Bunuel wrote:
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.
Are You Up For the Challenge: 700 Level QuestionsSolution
Step 1: Analyse Question Stem
• Total number of cars = \(420\)
• Let \(a\) be the number of automatic gear cars.
o The number of manual gear cars = \(420 – a\)
We need to find; is the percentage of hybrid cars at least \(40%\)
• Is the number of hybrid vehicles \(≥ 40/100*420\)
• Or, is hybrid vehicles ≥ \(164\)
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: \(30%\) of the automatic cars with automatic gear are hybrid vehicles.
• The number of hybrid cars with automatic gear =\( \frac{30}{100}*a = \frac{3}{10}*a\)
o We don’t know how many cars with manual gears are hybrid.
o We also don't know the value of a
Hence, statement 1 is not sufficient, we can eliminate answer options A and D.
Statement 2: \(80%\) of the cars with manual gears are hybrid vehicles.
• The number of hybrid care with manual gears =\(\frac{80}{100}*(420-a)\)
• We don’t know how many cars with automatic gears are hybrid.
• we also don't know the value of a.
Hence, statement 2 is also not sufficient, we can eliminate the answer options B.
Step 3: Analyse Statements by combining.
From statement 1: Number of hybrid cars with automatic gears = \(\frac{3}{10}*a\)
From statement 2: Number of hybrid cars with manual gears = \(\frac{80}{100}*(420-a)\)
• The total number of hybrid cars = \(\frac{3}{10}*a + \frac{80}{100}*(420-a)\)
o Since we don’t know the value of \(a\), we can’t find the exact number of hybrid cars.
Hence, the correct answer is
Option E. _________________
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