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Apr 2808:00 AM PDT
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08 Jun 2022, 18:30
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B
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Difficulty:
25%
(medium)
Question Stats:
80% (02:36) correct
20%
(02:59)
wrong
based on 148
sessions
History
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One-quarter of the cars that an automobile manufacturer produces are sports cars, and the rest are sedans. If one-fifth of the cars that the manufacturer produces are red and one-third of the sports cars are red, then what fraction of the sedans is red?
A. 1/9
B. 7/45
C. 1/5
D. 11/45
E. 38/45
A. 1/9
B. 7/45
C. 1/5
D. 11/45
E. 38/45
08 Jun 2022, 20:37
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Bunuel
Let's make the total number of cars X.
Lol, I'm kidding. Variables are no fun, and fractional variables are even worse. Why would I do that to myself?!?!
Let's pick a number for the total number of cars. Two approaches, either of which works, and some people are better at one while others are better at the other, so I'll show both.
First, percentages:
The total number of cars is 100.
25 are sports cars; 75 are sedans.
20 red cars, 8.333 of which are red sports cars, so the other 11.667 red cars are red sedans.
11.667/75...between 1/6 and 1/7
Let's look at the answer choices.
A. 1/9 Too low. Eliminate.
B. 7/45 Keep it.
C. 1/5 Too high. Eliminate.
D. 11/45 Too high. Eliminate.
E. 38/45 Way too high. Eliminate.
Answer choice B
Second, picking a logical number:
We have 1/4, 1/5, and 1/3 in the question. Let's use something that might fit well with the denominators. How about 60?
The total number of cars is 60.
15 are sports cars; 45 are sedans.
12 are red cars, 5 of which are red sports cars, so the other 7 red cars are red sedans.
7/45
Answer choice B
ThatDudeKnowsHiddenPlugIn
05 Sep 2022, 09:20
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Bunuel
lets say the total is 120 ( just because it is divisible by 3,4and 5).
no. of sports cars - 120/4 = 30 ==> sedans - 120-30 = 90
no. of red sports cars = 30/3 = 10
no. of sports cars = 120/5 = 24 ==> red sedans = 24-10 = 14.
req. ratio = red sedans / total sedans = 14/90 = 7/45 --> B.
