Peter is John's friend

Expert replies

logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

by logitech » Tue Nov 25, 2008 10:40 pm

In a room filled with 7 people, 4 people have exactly 1 friend in the room and 3 people have exactly 2 friends in the room (Assuming that friendship is a mutual relationship, i.e. if John is Peter's friend, Peter is John's friend). If two individuals are selected from the room at random, what is the probability that those two individuals are NOT friends?

OA [spoiler]16/21[/spoiler]

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

Like this post

Source: Beat The GMAT — Problem Solving | Tue Nov 25, 2008 10:40 pm

mals24: Legendary Member; Posts: 683; Joined: Tue Jul 22, 2008 1:58 pmFollowed by: 2 members; Location: Dubai; Thanked: 73 times

by mals24 » Wed Nov 26, 2008 2:38 am

Ok say there are 7 guys A B C D E F G

Now 4 have exactly 1 friend and 3 have exactly 2

So the total number of pairs of friends:

A-B
C-D
E-F+G
F-E+G
G-E+F

That makes it a total of 5 pair of friends.

Total number of ways of selecting 2 people out of 7 = 7C2 = 21

Hence probability of selecting 2 people who are NOT friends:

1-probability of selecting 2 friends = 1-5/21 = 16/21

Like this post

vivek.kapoor83: Legendary Member; Posts: 833; Joined: Mon Aug 04, 2008 1:56 am; Thanked: 13 times

by vivek.kapoor83 » Wed Nov 26, 2008 2:45 am

Mals !!
How u arrived on pairs of friends...pls elaborate

Like this post

mals24: Legendary Member; Posts: 683; Joined: Tue Jul 22, 2008 1:58 pmFollowed by: 2 members; Location: Dubai; Thanked: 73 times

by mals24 » Wed Nov 26, 2008 3:51 am

See there are 7 people in the party

A B C D E F G

Now exactly 4 people have 1 friend

Lets say A B C D have exactly 1 friend

A is B's friend
C is D's friend

Now in the question its given that friendship is a mutual relationship, i.e. if John is Peter's friend, Peter is John's friend

This means if A is B's friend, then B is also A's friend and since we assumed that B has only 1 friend A will be B's only friend right.

So we have 1 pair of friendship A-B
Same logic for C and D

So that gives us 2 pairs, A-B; C-D

Now exactly 3 people have 2 friends

Lets say E F G each has exactly 2 friends. But neither one of them can be friends with A, B, C and D (because they are done with their share of friendship)

So E will have 2 friends F and G
F will have 2 friends E and G
G will have 2 friends E and F

So now we have 3 more pairs.

E = F+G
F = E+G
G = F+E

So in total 5 pairs.

Still confused

Like this post

logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

by logitech » Wed Nov 26, 2008 8:27 am

Mals24 in da house!!! Beautiful solution.

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

Like this post

jimmiejaz: Master | Next Rank: 500 Posts; Posts: 207; Joined: Sun Mar 11, 2007 6:16 pm; Location: Mumbai; Thanked: 11 times

by jimmiejaz » Wed Nov 26, 2008 9:08 am

Logitech,

What should be the approach to solve these type of questions if the numbers are too large??? I mean here there are 7 people. What if the question asks about 20 people?
Is there any approach we shall follow?

What if i have not yet beat the beast, I know i will beat it!!!!!!!!

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