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16 Sep 2014, 01:04
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C
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Difficulty:
45%
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Question Stats:
73% (02:36) correct
27%
(03:04)
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based on 222
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Among the 200 cars exhibited at an auto show, 50 were equipped with built-in air conditioners and 63 with traction control systems. If 12% of the cars with air conditioners were also equipped with traction control systems, what percentage of the cars without air conditioners were equipped with traction control systems?
A. 35
B. 36
C. 38
D. 40
E. 45
A. 35
B. 36
C. 38
D. 40
E. 45
16 Sep 2014, 01:04
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Official Solution:
Among the 200 cars exhibited at an auto show, 50 were equipped with built-in air conditioners and 63 with traction control systems. If 12% of the cars with air conditioners were also equipped with traction control systems, what percentage of the cars without air conditioners were equipped with traction control systems?
A. 35
B. 36
C. 38
D. 40
E. 45
Out of the 50 cars equipped with air conditioners, 6 (\(12\%\) of \(50 = 0.12*50 = 6\)) also had traction control systems. This implies that there were \(63 - 6 = 57\) cars equipped with traction control systems but lacking air conditioners. Since there were \(200 - 50 = 150\) cars without air conditioners, the percentage of cars without air conditioners that were equipped with traction control systems is \(\frac{57}{150}*100\% = 38\%\).
Another way to solve this is by using a two-set matrix, as shown below. The black numbers are what we already know from the problem. The red numbers are what we figure out based on that info. What we're really looking for is the ratio between the numbers in the yellow boxes.
Answer: C
Among the 200 cars exhibited at an auto show, 50 were equipped with built-in air conditioners and 63 with traction control systems. If 12% of the cars with air conditioners were also equipped with traction control systems, what percentage of the cars without air conditioners were equipped with traction control systems?
A. 35
B. 36
C. 38
D. 40
E. 45
Out of the 50 cars equipped with air conditioners, 6 (\(12\%\) of \(50 = 0.12*50 = 6\)) also had traction control systems. This implies that there were \(63 - 6 = 57\) cars equipped with traction control systems but lacking air conditioners. Since there were \(200 - 50 = 150\) cars without air conditioners, the percentage of cars without air conditioners that were equipped with traction control systems is \(\frac{57}{150}*100\% = 38\%\).
Another way to solve this is by using a two-set matrix, as shown below. The black numbers are what we already know from the problem. The red numbers are what we figure out based on that info. What we're really looking for is the ratio between the numbers in the yellow boxes.
Answer: C
