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# A total of n trucks and cars are parked in a lot. If the num

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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, 16:11
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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

[Reveal] Spoiler:
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???
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Oct 2013, 01:03, 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, 01:20
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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, 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?

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

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Re: A total of n trucks and cars [#permalink]

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05 Jan 2011, 17:23
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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05 Jan 2011, 23:31
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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

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

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Re: A total of n trucks and cars [#permalink]

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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

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, 19:57
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

[Reveal] Spoiler:
D

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.

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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, 06:36
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, 05:43
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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

[Reveal] Spoiler:
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 $$P = \frac{8}{15} n.$$

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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, 08:03
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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
pick-up 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, 11:26
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, 08:17
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, 10:43
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

[Reveal] Spoiler:
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

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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, 15:54
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Expert's post
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.

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Re: A total of n trucks and cars are parked in a lot. If the num   [#permalink] 22 Oct 2017, 15:54
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