Fraction

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.

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,
Brent