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sunroof cars

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sunroof cars

by mehrasa » Sat Nov 19, 2011 9:40 pm
a good Q:
a car dealership sell only sport cars and luxury cars. if 1/7 of sport car and 1/2 luxury car has sunroof. and he has total of 42 cars in his lot. what is the smallest number of cars with sunroof?

[spoiler]OA: 11[/spoiler]
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by shankar.ashwin » Sat Nov 19, 2011 9:45 pm
THis was solved a couple of days back..
Refer https://www.beatthegmat.com/car-dealership-t96369.html
mehrasa wrote:a good Q:
a car dealership sell only sport cars and luxury cars. if 1/7 of sport car and 1/2 luxury car has sunroof. and he has total of 42 cars in his lot. what is the smallest number of cars with sunroof?

[spoiler]OA: 11[/spoiler]
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by Anurag@Gurome » Sun Nov 20, 2011 12:06 am
mehrasa wrote:a car dealership sell only sport cars and luxury cars. if 1/7 of sport car and 1/2 luxury car has sunroof. and he has total of 42 cars in his lot. what is the smallest number of cars with sunroof?
This question is different form the original question that was posted in the other thread. The original question has this words in it: ...and has at least some of each type of car in stock at all times.

Because of this little difference, the answer to this question should be 6, whereas the answer to the original question is 11.

We have to minimize the number of cars with sunroof. As 1/7 < 1/2, we have to maximize the number of sports car and minimize the number of luxury cars. Obvious way to do that is assuming all the cars are sports car.

Hence, there are 42 sports car but no luxury car.
Hence, 42/7 = 6 cars have sunroof.
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by ollapodrida » Sun Nov 20, 2011 5:21 pm
The number of sports cars must be divisible by 7, and the number of luxury cars must be divisible by 2.

Since, the LCM of 2 and 7 is 14, 14 is the smallest total number of cars that would allow these numbers to work. Other multiples of 14 will work as well.

Since we are told there are 42 cars in the lot, we will either have 14 sports cars and 28 luxury cars (14+28=42) or 28 luxury cars and 14 sports cars. Other combinations such as 7SC and 35LC or 35SC and 7LC will not work because we will get fractional cars when we multiply by 1/7 and 1/2.

Case 1: 14SC and 28 LC
1/7*14+1/2*28=2+14=16

Case 2: 14LC and 28SC
1/7*28+1/2*14=4+7=11

Therefore, the smallest number of sunroof cars = 11.

I had to assume here that there were enough cars to make the numbers work. Otherwise, telling us there were at least some of each car in stock wouldn't make much of a difference, since there could be 1 luxury car and 41 sports cars in stock, or vice versa.
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