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

 It is currently 14 Dec 2018, 05:52

### 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

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

December 14, 2018

December 14, 2018

09:00 AM PST

10:00 AM PST

10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.
• ### Typical Day of a UCLA MBA Student - Recording of Webinar with UCLA Adcom and Student

December 14, 2018

December 14, 2018

10:00 PM PST

11:00 PM PST

Carolyn and Brett - nicely explained what is the typical day of a UCLA student. I am posting below recording of the webinar for those who could't attend this session.

# Minimum of how many people are needed to have the probability of more

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51214
Minimum of how many people are needed to have the probability of more  [#permalink]

### Show Tags

20 Aug 2018, 04:50
21
00:00

Difficulty:

95% (hard)

Question Stats:

32% (00:56) correct 68% (01:12) wrong based on 190 sessions

### HideShow timer Statistics

GMAT CLUB TESTS' FRESH QUESTION:

Minimum of how many people are needed to have the probability of more than 1/2 that at lease one of them was born on either on Monday or on Tuesday?

A. 2
B. 3
C. 4
D. 5
E. 6

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7106
Re: Minimum of how many people are needed to have the probability of more  [#permalink]

### Show Tags

20 Aug 2018, 05:09
1
Bunuel wrote:

GMAT CLUB TESTS' FRESH QUESTION:

Minimum of how many people are needed to have the probability of more than 1/2 that at lease one of them was born on either on Monday or on Tuesday?

A. 2
B. 3
C. 4
D. 5
E. 6

Say there are only 2 person..
Prob = 2/7+2/7-2/7*2/7=4/7-4/49=24/49<1/2
Ans will be 3 because with 2, we had answer almost close to 1/2
No calculations required therefore
B
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Manager
Joined: 08 Oct 2015
Posts: 241
Re: Minimum of how many people are needed to have the probability of more  [#permalink]

### Show Tags

20 Aug 2018, 05:13
chetan2u can you please explain a little bit more?

Posted from my mobile device
Manager
Joined: 01 Nov 2017
Posts: 95
GMAT 1: 700 Q50 V35
GMAT 2: 640 Q49 V28
GMAT 3: 680 Q47 V36
GMAT 4: 700 Q50 V35
Re: Minimum of how many people are needed to have the probability of more  [#permalink]

### Show Tags

01 Oct 2018, 05:06
Need Expert to help with this one please!
Manager
Joined: 14 Jun 2018
Posts: 220
Re: Minimum of how many people are needed to have the probability of more  [#permalink]

### Show Tags

01 Oct 2018, 06:38
2
Suppose there are 2 people A and B
Probability of one on monday/tuesday = 2c1 * 2/7 * 5/7
Prob of both on monday/tuesday = 2/7*2/7
Total = 20/4 + 4/49 = 24/49 < 1/2

Now increase the no of people to 3 : A, B and C
Prob of one on monday/tuesday = 3c1 * 2/7 * 5/7 * 5/7 = 150/343
Prob of two on monday/tuesday = 3c2 * 2/7 * 2/7 * 5/7 = 60/343
Prob of three on monday/tuesday = 2/7* 2/7 * 2/7 = 8/343

Total = 218/343 > 1/2
Intern
Joined: 14 Aug 2018
Posts: 2
Re: Minimum of how many people are needed to have the probability of more  [#permalink]

### Show Tags

02 Oct 2018, 21:37
1
Bunuel wrote:

GMAT CLUB TESTS' FRESH QUESTION:

Minimum of how many people are needed to have the probability of more than 1/2 that at lease one of them was born on either on Monday or on Tuesday?

A. 2
B. 3
C. 4
D. 5
E. 6

My approach was like this:
As, question stated that at least one of the people have to have birthday on either Monday or Tuesday, I need to figure out the probability of all of them having birthday on remaining 5 days of week (other than Monday and Tuesday), then simply asses the value whether it is less than 0.5. If it is less than 0.5 then we have our answer.
First option 2 people: probability of both of them having birthday of remaining 5 days out of 7 days : $$\frac{5}{7} * \frac{5}{7}$$ =$$\frac{25}{49}$$ > 0.5
2nd Option 3 people: probability of all 3 of them having birthday of remaining 5 days out of 7 days : $$\frac{5}{7}*\frac{5}{7}*\frac{5}{7} = \frac{125}{363}$$< 0.5 ---> so 3 people is our answer or option [B]
Manager
Status: Started with mock tests,Kaplan and manhattan score's below
Joined: 11 Jun 2017
Posts: 110
Location: India
GMAT 1: 630 Q44 V33
GMAT 2: 680 Q47 V37
GPA: 3.2
Re: Minimum of how many people are needed to have the probability of more  [#permalink]

### Show Tags

10 Oct 2018, 19:45
chetan2u wrote:
Bunuel wrote:

GMAT CLUB TESTS' FRESH QUESTION:

Minimum of how many people are needed to have the probability of more than 1/2 that at lease one of them was born on either on Monday or on Tuesday?

A. 2
B. 3
C. 4
D. 5
E. 6

Say there are only 2 person..
Prob = 2/7+2/7-2/7*2/7=4/7-4/49=24/49<1/2
Ans will be 3 because with 2, we had answer almost close to 1/2
No calculations required therefore
B[/quote

Hi Experts,can you please explain Prob = 2/7+2/7-2/7*2/7 .
I am not able to understand this.
_________________

Thanks,
Ankit
Target Score:730+

If the post was useful,please send the kudos

Intern
Joined: 06 Nov 2014
Posts: 14
Location: Viet Nam
GMAT 1: 720 Q50 V36
GMAT 2: 740 Q50 V40
GPA: 3.67
Re: Minimum of how many people are needed to have the probability of more  [#permalink]

### Show Tags

10 Oct 2018, 20:45
2
For "AT LEAST" probability question, it would be a good choice to use P(A) = 1 - P(not A)

Let's say
A - There is at least 1 person born on Monday or Tuesday
B - There is no one born on Monday or Tuesday
Clearly, P(A) = 1 - P(B)

The problem asks when P(A) > 1/2. Or in other words, when P(B) < 1/2.

If we have 1 person, P(B) = 5/7
If we have 2 people, P(B) = (5/7)^2 = 25/49
If we have 3 people, P(B) = (5/7)^3 = something that I am pretty sure that < 1/2

Re: Minimum of how many people are needed to have the probability of more &nbs [#permalink] 10 Oct 2018, 20:45
Display posts from previous: Sort by