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# Four cups of milk are to be poured into a 2-cup bottle and a

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Manager
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Four cups of milk are to be poured into a 2-cup bottle and a [#permalink]  08 May 2008, 10:30
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Four cups of milk are to be poured into a 2-cup bottle and a 4-cup bottle. If each bottle is to be filled to the same fraction of its capacity, how many cups of milk should be poured into the 4-cup bottle?
(A) 2/3
(B) 7/3
(C) 5/2
(D) 8/3
(E) 3
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Joined: 28 Dec 2004
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Re: PS 7-17 [#permalink]  08 May 2008, 10:39
i am sure there is a fancier way to do this...

but i was a bit overwhlemed so just picked numbers..

if 2/3 cups are used in 4-cup bottle then 1/3 will be used in the 2 cup bottle..

now..fraction= {math}frac{2/3*4} = frac{1/3*2} {/math}

A it is..
Manager
Joined: 16 Sep 2007
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Re: PS 7-17 [#permalink]  08 May 2008, 10:44
(4-x)/2=x/4
-> x=8/3

D
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Re: PS 7-17 [#permalink]  08 May 2008, 10:44
fresinha12 wrote:
i am sure there is a fancier way to do this...

but i was a bit overwhlemed so just picked numbers..

if 2/3 cups are used in 4-cup bottle then 1/3 will be used in the 2 cup bottle..

now..fraction= {math}frac{2/3*4} = frac{1/3*2} {/math}

A it is..

I get D 8/3 !!

x/2= (4-x)/4 , solving for this 4-x= 8/3 .
Manager
Joined: 27 Jun 2007
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Re: PS 7-17 [#permalink]  08 May 2008, 10:55
el1981 wrote:
Four cups of milk are to be poured into a 2-cup bottle and a 4-cup bottle. If each bottle is to be filled to the same fraction of its capacity, how many cups of milk should be poured into the 4-cup bottle?
(A) 2/3
(B) 7/3
(C) 5/2
(D) 8/3
(E) 3

Let x be the # of cups going into the 4 cup bottle.

so.... x/4 = ((4-x)/2)

16 - 4x = 2x

16 = 6x

x = 16/6... reduce out 2 = 8/3

So D.
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Re: PS 7-17 [#permalink]  08 May 2008, 11:23
i have no clue why i couldnt do this..grrrr
Current Student
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Re: PS 7-17 [#permalink]  08 May 2008, 11:29
el1981 wrote:
Four cups of milk are to be poured into a 2-cup bottle and a 4-cup bottle. If each bottle is to be filled to the same fraction of its capacity, how many cups of milk should be poured into the 4-cup bottle?
(A) 2/3
(B) 7/3
(C) 5/2
(D) 8/3
(E) 3
..

grrr..gotta do it again..

let x be the number of cups in 4-cup bottle

x/4 =(4-x)/2
8-2x=x
x=8/3...

I feel so stupid for missing this ..grrrr
Manager
Joined: 05 Sep 2007
Posts: 144
Location: New York
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Re: PS 7-17 [#permalink]  08 May 2008, 12:09
fresinha12 wrote:
el1981 wrote:
Four cups of milk are to be poured into a 2-cup bottle and a 4-cup bottle. If each bottle is to be filled to the same fraction of its capacity, how many cups of milk should be poured into the 4-cup bottle?
(A) 2/3
(B) 7/3
(C) 5/2
(D) 8/3
(E) 3
..

grrr..gotta do it again..

let x be the number of cups in 4-cup bottle

x/4 =(4-x)/2
8-2x=x
x=8/3...

I feel so stupid for missing this ..grrrr

don't! I made the same mistake. it happens . thanks!
Senior Manager
Joined: 20 Feb 2008
Posts: 296
Location: Bangalore, India
Schools: R1:Cornell, Yale, NYU. R2: Haas, MIT, Ross
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Re: PS 7-17 [#permalink]  08 May 2008, 15:51
Hi , this is how I did it.

We want the ratio of number of cups in bottle with capacity 2 to equal number of cups in bottle with capacity 4.
x= number of cups in bottle with capacity 2
y=number of cups in bottle with capacity4

x/2=y/4; x=1/2y

and we know that x+y=4
1/2y+y=4
3/2y=4
y=8/3
Re: PS 7-17   [#permalink] 08 May 2008, 15:51
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