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PERCENT PROBLEM

by Gurpinder » Mon Aug 16, 2010 12:37 pm
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?

OA:[spoiler] 8/15n[/spoiler]


I get 1/2n. And its wrong! Please explain how to answer this question.
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by beatthegmatinsept » Mon Aug 16, 2010 12:52 pm
Gurpinder 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?

OA:[spoiler] 8/15n[/spoiler]


I get 1/2n. And its wrong! Please explain how to answer this question.
Got it :D

Given:
n = c + t
Also, c = t/4

Therefore, n = t/4 + t = (4/5)n
So now, n = (4/5)t............(Equation 1)

Give, Pickup trucks are (2/3)t

Plug that in your Equation 1,
2/3 t = (2/3)*(4/5)*n = (8/15)n

Hope this helps.
Last edited by beatthegmatinsept on Mon Aug 16, 2010 12:53 pm, edited 1 time in total.
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by clock60 » Mon Aug 16, 2010 12:53 pm
trucks+ cars=t+c=n
c=(1/4)t
(1/4)t+t=n
n=(5/4)t
t=(4/5)n
pickup=(4/5)n*2/3=(8/15)n
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by Makushr1 » Mon Aug 16, 2010 1:08 pm
I decided to replace the variables with numbers, and keep getting 1/2...

If there are 12 vehicles in the lot, 3 are cars and 9 are trucks. (1/4*12=3, 3/4*12=9)
Of the Trucks, 2/3 are pickups. So, there will be (2/3*9) 6 pickups.
So, 1/2n.

Where am I going wrong here?
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by Gurpinder » Mon Aug 16, 2010 1:17 pm
Makushr1 wrote:I decided to replace the variables with numbers, and keep getting 1/2...

If there are 12 vehicles in the lot, 3 are cars and 9 are trucks. (1/4*12=3, 3/4*12=9)
Of the Trucks, 2/3 are pickups. So, there will be (2/3*9) 6 pickups.
So, 1/2n.

Where am I going wrong here?
i was doing the same thing
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by e-GMAT » Mon Aug 16, 2010 2:54 pm
Makushr,

Since most people have found the answer, I will only focus on addressing your question.

You have made an error in the first step. Note the question states that number of cars = 1/4th of the number of trucks.

Therefore, if the number of trucks = 12 (assumption)
Number of cars = 12/4 = 3.

Total vehicles = 12 + 3 = 15

Number of pickups = (2/3)*12 = 8

Ratio of pickups to total = 8/15. I hope that it helps!!
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