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# Nancy, a car dealer, put 420 cars on sale. All cars on sale belong to

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Math Expert
Joined: 02 Sep 2009
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Nancy, a car dealer, put 420 cars on sale. All cars on sale belong to  [#permalink]

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11 Nov 2019, 04:34
1
1
00:00

Difficulty:

65% (hard)

Question Stats:

60% (02:17) correct 40% (02:19) wrong based on 34 sessions

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Nancy, a car dealer, put 420 cars on sale. All cars on sale belong to one of two gear models: automatic or manual gear. Of the cars on sale, is the percent of hybrid vehicles at least 40%?

(1) Of the cars Nancy put on sale, 30 percent of the cars with automatic gear are hybrid vehicles.

(2) Of the cars Nancy put on sale, 80 percent of the cars with manual gear are hybrid vehicles.

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Nancy, a car dealer, put 420 cars on sale. All cars on sale belong to  [#permalink]

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11 Nov 2019, 09:10
1
let automatic cars = x% , and manual = (100-x)%

from sentence (1), hybrid automatic = $$\frac{3x}{10}$$ --> insufficient
from sentence (2), hybrid manual = $$80 - \frac{8x}{10}$$ --> insufficient

by combining, hybrid = $$80 - \frac{5x}{10}$$
the least value of x is 10 (must be divisible by 10 so that hybrid automatic become an integer),
and the maximum value of hybrid = 75, which is more than 40%

the highest value of x is 90
and the least value of hybrid = 35, which is less than 40%

so Insufficient E
Nancy, a car dealer, put 420 cars on sale. All cars on sale belong to   [#permalink] 11 Nov 2019, 09:10
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