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camping

by aakash82 » Tue Mar 10, 2009 7:41 pm
On a camping trip, x campers each paid y dollars for food.What percent of total food expenses did each camper pay?

1. If there were one fewer camper, each camper would owe 1 dollar more
2. If there were half as many campers, each camper would owe 7 dollars more.

OA to follow after some discussion. Also can we generalize a strategy on such questions?
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Re: camping

by Vemuri » Tue Mar 10, 2009 11:34 pm
My answer is B.

If x campers each pay $y. They the total amount is $xy. The question is asking us to find out the percentage of total food expense each camper contributed. This can be converted to x/xy = ?

Statement I: If one camper was less (x-1), then the rest will have to pay $(y+1). So, in effect we can equal $xy = $(x-1)(y+1)
==> xy = xy+x-y-1
==> x=y+1 (insufficient)

Statement II: If there were half as many campers (x-x/2), then they would have to pay $(y+7). So, in effect we can equal $xy=$(x-x/2)(y+7)
==> xy=xy+7x-xy/2-7x/2
==> x(y/2+7/2)=7x
==> 7+y=14
==> y=7
If we know the value of y, by substitution we can get the value of x. This will help us get the total percentage of food expenses each camper paid.

B is sufficient to answer the question.
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Re: camping

by marcusking » Wed Mar 11, 2009 6:39 am
Similar to Vemuri I just factored a bit differently

xy = (x-x/2)(y+7)
xy = xy+7x-[xy/2]-[7x/2]
xy = [xy/2]+[7x/2]
2xy = xy+7x
xy = 7x
y = 7

B.
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Re: camping

by aakash82 » Wed Mar 11, 2009 9:37 am
marcusking wrote:Similar to Vemuri I just factored a bit differently

xy = (x-x/2)(y+7)
xy = xy+7x-[xy/2]-[7x/2]
xy = [xy/2]+[7x/2]
2xy = xy+7x
xy = 7x
y = 7

B.
Even I went for B, but the OA given is C. It is a question from Princeton Review
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by scoobydooby » Wed Mar 11, 2009 11:31 am
i made the same mistake..

from B:
xy = 7x , we get y=7, but we can never get x (x simply cancels on both sides)

we do need the equation from A: x=y+1 to compute the value of x and find y/xy
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by Vemuri » Wed Mar 11, 2009 11:09 pm
scoobydooby wrote:i made the same mistake..

from B:
xy = 7x , we get y=7, but we can never get x (x simply cancels on both sides)

we do need the equation from A: x=y+1 to compute the value of x and find y/xy
Very true. This is a tricky question (when we have just under 2 mins) in the real time :evil:

Thanks for posting.
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Re: camping

by mightybuckz » Thu Mar 12, 2009 8:35 pm
Vemuri wrote:My answer is B.

If x campers each pay $y. They the total amount is $xy. The question is asking us to find out the percentage of total food expense each camper contributed. This can be converted to x/xy = ?

Statement I: If one camper was less (x-1), then the rest will have to pay $(y+1). So, in effect we can equal $xy = $(x-1)(y+1)
==> xy = xy+x-y-1
==> x=y+1 (insufficient)

Statement II: If there were half as many campers (x-x/2), then they would have to pay $(y+7). So, in effect we can equal $xy=$(x-x/2)(y+7)
==> xy=xy+7x-xy/2-7x/2
==> x(y/2+7/2)=7x
==> 7+y=14
==> y=7
If we know the value of y, by substitution we can get the value of x. This will help us get the total percentage of food expenses each camper paid.

B is sufficient to answer the question.

the question asks if we can find the ratio of y/xy = 1/x (NOT 1/y)
Hence you need both the statements, C is the ans.
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by Tryingmybest » Sun Mar 15, 2009 9:18 am
IMO B

X be total no .of persons, Y - total amount paid
Say each person paid n$

then nx=y (given) we are asked y/x ie share of each person


We all know A is noy sufficient
Frm B=> (n+7)(x/2)=Y
nx/2 + 7x/2 =Y
y/2 + 7x/2= y
7x/2 = y/2
y/x= 7

Please let me know if I have a logic error somewhere

Thanks.
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by Morgoth » Sun Mar 15, 2009 9:22 pm
Tryingmybest wrote:IMO B

X be total no .of persons, Y - total amount paid
Say each person paid n$

then nx=y (given) we are asked y/x ie share of each person


We all know A is noy sufficient
Frm B=> (n+7)(x/2)=Y
nx/2 + 7x/2 =Y
y/2 + 7x/2= y
7x/2 = y/2
y/x= 7

Please let me know if I have a logic error somewhere

Thanks.
There is no logic error but in fact there is an error in reading.

x campers, EACH paid y dollars, total cost x*y

Question : [y/xy] * 100 = ?

Simplified version : 100/x = ?

Further simplified : x = ?

Hope this helps.
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by Tryingmybest » Mon Mar 16, 2009 6:46 am
Thanks !!
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