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