In a certain parking lot with 220 cars, all but 20 cars are either

Question

In a certain parking lot with 220 cars, all but 20 cars are either white or black or have sunroofs. If 60% of the cars are white of which one-fourth have sunroofs, and 30% of the cars are black of which a third have sunroofs, how many cars have sunroofs? (No car is both black and white in color)

A. 24
B. 35
C. 55
D. 57
E. 77

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A. 24
B. 35
C. 55
D. 57
E. 77

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ManifestDreamMBA · Answer

The trick here is to check that the totals don't add up
132+66+20 is still 2 short of 220, which means there are other cars with sunroof

Setting up the matrix

White 
 Black 
 Others 
 Total 
 
  Sunroof 
 =132 * 1/4 = 33 
 =66 * 1/3 = 22 
 =22-20 = 2 
 =22+22+2=57 
 
  No Sunroof

20

Total 
 =220*0.6 = 132 
 =220*0.3 = 66 
 =220 - 132-66 =22  
 220

GMATinsight · Answer

Given:  
 • Total cars =  220  
 • Cars that are either white, black, or have sunroofs =  220 - 20 = 200  
 •  60%  of the cars are  white  →  0.6 	imes 220 = 132   
 •  30%  of the cars are  black  →  0.3 	imes 220 = 66   
 • No car is both black and white. 
 •  One-fourth  of white cars have sunroofs →  \frac{1}{4} 	imes 132 = 33   
 •  One-third  of black cars have sunroofs →  \frac{1}{3} 	imes 66 = 22   
 • We need to find the total number of cars that have sunroofs.

Step 1: Calculate Sunroof Cars  
 1.  White cars with sunroofs  =  33  
 2.  Black cars with sunroofs  =  22  
 3.  Other cars that have sunroofs : 
 • There are  200  cars that are white, black, or have sunroofs. 
 • White + Black cars =  132 + 66 = 198 . 
 • Therefore, the number of  non-white, non-black cars with sunroofs  = 200 - 198 = 2 .

Step 2: Total Sunroof Cars

Total sunroof cars =  White sunroof cars + Black sunroof cars + Other sunroof cars  
 =  33 + 22 + 2 = 57

Answer:

Answer: Option D

Similar official question:

https://www.youtube.com/watch?v=Q7rQpmdSSwU

GMATinsight · Answer

If you add 132 and 66 as highlighted in the table then it totals 198 i.e. two cars have not been spoken about here out of (220-20 =200 200) cars those two cars are not white and not black i.e. those two cars must have the sunroof hence total sunroof cars = 55+2 = 57 Quite tricky actually

ManifestDreamMBA · Answer

Yup, I realised when posted. Have been facing issues with the formatting, so couldn't fix it yet. Thanks for pointing out

bhargavhhhhhhhh · Answer

1. Total cars = 220
2. Cars that are NOT white, black, or with sunroofs = 20
 → So, cars that are either white, black, or have sunroofs = 220 - 20 = 200
3. White cars = 60% of 220 = 132
 - White cars with sunroofs = 1/4 of 132 = 33
4. Black cars = 30% of 220 = 66
 - Black cars with sunroofs = 1/3 of 66 = 22
5. Other cars with sunroofs = Total cars with sunroofs (not counted yet) 
 = 200 - (White cars 132 + Black cars 66) 
 = 200 - 198 = 2
6. Total cars with sunroofs = 33 + 22 + 2 extra = 57

Answer: D. 57

Sowmya_10 · Answer

I feel the question itself is incorrect ...All the solutions I looked up say that 20 cars are  NOT  black , white or have sunroofs whereas in the question it mentions  either black or white or have sunroofs  .. So I feel the question has to be the  "all but 20 cars are neither white or black or have sunroofs".

Krunaal · Answer

The phrase  "   all  but  20 cars"  means all 200 cars are either black or white or have sunroof, and 20 don't.

Lajsek · Answer

First, let's create a matrix with all the information we can easily deduce from the question. To avoid wasting time for calculations, I decided to stick to %
    
 no sunroof 
 sunroof 
  TOTAL  
 
  White 
 3/4*60%=45% 
 1/4*60%= 15%  
 60% 
 
  Black 
 2/3*30%=20% 
 1/3*30%= 10%  
 30% 
 
  Other

10% 
 
   TOTAL

100%

Now let's try to find number of cars in other color that have sunroof:

1. There are  200  cars which are white or balck or have sunroofs.
 
2. There are 90% black or white cars --> 10% of cars have different color. 10%*220= 22 
 
3. Combining 1 & 2: total number of cars is higher than cars on the parking lot, which means that sets are overlapping. There has to be  2  cars in other color with sunroof and  20  cars in other color without sunroof

no sunroof 
 sunroof 
  TOTAL  
 
  White 
 45% 
 15% 
 60% 
 
  Black 
 20% 
 10% 
 30% 
 
  Other 
  20 cars  
  2 cars  
 10% 
 
   TOTAL  
  
  25%+2 cars  
 100%

Now we can convert % to numbers to anwser the question - total number of cards with sunroof = 25% of all cars + 2 cars -->25%*220+2= 57 
 --- 
As others have shown, you can also convert % to numbers at the beginning, but I prefer to keep the number of calculations to a minimum

pappal · Answer

as per given 200 cars are either white or black or have sunroof. ---------i
white=132 white sunroof=33
black=66 black sunroof=22
total black + white=198 and total of black sunroof + white sunroof=55
so, from (i) 2 cars neither black or white but have sunroof.
so total sunroof=55+2=57

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=88335 - Out of 200, all but 20 are either black or white or have a sunroof. So, there are 20 cars which are --- neither white, nor black, nor have a sunroof. - 60% of 220 = 132 white cars. Out of these, 1/4 x 132 = 33 cars have sunroof. - So, 132 - 33 = 99 white cars do not have sunroof. - Similarly, 30% of 220 = 66 black cars. Out of these, 1/3 x 66 = 22 cars have sunroof. - So, 66 - 22 = 44 black cars do not have sunroof. The rest of the table can be easily filled. Our final answer is 57. GMAT-Club-Forum-6dp4nqth.png

	White	Black	Total
Sunroof	132*1/4 = 33	66*1/3 = 22	55
No sunroof	132-33 = 99	66-22 = 44
Total	220*.6 = 132	220*.3 = 66

	White	Black	Total
Sunroof	132*1/4 = 33	66*1/3 = 22	55
No sunroof	132-33 = 99	66-22 = 44
Total	220*.6 = 132	220*.3 = 66

In a certain parking lot with 220 cars, all but 20 cars are either

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	White	Black	Others	Total
Sunroof	=132 * 1/4 = 33	=66 * 1/3 = 22	=22-20 = 2	=22+22+2=57
No Sunroof			20
Total	=220*0.6 = 132	=220*0.3 = 66	=220 - 132-66 =22	220

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In a certain parking lot with 220 cars, all but 20 cars are either

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