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A total of n trucks and cars are parked in a lot. If the num [#permalink]
24 Oct 2009, 16:11

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Difficulty:

25% (medium)

Question Stats:

75% (02:39) correct
25% (01:22) wrong based on 159 sessions

A total of n trucks and cars are parked in a lot. If the number of cars is 1/4 the number of trucks, and 2/3 of the trucks are pickups, how many pickups, in terms of n, are parked in the lot?

I decided to use 100 for the total of trucks + cars. So n = 100. Number of cars = 1/4 # of trucks, then there are 25 cars and 75 trucks 2/3 of the trucks are pickups, so 2/3 of 75 is 50.

Therefore, the number of pickups (50) in terms of n would be (1/2)n, which equals 100 * 1/2 = 50, the number of pickups. = C

However, this is not the correct answer- the correct answer is D, 8/15. Can someone explain???

A total of n trucks and cars [#permalink]
05 Jan 2011, 17:19

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A total of n trucks and cars are parked in a slot. If the number of cars is 1/4 the number of trucks, and 2/3 of the trucks are pickups, how many pickups, in terms of n, are parked in the slot?

Re: A total of n trucks and cars [#permalink]
05 Jan 2011, 23:31

ajit257 wrote:

A total of n trucks and cars are parked in a slot. If the number of cars is 1/4 the number of trucks, and 2/3 of the trucks are pickups, how many pickups, in terms of n, are parked in the slot?

A. 1/6 n B. 5/12 n C. 1/2 n D. 8/15 n E. 11/12 n

not sure about the ans.

Let there be c cars and t trucks and p pickup trucks n = t+c t=4c So n = 5c (2/3)t = p p = (2/3)t = (2/3)(4c) = (8/3)c = (8/3)(n/5) = (8/15)n

Re: A total of n trucks and cars [#permalink]
06 Jan 2011, 21:30

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Expert's post

ajit257 wrote:

A total of n trucks and cars are parked in a slot. If the number of cars is 1/4 the number of trucks, and 2/3 of the trucks are pickups, how many pickups, in terms of n, are parked in the slot?

A. 1/6 n B. 5/12 n C. 1/2 n D. 8/15 n E. 11/12 n

not sure about the ans.

Try and use ratios where possible. They make your life very easy.

No of cars : No of trucks = 1:4 (Since for every 4 trucks, there is 1 car) So total cars and trucks (n) in ratio terms = 1+4 = 5 Now out of 4 trucks, 2/3 are pickup (p) i.e. 4*2/3 = 8/3 are pick up. So p/n = (8/3)/5 or p = 8/15 n _________________

Re: A total of n trucks and cars are parked in a lot. If the num [#permalink]
28 May 2014, 05:43

cronkey7 wrote:

A total of n trucks and cars are parked in a lot. If the number of cars is 1/4 the number of trucks, and 2/3 of the trucks are pickups, how many pickups, in terms of n, are parked in the lot?

I decided to use 100 for the total of trucks + cars. So n = 100. Number of cars = 1/4 # of trucks, then there are 25 cars and 75 trucks 2/3 of the trucks are pickups, so 2/3 of 75 is 50.

Therefore, the number of pickups (50) in terms of n would be (1/2)n, which equals 100 * 1/2 = 50, the number of pickups. = C

However, this is not the correct answer- the correct answer is D, 8/15. Can someone explain???

C = Cars, T = Trucks, and P = Pickups.

C + T = n

C = \frac{1}{4} T \frac{2}{3}T = P

We'd like to write everything in terms of Pickups, since that's what the question is asking us about. Thus,

T = \frac{3}{2}P, C = \frac{1}{4}T = \frac{1}{4} * \frac{3}{2} P = \frac{3}{8}P

Therefore,

n = C + T = \frac{3}{8} P + \frac{3}{2} P = \frac{30}{16}P = \frac{15}{8}P.

Re: A total of n trucks and cars [#permalink]
09 Feb 2015, 23:04

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