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805+ Level|   Overlapping Sets|         
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Bunuel
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Around the World in 80 Questions (Day 6): In a certain car dealership 24 Jul 2023, 08:00
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In a certain car dealership, 80 percent of all cars are German, and 40 percent of all cars are priced at $100,000 or more. If 35 percent of cars are priced at $100,000 or more and are German, what percent of cars priced under $100,000 are not German?

(A) 5%
(B) 15%
(C) 20%
(D) 25%
(E) 35%


 


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D
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ankitgoswami
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Around the World in 80 Questions (Day 6): In a certain car dealership 24 Jul 2023, 08:23
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Bunuel
In a certain car dealership, 80 percent of all cars are German, and 40 percent of all cars are priced at $100,000 or more. If 35 percent of cars are priced at $100,000 or more and are German, what percent of cars priced under $100,000 are not German?

(A) 5%
(B) 15%
(C) 20%
(D) 25%
(E) 35%


 


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Look at the table below.

The information given is put together.

Now the question asks
What percent of cars priced under $100,000 are not German?

So it will be (15/60) * 100 = 25%

Ans D

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pinkguy
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Around the World in 80 Questions (Day 6): In a certain car dealership 24 Jul 2023, 08:24
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-Let's assume there are 100 cars. We have the following deductions:
1) 80 are German, 20 are non German
2) 40 are higher than 100k, 60 are lower than 100k
3) 35 are higher than 100k and are German
-From (2) and (3)=> 5 are higher than 100k and are non-German (4)
-From (1) and (4)=>15 are lower than 100k and are non German.
-The question asks "what percent of cars priced under 100k are not German"=>The numerator is 15 and the denominator is 60
=>The percentage= \(\frac{15}{60}=25%\)
The answer is D
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Around the World in 80 Questions (Day 6): In a certain car dealership 24 Jul 2023, 08:24
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G -G
>100,000 35 5 40
<100,000 45 15 60
Total 80 20 100
The question what % of below 100,000 are not German
Hence (15/60)*100 =25%
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Around the World in 80 Questions (Day 6): In a certain car dealership 24 Jul 2023, 08:33
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Given: In a certain car dealership, 80 percent of all cars are German, and 40 percent of all cars are priced at $100,000 or more.
Asked: If 35 percent of cars are priced at $100,000 or more and are German, what percent of cars priced under $100,000 are not German?


GermanNot GermanTotal
Priced at $100,000 or more35%40%-35%=5%40%
Priced under $100,00080%-35%=45%60%-45%=15%60%
Total80%20%100%

The percent of cars priced under $100,000 are not German = 15%/60% * 100% = 25%

IMO D
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Around the World in 80 Questions (Day 6): In a certain car dealership 24 Jul 2023, 08:42
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solve using 2x2 matrix
let total cars be 100

---------German---Not german----total
>10^5---- 35-------5------------40
<10^5----45-------15------------60
total-----80-------20-------------100

percent of cars priced under $100,000 are not German
15/60 ; 25%
OPTION D



Bunuel
In a certain car dealership, 80 percent of all cars are German, and 40 percent of all cars are priced at $100,000 or more. If 35 percent of cars are priced at $100,000 or more and are German, what percent of cars priced under $100,000 are not German?

(A) 5%
(B) 15%
(C) 20%
(D) 25%
(E) 35%


 


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Around the World in 80 Questions (Day 6): In a certain car dealership 24 Jul 2023, 20:31
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Let's use the double matrix method here.
We know that 80% of all cars are German, and 40% of all cars are priced at $100,000 or more.

For simplicity, let's assume that the total number of cars is 100
Now, as per the given statement, we can draw this table.
(I was not aware that I could create neat tables in the answer until today. So I tried that here. :D )

The matrix:

Total cars = 100German CarsNon German CarsTotal
$100k or more35?40
Less than $100k???
Total80?100


Now let's complete the matrix:

Total cars = 100German CarsNon German CarsTotal
$100k or more35540
less than $100k451560
Total8020100


We are asked to find the percentage of cars priced under $100,000 that are not German. There are 60 cars priced under $100,000 in total (in bold), 15 of which are not German. So, the percentage of cars priced under $100,000 that are not German is (15/60) x 100% = 25%.

I will go with D.
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Around the World in 80 Questions (Day 6): In a certain car dealership 26 Jul 2023, 20:57
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Bunuel
In a certain car dealership, 80 percent of all cars are German, and 40 percent of all cars are priced at $100,000 or more. If 35 percent of cars are priced at $100,000 or more and are German, what percent of cars priced under $100,000 are not German?

(A) 5%
(B) 15%
(C) 20%
(D) 25%
(E) 35%


 


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for the Around the World in 80 Questions

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We have:

Attachment:
11.jpg
11.jpg [ 15.51 KiB | Viewed 1888 times ]

Assuming total cars as 100, we have:
80 are German, so 20 are non-German
40 are priced at $100,000 or more, so 60 are priced less than $100,000
35 are German and priced at $100,000 or more
So 40 - 35 = 5 are non-German and priced at $100,000 or more
Also 80 - 35 = 45 are German and and priced at less than $100,000
And 60 - 45 = 15 are non-German and and priced at less than $100,000

Number of cars priced less than $100,000 = 60
Number of non-German cars among these 60 = 15
Required percent = 15/60 * 100 = 25%

Answer D
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Around the World in 80 Questions (Day 6): In a certain car dealership 26 Oct 2024, 07:10
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