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19 Feb 2018, 23:18
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Difficulty:
15%
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Question Stats:
87% (01:34) correct
13%
(02:20)
wrong
based on 105
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In a certain shipment of 120 new cars, 2/3 of the cars are equipped with radios and 2/5 are equipped with air conditioners. If 20 of the cars are equipped with neither a radio nor with an air conditioner, how many cars in the shipment are equipped with both a radio and an air conditioner?
(A) 20
(B) 28
(C) 32
(D) 58
(E) 76
(A) 20
(B) 28
(C) 32
(D) 58
(E) 76
19 Feb 2018, 23:54
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Known Information:
Total cars = 120
Cars with Radio = 2/3 = 80 Cars
Cars with Air conditioner = 2/5 = 120 Cars
Cars with neither Radio nor A/C = 20 Cars
With the information above we can derive the data below
Cars with No Air conditioner = Total cars - cars with air conditioner = 120 - 48 = 72 cars
Cars with No Air conditioner but with radio = Total cars with no air conditioner - Cars with no radio / no air conditioner = 72 - 20 = 52 cars
Now we can derive our answer based on above given value
Cars with both radio and air conditioner = Total cars with radio - cars with no air conditioner = 80 - 52 = 28 cars
Ans: B
PS: Overlapping sets are easier to understand when we solution are presented in a matrix form
Total cars = 120
Cars with Radio = 2/3 = 80 Cars
Cars with Air conditioner = 2/5 = 120 Cars
Cars with neither Radio nor A/C = 20 Cars
With the information above we can derive the data below
Cars with No Air conditioner = Total cars - cars with air conditioner = 120 - 48 = 72 cars
Cars with No Air conditioner but with radio = Total cars with no air conditioner - Cars with no radio / no air conditioner = 72 - 20 = 52 cars
Now we can derive our answer based on above given value
Cars with both radio and air conditioner = Total cars with radio - cars with no air conditioner = 80 - 52 = 28 cars
Ans: B
PS: Overlapping sets are easier to understand when we solution are presented in a matrix form
Bunuel
In a certain shipment of 120 new cars, 2/3 of the cars are equipped with radios and 2/5 are equipped with air conditioners. If 20 of the cars are equipped with neither a radio nor with an air conditioner, how many cars in the shipment are equipped with both a radio and an air conditioner?
(A) 20
(B) 28
(C) 32
(D) 58
(E) 76
(A) 20
(B) 28
(C) 32
(D) 58
(E) 76
Let's visualize this problem; refer to the Venn diagram attached.
- We know the total number of cars = 120.
- Number of cars with radio = \(\frac{2}{3}*120\) = \(80\) → This is the region marked 'x' in the Venn diagram
- Number of cars with AC = \(\frac{2}{5}*120\) = \(48\) → This is the region marked 'z' in the Venn diagram.
- Number of cars with neither radio nor AC = 20 → This is the region marked with the red lines
We need to find the number of cars with radio AND AC → This is the region marked 'y' in the Venn diagram.
Based on the information provided:
Total number of cars = x + z + (area marked with red lines) - y
120 = 80 + 48 + 20 - y
=> y = 28
Answer choice is (B).
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