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A total of n trucks and cars are parked in a lot. If the num [#permalink]
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24 Oct 2009, 17:11
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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? A. 1/6 n B. 5/12 n C. 1/2 n D. 8/15 n E. 11/12 n 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???
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Last edited by Bunuel on 09 Oct 2013, 02:03, edited 1 time in total.
Renamed the topic, edited the question and added the OA.



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Re: Picking numbers on algebra question Something is wrong! [#permalink]
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25 Oct 2009, 02:20
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n = t+c. c=1/4 *t so the total number of vehicles in terms of t is n=5/4 *t Now, 2/3 * t are pickups
Q asks: 2/3 * t = n * F ( F is the required fraction ) 2/3 * t = 5/4 * F => F = 8/15.



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A total of n trucks and cars [#permalink]
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05 Jan 2011, 18:19
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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? 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.
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Re: A total of n trucks and cars [#permalink]
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05 Jan 2011, 18:23
D. x+x/4=n => x=4n/5 => 2x/3=8n/15



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Re: A total of n trucks and cars [#permalink]
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06 Jan 2011, 00:31
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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 Answer is (d)
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Re: A total of n trucks and cars [#permalink]
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06 Jan 2011, 22:30
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
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Re: Quants  FDP  Plz help on this [#permalink]
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17 Sep 2012, 20:57
SreeViji wrote: Hi, Can anyone help me in resolving this problem? I know it is simple. But I'm missing a small step somewhere..... 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? (A) 1n/6 (B) 5n/12 (C) 1n/2 (D) 8n/15 (E) 11n/12 Lets consider the number of trucks = x Hence, total number of cars is = x/4 from the question we know, x+x/4 = n = > x = 4n/5 Number of trucks that are pickups = (2/3)4n/5 = 8n/15. D is the answer. Cheers!
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Re: A total of n trucks and cars are parked in a lot. If the num [#permalink]
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21 Mar 2014, 07:36
Lets say Total truck is 12. So car is 3. Now pickups are =2/3rd of 12= 8 so total fraction is 8/15 ..ans



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Re: A total of n trucks and cars are parked in a lot. If the num [#permalink]
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28 May 2014, 06:43
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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? A. 1/6 n B. 5/12 n C. 1/2 n D. 8/15 n E. 11/12 n 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, \(n = C + T = \frac{3}{8} P + \frac{3}{2} P = \frac{30}{16}P = \frac{15}{8}P.\) Solving for P, we see that \(P = \frac{8}{15} n.\) Answer: D



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Re: A total of n trucks and cars are parked in a lot. If the num [#permalink]
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21 Dec 2015, 09:03
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This is all variables in answer choices question. So lets pick smart numbers. Let n=15 {why 15? Since cars=1/4*trucks, total trucks+cars should be divisible by 5 (1+4). Additionally since we have another fraction 2/3 to work with, the total should be divisible by 3} n=15 cars+trucks= 15 cars+4*cars = 15 > cars=3 so trucks=12 pickup trucks = 12*2/3 = 8 Now plug 15 in answer choices. Only D gives 8. Ans D
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A total of n trucks and cars are parked in a lot. If the num [#permalink]
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25 Mar 2016, 12:26
let t=number of trucks n=t+(t/4)=5t/4 let p=number of pickups t=3p/2 substituting, n=5(3p/2)/4 p=8/15 n



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Re: A total of n trucks and cars are parked in a lot. If the num [#permalink]
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18 Oct 2017, 09:17
Number of trucks = x Number of cars = 1/4x
Therefore, x +1/4x = n ( Total number of vehicles parked) X= 4n/5
We are given 2/3 of x are pick up trucks. So 2/3 *4n/5 = 8/15n



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Re: A total of n trucks and cars are parked in a lot. If the num [#permalink]
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18 Oct 2017, 11:43
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? A. 1/6 n B. 5/12 n C. 1/2 n D. 8/15 n E. 11/12 n 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??? t+c = n c = t/4 t+t/4 = n t = 4/5 n c = 2/3 t = 2/3 * 4/5 = 8/15 n Answer D
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Re: A total of n trucks and cars are parked in a lot. If the num [#permalink]
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22 Oct 2017, 16:54
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?
A. 1/6 n B. 5/12 n C. 1/2 n D. 8/15 n E. 11/12 n We can let the number of cars = c and number of trucks = t; thus: c + t = n and c = (1/4)t Thus: (1/4)t + t = n t + 4t = 4n 5t = 4n t = 4n/5 Since 2/3 of the trucks are pickups, there are (2/3)(4n/5) = 8n/15 pickups in the parking lot. Answer: D
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