Truck

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Anna-Lisa: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Wed Aug 18, 2010 12:32 am

by Anna-Lisa » Fri Aug 27, 2010 5:53 am

HI GUYS, you might help me with this question.
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 pcikups, in terms of n, are parked in the lot?
I do already know that the answer is 8/15 n

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Source: Beat The GMAT — Problem Solving | Fri Aug 27, 2010 5:53 am

niksworth: Legendary Member; Posts: 520; Joined: Mon Jun 14, 2010 10:44 amFollowed by: 6 members; Thanked: 70 times

by niksworth » Fri Aug 27, 2010 6:20 am

Let the number of trucks be z
Then, no. of cars = z/4
Thus, Total no. of cars and trucks z/4 + z = 5z/4

No. of trucks which are pickups = 2z/3

We also know that total no. of cars and trucks = n
Therefore, 5z/4 = n
Or, z = 4n/5

Thus no. of trucks which are pickups = 2z/3 = (2*(4n/5))/3 = 8n/15

Hope that helps.

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scorpionz: Senior | Next Rank: 100 Posts; Posts: 98; Joined: Thu Aug 19, 2010 10:00 amFollowed by: 1 member; Thanked: 7 times; GMAT Score:760

by scorpionz » Fri Aug 27, 2010 6:50 am

Anna-Lisa wrote:HI GUYS, you might help me with this question.
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 pcikups, in terms of n, are parked in the lot?
I do already know that the answer is 8/15 n

The above approach suggested by @niksworth is perfect... Alternately, you could use the "plugging in numbers" approach.. See if it works for you..

Go backwards..
2/3 of the trucks are pickups... ===> if there are 300 trucks, then there are 200 pickups
cars are 1/4th no. of trucks ===> no. of cars = (1/4)*300 = 75
total no. of cars + trucks ("n" as mentioned in the problem) = 75(cars) +300(trucks) = 375

no. of pickups (200) in terms of "n" = (8/15) * 375 = 8*25 = 200

There will be only one option amongst the 5 that will give you 200 as the answer and that's the correct option!

Cheers!!

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shibal: Master | Next Rank: 500 Posts; Posts: 345; Joined: Wed Mar 18, 2009 6:53 pm; Location: Sao Paulo-Brazil; Thanked: 12 times; GMAT Score:660

by shibal » Sat Aug 28, 2010 5:51 am

Anna-Lisa wrote:HI GUYS, you might help me with this question.
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 pcikups, in terms of n, are parked in the lot?
I do already know that the answer is 8/15 n

just go through the equations and replace....

n=c+t ; c=1/4t ; p=2/3t

substitute c in n=c+t ===> n=5/4t

substitute t in n=5/4t ===> n=15/8p

solve it for p===> p=8/15n

hope it helps

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diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Sat Aug 28, 2010 11:00 am

Anna-Lisa wrote:HI GUYS, you might help me with this question.
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 pcikups, in terms of n, are parked in the lot?
I do already know that the answer is 8/15 n

C+T=n
C=1/4T thus 1/4T+T=5/4T=n => T=4/5n
2/3 of T =2/3*4/5n=8/15n was picked and its the answer
hope it helps

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