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by neeti2711 » Mon Oct 22, 2012 4:57 am
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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by Anurag@Gurome » Mon Oct 22, 2012 4:59 am
neeti2711 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 fraction of the capacity of each bottle, which is to be filled.
Then 2x + 4x = 4
6x = 4
x = 2/3

So, each bottle is to be filled to 2/3 of its capacity.
Hence, the 4-cup bottle should be filled with 4 * (2/3) = [spoiler]8/3[/spoiler] cups.

The correct answer is D.
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by Brent@GMATPrepNow » Mon Oct 22, 2012 5:07 am
neeti2711 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
This is a clever way of telling us to take 4 cups of milk and divide it into a 1:2 ratio.
Here's why: in order to fill both bottles to the same fraction of their capacity, we need to put 2 drops of milk in the big bottle for every 1 drop of milk in the small bottle (since the big bottle has twice the capacity of the small bottle).

To divide 4 cups of milk into a 1:2 ratio, first add 1+2 to get 3.
Now take the 4 cups and divide it into 3 parts. So, we get 4/3, 4/3, 4/3
Divide the 3 parts into 1:2 = 4/3 : 4/3 + 4/3
Simplify: 4/3 : 8/3

So, the big bottle gets 8/3 cups = D

Cheers,
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by anuprajan5 » Mon Oct 22, 2012 5:14 am
Answer is D.

I plugged in the answers to get 8/(3*4) and remaining 4/(3*2)

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by mariofelixpasku » Tue Oct 23, 2012 7:29 am
easier way:

(4-x)/2 = x/4

solve i and you get 8/3 for x
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