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19 Feb 2025, 01:30
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D
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Difficulty:
95%
(hard)
Question Stats:
45% (03:11) correct
55%
(02:51)
wrong
based on 141
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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
A. 24
B. 35
C. 55
D. 57
E. 77
Updated on: 19 Feb 2025, 02:54
Originally posted by ManifestDreamMBA on 19 Feb 2025, 01:51.
Last edited by ManifestDreamMBA on 19 Feb 2025, 02:54, edited 2 times in total.
Last edited by ManifestDreamMBA on 19 Feb 2025, 02:54, edited 2 times in total.
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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
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 |
Bunuel
19 Feb 2025, 02:29
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Bunuel
Given:
• Total cars = 220
• Cars that are either white, black, or have sunroofs = 220 - 20 = 200
• 60% of the cars are white → \(0.6 \times 220 = 132\)
• 30% of the cars are black → \(0.3 \times 220 = 66\)
• No car is both black and white.
• One-fourth of white cars have sunroofs → \(\frac{1}{4} \times 132 = 33 \)
• One-third of black cars have sunroofs → \(\frac{1}{3} \times 66 = 22 \)
• 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
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