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

Therefore, Our answer = 0.108 (Back Cams) = 0.108 * 250 .= 27