than 10; the number of students get more than 100 which is not possible.

In this case; 0 students fit the criterion of not having either. Because all students have brown hair, blue eyes or both.

Probability becomes 0/100 = 0

Difference between two probabilities = 0.3-0 = 0.3

Ans: "B"
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

General Discussion
Director
Director
avatar
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 769
Reviews Badge
Re: Simple but difficult !  [#permalink]

Show Tags

New post 09 Mar 2011, 23:23
I think its B.

Min overlap
70 + 40 = 110. Therefore min overlap is 10%. In this case the neither (brown and blue) is zero

Max overlap
100 - 70 = 30 = Neither (brown and blue)

Difference is 30% ie 0.3

AnkitK wrote:
If 40 percent of all students at college X have brown hair and 70 percent of all students at college X have blue eyes what is the difference between the minimum and maximum probability of picking a student from college X who has neither brown hair nor blue eyes?

A.0.2
B.0.3
C.0.4
D.0.6
E.0.7
Manager
Manager
avatar
Joined: 24 Nov 2010
Posts: 180
Location: United States (CA)
Concentration: Technology, Entrepreneurship
Schools: Ross '15, Duke '15
GMAT ToolKit User
Re: Simple but difficult !  [#permalink]

Show Tags

New post 09 Mar 2011, 23:27
min prob = 0 (10% overlap b/w blue eyes and brown hair)
max prob = .7 (100% overlap b/w blue eyes and brown hair)
diff = .3

ans B
Manager
Manager
User avatar
Joined: 11 Feb 2011
Posts: 120
Re: Simple but difficult !  [#permalink]

Show Tags

New post 09 Mar 2011, 23:39
Thankzz to all.

But i am still confused about the logic behind below concept . Dear Fluke pls elaborate :

"x will be maximum when y is maximum. What is the maximum value for
Max value for y = minimum of (40,70).
Because the number of students with brown hair is 40, the maximum number of students to have both brown hair and blue eyes can only be 40"
_________________

target:-810 out of 800!

Retired Moderator
avatar
Joined: 20 Dec 2010
Posts: 1868
Re: Simple but difficult !  [#permalink]

Show Tags

New post 10 Mar 2011, 00:19
4
AnkitK wrote:
Thankzz to all.

But i am still confused about the logic behind below concept . Dear Fluke pls elaborate :

"x will be maximum when y is maximum. What is the maximum value for y
Max value for y = minimum of (40,70).
Because the number of students with brown hair is 40, the maximum number of students to have both brown hair and blue eyes can only be 40"


How can the number of students having neither brown hair nor blue eyes be maximized?

If the overlap between blue eyed guys and brown hair guys is increased; means the number of students having BOTH blue eyes and brown hair be increased. In terms of the set \(n(A\cap B) is increased\)

For simplicity;

Ex: Say there are 4 students(a,b,c,d);
1 student has brown hair and 2 students have blue eyes;


Stem says: 1 student has brown hair and 2 students have blue eyes;
minimum number of students who neither have blue eyes nor brown hair

Say
a-> brown hair (1 student has brown hair)
b,c-> blue eyes (2 students have blue eyes)
Number of students to have both blue eyes AND brown hair = 0
d-> doesn't have either blue eyes or brown hair. Count: 1

Maximum number of students who neither have blue eyes nor brown hair
Say
a-> brown hair & blue eyes
b-> blue eyes
Number of students to have both blue eyes AND brown hair = 1(a)
c,d-> doesn't have either blue eyes or brown hair: Count: 2

Mathematically; you can see;
To find the maximum number of students that have neither. We need to have maximum possible number of students that can have both.

Why the maximum number of students that have both can't be greater than the minimum of the two.

Maximum number of students having both = min(Students with brown hair, Students with blue eyes)
Students with brown hair = 1
Students with blue eyes = 2

Can the number of students having both be "2". NO... if out of 4 students; only 1, just ONE student has brown hair, how can there be 2 students with brown hair and blue eyes. It is clearly mentioned in the question;

Likewise;
Because the number of students with brown hair is 40, the maximum number of students to have both brown hair and blue eyes can only be 40". If only 40 students have brown hair, how can 41 students have both. It can never be any number more than 40.

Thus the maximum number of intersection is always the minimum of two counts.

Now, if 40 students have both blue eyes and brown hair and question says there are 70 students to have blue eyes. There are another 30 students who have blue eyes but no brown hair.

Total becomes 70: 40(Both brown and blue), 30(just blue).
Total students=100
Neither = 100-70=30

Coming to the find the minimum number of intersection;
if there are 40 students - brown hair
70 - blue eyes

it becomes 40+70=110. But, the total strength is 100. Thus, 10 students have both blue and brown, but 0 zero students who have neither.

*****
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Manager
Manager
User avatar
Joined: 11 Feb 2011
Posts: 120
Re: Simple but difficult !  [#permalink]

Show Tags

New post 10 Mar 2011, 00:32
Thnkxxxx a ton Fluke..U ROK MAN!
_________________

target:-810 out of 800!

Director
Director
avatar
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 769
Reviews Badge
Re: Simple but difficult !  [#permalink]

Show Tags

New post 10 Mar 2011, 00:34
fluke +1 Its very nice of you to write a lengthy explanation as this one !
Senior Manager
Senior Manager
User avatar
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 421
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: If 40 percent of all students at college X have brown hair a  [#permalink]

Show Tags

New post 18 Jun 2015, 06:58
Hello,

I used another way to solve this one, and would like to see if it makes sense.

So, I created a table:
BE=blue eyes, NBE=not blue eyes, BH=blond hair, NBH=not blond hair. I chose 100 as total # students, and based on the information completed the third line for ALL.

............BE.......NBE......ALL
BH...............................40
NBH...................?.........60
ALL......70.........30.......100

Now, we are looking for the number that would go to ?, for two different cases (least and most).
So, my thought was that if ALL the 70 people with BE also had BH, then 0 people would have NBH, which would mean that 60 people would have NBH/NBE:


............BE.......NBE......ALL
BH.......70........................
NBH......0..........60........60
ALL......70.........30.......100

Similarly, if ALL the people with NBE would be moved to NBE/NBH, then 30 people would be at NBE/NBH:

............BE.......NBE......ALL
BH.................................
NBH..................30.......60
ALL......70.........30.......100

So, in the end 60-30 = 30. And since we have 100 people, this is 30% or 0.3.
SVP
SVP
User avatar
P
Joined: 08 Jul 2010
Posts: 2302
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: If 40 percent of all students at college X have brown hair a  [#permalink]

Show Tags

New post 18 Jun 2015, 08:17
1
AnkitK wrote:
If 40 percent of all students at college X have brown hair and 70 percent of all students at college X have blue eyes what is the difference between the minimum and maximum probability of picking a student from college X who has neither brown hair nor blue eyes?

A. 0.2
B. 0.3
C. 0.4
D. 0.6
E. 0.7



Answer: Option

Please check the explanation as per Double Matrix Method
Attachments

File comment: www.GMATinsight.com
121.jpg
121.jpg [ 176.54 KiB | Viewed 5736 times ]


_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Current Student
User avatar
Status: GMAT Date: 10/08/15
Joined: 17 Jul 2014
Posts: 89
Location: United States (MA)
Concentration: Human Resources, Strategy
GMAT 1: 640 Q48 V35
GPA: 3.5
WE: Human Resources (Consumer Products)
Re: If 40 percent of all students at college X have brown hair a  [#permalink]

Show Tags

New post 22 Jun 2015, 05:51
GMATinsight wrote:
AnkitK wrote:
If 40 percent of all students at college X have brown hair and 70 percent of all students at college X have blue eyes what is the difference between the minimum and maximum probability of picking a student from college X who has neither brown hair nor blue eyes?

A. 0.2
B. 0.3
C. 0.4
D. 0.6
E. 0.7



Answer: Option

Please check the explanation as per Double Matrix Method


Could you please explain how you reached at 30%?

When you say 30% for x is the limiting factor - do you mean that we need to pick those with no Brown hair from the set with no blue eyes i.e 30% ?

Would be a great help if you could clarify if I am correct in my understanding?

Thanks much!
_________________

Thanks,
aimtoteach


~~~~~~~~~~~~~~~~~

Please give Kudos if you find this post useful.

SVP
SVP
User avatar
P
Joined: 08 Jul 2010
Posts: 2302
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: If 40 percent of all students at college X have brown hair a  [#permalink]

Show Tags

New post 22 Jun 2015, 06:00
1
aimtoteach wrote:
GMATinsight wrote:
AnkitK wrote:
If 40 percent of all students at college X have brown hair and 70 percent of all students at college X have blue eyes what is the difference between the minimum and maximum probability of picking a student from college X who has neither brown hair nor blue eyes?

A. 0.2
B. 0.3
C. 0.4
D. 0.6
E. 0.7



Answer: Option

Please check the explanation as per Double Matrix Method


Could you please explain how you reached at 30%?

When you say 30% for x is the limiting factor - do you mean that we need to pick those with no Brown hair from the set with no blue eyes i.e 30% ?

Would be a great help if you could clarify if I am correct in my understanding?

Thanks much!


You are right about it.

See if x is taken anything greater than 30% then the value in the adjacent cell to the left will be negative which is UNACCEPTABLE. Hence the maximum value of x is limited by smaller of the two adjacent summations i.e. 30% and 60%
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Manager
Manager
User avatar
B
Status: Final Call! Will Achieve Target ANyHow This Tym! :)
Joined: 05 Jan 2016
Posts: 88
Location: India
GMAT 1: 620 Q49 V25
GPA: 3.8
Reviews Badge
Re: If 40 percent of all students at college X have brown hair a  [#permalink]

Show Tags

New post 10 Jun 2016, 00:50
Nice explanation Fluke!
_________________

Regards,
Varun


Trying my best..... will succeed definitely! :)

The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long.
+1 Kudos if you find this post helpful. :)

Do Check OG 2017 SC Solutions - http://gmatwithcj.com/solutions-gmat-official-guide-2017-sentence-correction-questions/

Director
Director
User avatar
G
Joined: 26 Oct 2016
Posts: 652
Location: United States
Concentration: Marketing, International Business
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Re: If 40 percent of all students at college X have brown hair a  [#permalink]

Show Tags

New post 07 Jan 2017, 08:15
2
Please find the solution attached.
Attachments

prob2.PNG
prob2.PNG [ 33.67 KiB | Viewed 4011 times ]


_________________

Thanks & Regards,
Anaira Mitch

Senior Manager
Senior Manager
avatar
P
Joined: 31 Jul 2017
Posts: 459
Location: Malaysia
Schools: INSEAD Jan '19
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
CAT Tests
Re: If 40 percent of all students at college X have brown hair a  [#permalink]

Show Tags

New post 23 Jan 2018, 13:11
AnkitK wrote:
If 40 percent of all students at college X have brown hair and 70 percent of all students at college X have blue eyes what is the difference between the minimum and maximum probability of picking a student from college X who has neither brown hair nor blue eyes?

A. 0.2
B. 0.3
C. 0.4
D. 0.6
E. 0.7


Let the total students be 100, Brown Hair = 40, Blue Eyes = 70
100 = 40+70 - Both + Neither
Neither = Both - 10, Neither (Minimum) = 0 --> Both = 10,
Neither (maximum) = 30 --> Both = 40
Difference = 30 --> Probability = 30/100 = 0.3
_________________

If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!

Re: If 40 percent of all students at college X have brown hair a &nbs [#permalink] 23 Jan 2018, 13:11
Display posts from previous: Sort by

If 40 percent of all students at college X have brown hair a

  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®.