p > 1/3?

Expert replies

ttd: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Wed Mar 24, 2010 6:07 pm

by ttd » Wed Mar 31, 2010 3:14 pm

If 2 different members are to be selected at random from a
group of 8 people and if p is the probability that both
members selected will be older than 35 years old, is
p > 1/3 ?

(1) More than half of the group members are older than
35 years old.
(2) The probability that both members selected will be 35
years old or younger is greater than 1/10 .

Like this post

Source: Beat The GMAT — Data Sufficiency | Wed Mar 31, 2010 3:14 pm

ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Wed Mar 31, 2010 8:22 pm

ttd wrote:If 2 different members are to be selected at random from a
group of 8 people and if p is the probability that both
members selected will be older than 35 years old, is
p > 1/3 ?

(1) More than half of the group members are older than
35 years old.
(2) The probability that both members selected will be 35
years old or younger is greater than 1/10 .

1. There are at least 5 men older than 35 in the group, so the least probability of picking two people older than 35 years is 5C2/8C2 = 10/28 = 2/7; if there were 6 men older than 35 in the group, the probability of picking two people older than 35 is 15/28 which is more than 1/3 - Insufficient

2. if there were only 2 people who are less than 35 years old, probability of picking them both = 1/28 which is less than 1/10; if there were 3 people who are less than 35 years old, probability of picking 2 of them = 3/28 which is greater than 1/10. So this condition says there are at least 3 members of each kind.

Now this is a sufficient condition because, the probability of picking two 35 years olds in this case would be always less than 1/3. Sufficient
[spoiler]
So B[/spoiler]

Always borrow money from a pessimist, he doesn't expect to be paid back.

Like this post

liferocks: Legendary Member; Posts: 576; Joined: Sat Mar 13, 2010 8:31 pmFollowed by: 1 member; Thanked: 97 times

by liferocks » Wed Mar 31, 2010 10:31 pm

Hey,
I am getting the answerlike this

Form 1st point,
minimum number of people older than 35yr is 5 so p=10/28 which is >1/3 [30/84 vs 28/84] hence for all possible value it will be greater than 1/3-->point 1 is sufficient

From 2nd point,
minimum number of people less than or equal to 35yr is 3,this can be split like this
>35yr <=35yr p
5 3 >1/3
4 4 <1/3
3 5 <1/3
2 6 <1/3
1 7 <1/3
0 8 <1/3
-->point 2 is not sufficient.

So only point 1 is sufficient ie Ans is A
ttd, can you please confirm wat is correct. or somebody please point what I am doing wrong.

Like this post

ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Wed Mar 31, 2010 10:34 pm

ajith wrote:
ttd wrote:If 2 different members are to be selected at random from a
group of 8 people and if p is the probability that both
members selected will be older than 35 years old, is
p > 1/3 ?

(1) More than half of the group members are older than
35 years old.
(2) The probability that both members selected will be 35
years old or younger is greater than 1/10 .
1. There are at least 5 men older than 35 in the group, so the least probability of picking two people older than 35 years is 5C2/8C2 = 10/28 = 2/7; if there were 6 men older than 35 in the group, the probability of picking two people older than 35 is 15/28 which is more than 1/3 - Insufficient

2. if there were only 2 people who are less than 35 years old, probability of picking them both = 1/28 which is less than 1/10; if there were 3 people who are less than 35 years old, probability of picking 2 of them = 3/28 which is greater than 1/10. So this condition says there are at least 3 members of each kind.

Now this is a sufficient condition because, the probability of picking two 35 years olds in this case would be always less than 1/3. Sufficient
[spoiler]
So B[/spoiler]

I did a wrong calculation 10/28 is not equal to 2/7
Which makes A sufficient and B insufficient

A is the answer

Always borrow money from a pessimist, he doesn't expect to be paid back.

Like this post

ttd: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Wed Mar 24, 2010 6:07 pm

by ttd » Thu Apr 01, 2010 1:10 pm

Thanks for your input guys.
Now, here's what the book said (which makes more sense now that today's a new day ~).
I didn't understand why B wasn't sufficient at the time of posting.
___________
Answer given was "A".

n = number of members 35+

p of both members 35+ = n / 8 x (n-1) / 7

(1) Minimum number of 35+ = 5.
Thus p = 5/8 x 4/7 = 5/14.
Sufficient

(2) n = 5 is pretty much the minimum number for p to be > 3.
In second statement, if n = 5, p of 35 younger > 1/10. p of 35 older > 1/3.
But if n becomes less than 5, p of 35 younger is still > 1/10, but p of 35 older is not > 1/3.
So insufficient

Like this post

student22: Master | Next Rank: 500 Posts; Posts: 216; Joined: Mon Dec 21, 2009 10:26 am; Thanked: 16 times

by student22 » Thu Apr 01, 2010 2:29 pm

Statement 2 is saying that the probability of them NOT being 35 or older is at least 1/10...which means that it's possible that the probability is 1.0, or that 0/8 are older than 35. So p could be < 1/3. Not sufficient.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review