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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

32% (03:44) correct
68% (04:15) wrong based on 237 sessions

HideShow timer Statistics

There are 500 cars on a sales lot, all of which have either two doors or four doors. There are 165 two-door cars on the lot. There are 120 four-door cars that have a back-up camera. Eighteen percent of all the cars with back-up cameras have standard transmission. If 40% of all the cars with both back-up cameras and standard transmission are two-door cars, how many four-door cars have both back-up cameras and standard transmission?

There are 500 cars on a sales lot, all of which have either two doors or four doors. There are 165 two-door cars on the lot. There are 120 four-door cars that have a back-up camera. Eighteen percent of all the cars with back-up cameras have standard transmission. If 40% of all the cars with both back-up cameras and standard transmission are two-door cars, how many four-door cars have both back-up cameras and standard transmission?

First let's find the max these can be Say cars with camera is C.. So 18% of C have both C & S... Now 120 of 4-door cars have C.. Say all 2-door cars have C, that is 165.. So C has to be lesser than or equal to 120+165 or 285

What is the number of 4-door cars with C&S 60% of 18% of C or \(\frac{60*18}{100*100}*C= 0.108*C\)

But 0.108*C has to be an integer There are three DECIMALS, so it has to multiplied with 3 TENS or 3*2s and 3*5s.. 108 is a multiple of 4 so 2*2s are already there so C has to be multiple of (3-2)*2s and 3*5s.. That is 2*5*5*5=250.. so 250 or 250*2=500 Also C cannot be MORE than 285, so ONLY possible value is 250..

Re: There are 500 cars on a sales lot, all of which have either two doors [#permalink]

Show Tags

01 Jun 2017, 18:34

There are 500 cars on a sales lot, all of which have either two doors or four doors. There are 165 two-door cars on the lot. There are 120 four-door cars that have a back-up camera. Eighteen percent of all the cars with back-up cameras have standard transmission. If 40% of all the cars with both back-up cameras and standard transmission are two-door cars, how many four-door cars have both back-up cameras and standard transmission?

(A) 18 (B) 27 (C) 36 (D) 45 (E) 54

This is one from a set of 15 challenging problems. To see all 15, as well as the OE for this particular question, see: Challenging GMAT Math Practice Questions

@Bunuel..Can you pls provide a solution. Not able to understand. Thanks

Re: There are 500 cars on a sales lot, all of which have either two doors [#permalink]

Show Tags

16 Jun 2017, 20:00

1

This post received KUDOS

Chets25 wrote:

There are 500 cars on a sales lot, all of which have either two doors or four doors. There are 165 two-door cars on the lot. There are 120 four-door cars that have a back-up camera. Eighteen percent of all the cars with back-up cameras have standard transmission. If 40% of all the cars with both back-up cameras and standard transmission are two-door cars, how many four-door cars have both back-up cameras and standard transmission?

(A) 18 (B) 27 (C) 36 (D) 45 (E) 54

This is one from a set of 15 challenging problems. To see all 15, as well as the OE for this particular question, see: Challenging GMAT Math Practice Questions

@Bunuel..Can you pls provide a solution. Not able to understand. Thanks

There are 500 cars on a sales lot, all of which have either two doors or four doors. There are 165 two-door cars on the lot. There are 120 four-door cars that have a back-up camera. Eighteen percent of all the cars with back-up cameras have standard transmission. If 40% of all the cars with both back-up cameras and standard transmission are two-door cars, how many four-door cars have both back-up cameras and standard transmission? Hi, Here, In this question he is stating that 18 percent of all cars with Back-up cams have ST . 18%(BackCams) = Back cams + Std. Trans Now, Of these above 40 % are 2 doors . But, We need for 4-Doors. hence, 60% of those with Back Cams + Std.Trans are 4-doors.

Now what we need is 4-doors with Back cams + std.Trans = 60% of (Back Cams + std. Trans) = 60 % of (18%(BackCams)) = 0.108 * ( Back Cams ) ...........Equation 1

Now In the question we are given that 500 are 4-doors and 165 are 2-door cars. 4- door cars = 500 - 165 = 335 . Number of 4 - doors with Back Cams + Standard transmission can never be in decimals. Never seen a half built or 0.23 of a car.

Hence, In equation 1. 0.108 * ( Back Cams ) --- which represents the number of 4-doors + back cams + Std. Trans can never be in decimals. It is only possible when Back Cams are in the multiples of 250 i.e. Back Cams are 250 , 500, 750 .... But The maximum back Cams can take should be less than 500 . Because it is given that. - There are 120 four-door cars that have a back-up camera. that is there are some cars which do not have back up cameras. hence number of cars with Back Cams = 250

There are 500 cars on a sales lot, all of which have either two doors or four doors. There are 165 two-door cars on the lot. There are 120 four-door cars that have a back-up camera. Eighteen percent of all the cars with back-up cameras have standard transmission. If 40% of all the cars with both back-up cameras and standard transmission are two-door cars, how many four-door cars have both back-up cameras and standard transmission?

(A) 18 (B) 27 (C) 36 (D) 45 (E) 54

1. Let 120 four-door cars and x two-door cars have a back-up camera 2. 18% of (120+x) have standard transmission 3. 60% of the above are four-door cars with both. i.e., 60/100*18/100* (120+x). 4. Simplifying we get 12.96+0.108x . This number has to be an integer. 0.108*x has to end in 0.04 or x has to end in 3. 5. If we try 13 for x , we get an integer value which is 27.
_________________

Re: There are 500 cars on a sales lot, all of which have either two doors [#permalink]

Show Tags

06 Aug 2017, 03:31

mikemcgarry wrote:

There are 500 cars on a sales lot, all of which have either two doors or four doors. There are 165 two-door cars on the lot. There are 120 four-door cars that have a back-up camera. Eighteen percent of all the cars with back-up cameras have standard transmission. If 40% of all the cars with both back-up cameras and standard transmission are two-door cars, how many four-door cars have both back-up cameras and standard transmission?

Has to be a max of 285 cars (165 two doors and 120 4 door cars with back up transmission) Now use options Option b) 27*100/60=45 45*100/18=250. Rest all exceeds 285 using similar process.
_________________

Believe you can and you are halfway there-Theodore Roosevelt

There are 500 cars on a sales lot, all of which have either two doors [#permalink]

Show Tags

25 Aug 2017, 21:09

guhabhishek wrote:

Has to be a max of 285 cars (165 two doors and 120 4 door cars with back up transmission) Now use options Option b) 27*100/60=45 45*100/18=250. Rest all exceeds 285 using similar process.

Agree I think it's the best solution here

max 285 cars 18% of 285 makes 50, 60% of 50 makes 30, so C D E are out, top to bottom analysis now bottom top, lets take 27 and plug the numbers, 27 is 60% then 18 is 40% together 45 cars which makes 18% of total with back-up camera, 250 cars if we take 18, then 18 is 60% and 12 is 40% summing comes to 30, 30 is 18% of something...ooops not an integer

Re: There are 500 cars on a sales lot, all of which have either two doors [#permalink]

Show Tags

16 Sep 2017, 05:46

Let A be number 0f 2 door cars with back up camera. 120 - number of 4 door cars with back up camera.

Now 0.18 * (A + 120) is number of cars with backup camera and standard transmission. of this 40% - 2 doors, so remaining 60% - 4 doors

so our answer is 0.6 * 0.18 ( A + 120), Let our answer be x. => (3/5)*(9/50) * (A + 120) = x => (27/250) * (A+120) = x rearranging , A = (250/27) * x - 120,

Now note prime factorization of 250 is ( 2 * 5 ^ 3) and prime factorization of 27 is (3 ^ 3), so GCD of both 250 and 27 is 1, so to make A an integer, x has to be multiple of 27

Let x = 27, then A = 130 Let x = 54, then A = 380 , but this is not possible, as total of 2 - door cars is 165. so x has to be 27, which is B