nidhis.1408 wrote:A car dealership sells only sports cars and luxury cars and has at least some of each type of car in stock at all times. If exactly 1/7 of the sports cars and exactly 1/2 of the luxury cars have sunroofs and there are exactly 42 cars on the lot, what is the smallest number of cars that could have sunroofs?
a. 6
b. 8
c. 11
d. 13
e. 16
Let S = sports cars and L = luxury cars.
Sports cars with sunroofs = (1/7)S.
Luxury cars with sunroofs = (1/2)L.
A SMALLER fraction of sports cars have sunroofs.
Thus, to MINIMIZE the total number with sunroofs, we need to MAXIMIZE the value of S.
S must be a multiple of 7 (since 1/7 have sunroofs), and L must be even (since 1/2 have sunroofs).
The total number of cars is 42.
S=35, L=7.
Doesn't work, since L is not even.
S=28, L=14.
This works.
Total number with sunroofs = (1/7)28 + (1/2)14 = 4+7 = 11.
The correct answer is
C.
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