Counting - Set Problem - The Beat The GMAT Forum - Expert GMAT Help & MBA Admissions Advice

Counting - Set Problem

Expert replies

iikarthik: Senior | Next Rank: 100 Posts; Posts: 57; Joined: Sun Jul 06, 2008 10:52 am; Thanked: 1 times; GMAT Score:640

by iikarthik » Fri Feb 20, 2009 10:07 pm

If a town,16 people own Fords and 11 People own Toyotas.If exactly 15 people own only one type of two types of cars.how many people own both types of cars?

Soultion is : 6

I tried with the P(AUB) = P(Ford cars) + p(toyota cars) - P(Ford and Toyota)

15=16+11-P(Ford and Toyota)

P(Ford and Toyota)=12.

i dunno wats is wrong with my solution.

pls clarify

Like this post

Source: Beat The GMAT — Problem Solving | Fri Feb 20, 2009 10:07 pm

ontopofit: Senior | Next Rank: 100 Posts; Posts: 68; Joined: Sun Dec 21, 2008 12:00 am; Thanked: 3 times

by ontopofit » Fri Feb 20, 2009 10:47 pm

here 15 is the number of ppl with either one of the two cars so P(AUB) is not 15 , rather it is 15 + P(both A and B).....equate this and get the answer as 6.

Like this post

sureshbala: Master | Next Rank: 500 Posts; Posts: 319; Joined: Wed Feb 04, 2009 10:32 amFollowed by: 9 members; Location: Delhi; Thanked: 84 times

by sureshbala » Fri Feb 20, 2009 11:54 pm

Let x be the number of people who own both.

Hence people who own only Ford = 16-x and only Toyota = 11-x

Given (16-x)+(11-x)=15

So x =6

Like this post

iikarthik: Senior | Next Rank: 100 Posts; Posts: 57; Joined: Sun Jul 06, 2008 10:52 am; Thanked: 1 times; GMAT Score:640

by iikarthik » Mon Feb 23, 2009 1:51 am

hi,

Thanks for ur reply.

But i still dont understand what went erong.

karthik

Like this post

bmlaud: Master | Next Rank: 500 Posts; Posts: 174; Joined: Thu Jan 08, 2009 12:04 am; Thanked: 5 times; GMAT Score:620

by bmlaud » Mon Feb 23, 2009 4:36 am

Solve this problem in a other way

n(F) = 16
n(t) = 11
n(FUT) = ??
n(F int T) = ??
n(FUT) - n(F int T) = 15 given.....1

also n(FUT) = n(F) + n(T) - n(F int T)
= 16+11- n(F int T) ....2

solve 1 and 2 n(FUT) = 21 and n(F int T) = 6

"Great works are performed not by strength but by perseverance."

Like this post

x2suresh: Master | Next Rank: 500 Posts; Posts: 258; Joined: Thu Aug 07, 2008 5:32 am; Thanked: 16 times

by x2suresh » Mon Feb 23, 2009 7:46 pm

iikarthik wrote:hi,

Thanks for ur reply.

But i still dont understand what went erong.

karthik

Think this way.

16 Fords owned by 16 People
11 Toyotaq owned by 11 people
15 people owned only one vehicle.

16+11 -15= 12 vehicles owned by "no. people who owned 2 vehicles each"

obviously only 6 person can own 12 vehicles.
If 12 persons then they should own 24 vehicles.

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