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# In a certain shipment of 120 new cars, 2/3 of the cars are equipped wi

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Math Expert
Joined: 02 Sep 2009
Posts: 59561
In a certain shipment of 120 new cars, 2/3 of the cars are equipped wi  [#permalink]

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19 Feb 2018, 23:18
00:00

Difficulty:

5% (low)

Question Stats:

97% (01:30) correct 3% (03:28) wrong based on 51 sessions

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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
Senior Manager
Joined: 31 May 2017
Posts: 334
Re: In a certain shipment of 120 new cars, 2/3 of the cars are equipped wi  [#permalink]

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19 Feb 2018, 23:54
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
Re: In a certain shipment of 120 new cars, 2/3 of the cars are equipped wi   [#permalink] 19 Feb 2018, 23:54
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