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

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nikiki

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19 Mar 2025, 02:53

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the question says the bottles have to be filled with same fraction of its capacity,
so let that fraction be 1/x

2 cup bottle quantity = 2/x
4 cup bottle quantity = 4/x

2/x + 4/x = 4
==> x=3/2

4 cup bottle will have 4/x = 8/3 cups of milk.

vikalpjain91

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Wow! Lets say if we have one bottle of 3 cup and another bottle of 8 cup, and if we need to divide the 7 cup milk with equal fraction than it would be (8/11)*7 = 56/11. Really straight forward approach. Big Thanks.

KarishmaB

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No doubt, the answer is 8/3. The problem is how to do it practically?
I mean, just take a cup and try to fill 2/3 of it with milk.

I am a big fan of trying to solve most GMAT questions orally.
Look at it this way:
I have four cups of milk. I also have a 2 cup bottle and a 4 cup bottle. When will they have the same fraction of capacity? Since 4 cup bottle's capacity if twice of 2 cup bottle's capacity, they will have the same fraction when 4 cup bottle has twice the milk contained in 2 cup bottle. So we just have to divide the 4 cups of milk in the ratio 1:2 and give two parts to the 4 cup bottle.
So (2/3)* 4 = 8/3

Note: If they had given that the milk to be poured is 3 cups, you would have automatically said that we should put 1 cup and 2 cups in 2 cup bottle and 4 cup bottle respectively. They give such numbers to make the question a little harder.