Of the vehicles (cars and trucks) for sale at a certain dealership, 48

Question

Of the vehicles (cars and trucks) for sale at a certain dealership, 48 percent are cars that have 4 doors. If 80 percent of the cars for sale at the dealership have 4 doors, what percent of the vehicles are cars that do not have 4 doors?

(A) 12%
(B) 20%
(C) 24%
(D) 32%
(E) 40%

(A) 12%
(B) 20%
(C) 24%
(D) 32%
(E) 40%

MartyMurray · Accepted Answer

There are a few ways to answer this question.

I'd probably do it in my head this way.

48% of all vehicles = 80% of cars (the ones that have 4 doors)

100% - 80% = 20% of cars do not have 4 doors

20%/80% = 1/4

So, 20% of cars = 1/4 of 48% of all vehicles = 12% of all vehicles

The correct answer is (A).

Kinshook · Answer

DALC1

Given:  Of the vehicles (cars and trucks) for sale at a certain dealership, 48 percent are cars that have 4 doors. 
 Asked:  If 80 percent of the cars for sale at the dealership have 4 doors, what percent of the vehicles are cars that do not have 4 doors?

Cars  Trucks  Total  
  4 doors  48%      
  ~4 doors        
  Total  48%/80% = 60%    100%

Cars  Trucks  Total  
  4 doors  48%      
  ~4 doors  60%-48%= 12%       
  Total  48%/80% = 60%    100%

IMO A

DALC1 · Answer

MartyMurray  Thank you Sir!!!!!

mahi5shrivastav · Answer

how did you get 48/80??

GmatKnightTutor · Answer

Of the vehicles (cars and trucks) for sale at a certain dealership, 48 percent are cars that have 4 doors. If 80 percent of the cars for sale at the dealership have 4 doors, what percent of the vehicles are cars that do not have 4 doors?

(A) 12%
(B) 20%
(C) 24%
(D) 32%
(E) 40%

(A) 12%
(B) 20%
(C) 24%
(D) 32%
(E) 40%

Let's plug in a value. Let's say that 80 percent of cars that have 4 doors is actually 80 cars.

80 cars have 4 doors
20 cars do not have 4 doors

This would mean that...

80 vehicles is also 48% of all cars and trucks
160 vehicles is 96% of all cars and trucks

Our objective is to find out the percentage of   out of the  .

This is roughly 20/160 -> 2/16 -> 1/8 -> 0.125

But wait... the actual number of total vehicles is a bit more than 160 (160 is only equal to 96%). This means the final answer should be a bit LESS than 12.5 percent

(A) 12% is the answer.

ayushiii02 · Answer

Let the total vehicles be x 
Let the total cars be y 
Then — 48/100x = 80/100y 
Now, through this we get 60/100 = y/x

That is 60% are total cars, amongst which 48% are 4 doors, so the cars that donot have 4 doors = 60-48 = 12%.

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MoPouyan · Answer

Let the total number of vehicles at the dealership be V
Let the total number of cars at the dealership be C

We know that 48% of the total vehicles are cars with 4 doors:
Cars with 4 doors = 0.48⋅V

We also know that 80% of all cars have 4 doors:
Cars with 4 doors=0.8⋅C
These two quantities must be the same because they both represent the number of cars with 4 doors:
0.8⋅C=0.48⋅V

C= 0.48⋅V / 0.8 =0.6 V

This means that 60% of the total vehicles are cars.

Calculate the percentage of cars that do NOT have 4 doors:

Out of all the cars, 80% have 4 doors. Therefore, the remaining 20% of the cars do NOT have 4 doors.

The total number of cars is 0.6 ⋅ V and 20% of these do not have 4 doors:

Cars without 4 doors = 0.2⋅ (0.6⋅V)=0.12⋅V

HadjiMurad · Answer

all of this answers are too complicated for me, so I found easy one, like most simple. So 48% of 4d - is 80% of all cars, then 20% is  no 4d cars .  Proportion 48/x = 80/20 ; 48*20/80 = 12. I spent about 10 minutes to understand it, idk why my mind couldn't find so simple answer :/

BraydinWalters · Answer

Let's assume we're working with 100 cars

48 percent (or 48 of 100) are cars that have 4 doors

80 percent of the cars at dealership have 4 doors: 4/5x = 48 so x = 60

60 - 48 = 12

12/100 = 12%

Cars 
 Trucks 
 Total 
 
  Four Doors 
  48

Two Doors 
   12

Total 
  60  
  
  100

emtroy · Answer

If you use 100 as the total # vehicles, then you can say that there are 48 cars with 4 doors. Since we know that 80% of cars have 4 doors, then we can do 48= 0.8*cars and solve for cars, which = 60. In this solution, it's basically the same -- you end up doing 48% divided by 80% to get the % of vehicles that are cars. IMO, it's easier to think about in #s.

To finish it out and to get cars without 4 doors, do 60-48 which is 12. Recall that we are using 100 as the placeholder for all vehicles, so we can say that 12% of all vehicles are cars without 4 doors.

emtroy · Answer

If you use 100 as the total # vehicles, then you can say that there are 48 cars with 4 doors. Since we know that 80% of cars have 4 doors, then we can do 48= 0.8*cars and solve for cars, which = 60. In this solution, it's basically the same -- you end up doing 48% divided by 80% to get the % of vehicles that are cars. IMO, it's easier to think about in #s.

To finish it out and to get cars without 4 doors, do 60-48 which is 12. Recall that we are using 100 as the placeholder for all vehicles, so we can say that 12% of all vehicles are cars without 4 doors.

Of the vehicles (cars and trucks) for sale at a certain dealership, 48

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	Cars	Trucks	Total
4 doors	48%
~4 doors	60%-48%=12%
Total	48%/80% = 60%		100%

GMAT Problem Solving (PS) Questions

Of the vehicles (cars and trucks) for sale at a certain dealership, 48

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