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

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

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18 May 2009, 14:09
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 13 Dec 2012, 02:36, edited 1 time in total.
Renamed the topic and edited the question.

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21 May 2009, 07:51
D) 8/3

X/2 * x/4 = 4(total number of cups)
Cross multiply
you get 4x+2x =4
combine like terms
6x = 4
solve for x
x = 4/6, must reduce to 2/3

2(2/3)+4(2/3)=4
1 (1/3) + 2 (2/3) = 4 (1.333- + 2.6666- = 4) ((- = continuing to infinity.))
4 = 4 Verified.

4 cup = 2.6666- (8/3)

Actually now that I looked at it it's D), though my math is correct I forget it only applies to 4 cup glass so 8/3 would be in it.

Last edited by Goobers82 on 21 May 2009, 16:19, edited 7 times in total.

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21 May 2009, 08:31
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Shouldn't it be as follows?

Let the equal fraction be:
x/2 = y/4
=>x = y/2

Also, x+y=4 (The number of cups to be distributed)
=> x =4-y

Substituting for x:
y/2=4-y
=>y=8/3

Pls explain in case I'm wrong.

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21 May 2009, 09:38
Quote:
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

I tried by POE.
a) 4 cups - 2/3 cups -->Fraction -1/6
1/6 of 2 cup bottle =1/3 cup
2/3+1/3 =1 cup

b) 4 cups - 7/3 cups -->Fraction -7/12
7/12 of 2 cup bottle =7/6 cup
7/3+7/6 =2.3 cup

c)4 cups - 5/2 cups -->Fraction -5/8
5/8 of 2 cup bottle =5/4 cup
5/2+5/4 =3.75 cup
close to 4 cups

d)8/3 came up to 2 cups

e)3 cups- the total would be 4.5

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22 May 2009, 05:32
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let x be the fraction.
4x+2x=4
6x=4 ==>x=2/3
4x=4*2/3=8/3 cups

for confirmation,
4x+2x= 4*2/3+2*2/3==>8/3+4/3=12/3==>4

hence 8/3 is the right ans...

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13 Jun 2009, 09:49
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The OA is D
I had this question on my GMATPREP and got it correct
Here is my approach
let x is the amount of milk we will pour in the 2 cups bottle and y is the amount of milk we will pour in the 4 cups bottle
=> x/2=y/4 => x=y/2
x+y=4
3y/2=4
y=8/3

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06 Dec 2010, 09:54
I think the easiest way to approach fraction problems is by visually tie in the actual fractions to the problem.

so if X cups are poured into the 4C cup : To make the two fractions equal : X/4 (for the four Cup ) should be equal to whatever remains / 2 (to equal the 2 cup fraction-wise)!!

So the equation would become:

x/4 = (4-x)/2

Solving this:
=>x/2 = (4-x)
=>x = 8 - 2x
=>3x = 8
=>x = 8/3

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06 Dec 2010, 18:49
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Expert's post
nvgroshar wrote:
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.
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06 Dec 2010, 20:36
nice way to solve practically Karishma. What resources do you recommend for these types of problems, I always have trouble with them. Would it be the Manhattan GMAT word translations book? Thanks

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06 Dec 2010, 22:54
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Expert's post
gettinit wrote:
nice way to solve practically Karishma. What resources do you recommend for these types of problems, I always have trouble with them. Would it be the Manhattan GMAT word translations book? Thanks

Actually, these are not 'types of problems'. These are 'types of solutions'. Many GMAT problems need little to no calculations. Very few need you to define variables and solve equations. It is just about getting exposed to such approaches and putting in the effort to figure these out. The more you think, the less you need to solve. After you read a statement in the question, pause and think, "What does it imply?"
Quite often, by the time you reach the question, you will have the answer in your head! Saves you loads of time but the skill is acquired with practice.
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06 Dec 2010, 22:57
Got it thanks Karishma, thought I was missing something from my review, but need to just stop and think of a better approach rather than diving into solving.

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Re: PS 1000 Section7 Question 17 [#permalink]

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02 Apr 2011, 07:35
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x/2 = (4-x)/4

4x = 8 - 2x

=> x = 8/6 = 4/3

So 4 - 4/3 = 8/3

I think the answer is D, but it's a typo (also, 8/2 is 4).
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Re: PS 1000 Section7 Question 17 [#permalink]

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02 Apr 2011, 12:28
X/2 = Y/4

X+Y = 4

substituing equation 1 in 2 we get Y = 8/3

And I agree with subhashghosh on the typo, option D should have been 8/3 not 8/2

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12 Dec 2012, 15:50
Vavali 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

Kind of an idiosyncratic way to solve, but here it is:

we know that putting 1 cup in the 2 cups makes it 1/2 full
and that 2 cups in the 4 cups makes it 1/2 full

we have 1 cup left to distribute. need to distribute 1 part to the 2 cup and 2 parts to the 2 cup to keep the ratio.

1/3 + 2/3 =1

thus the 4 cup has 6/3+ 2/3 = 8/3

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Re: Four cups of milk are to be poured into a 2-cup bottle and [#permalink]

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29 Dec 2012, 01:44
10 Second Method!!!

Fraction of 2 cup bottle - x
Fraction of 4 cup bottle - 2x
The above is because the fractions have to be the same and one volume is double the other

x + 2x = 4

x = 4/3

2x (4 cup bottle ) = 8/3

Hence D
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Re: Four cups of milk are to be poured into a 2-cup bottle and [#permalink]

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Re: Four cups of milk are to be poured into a 2-cup bottle and [#permalink]

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Re: Four cups of milk are to be poured into a 2-cup bottle and [#permalink]

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24 Sep 2015, 11:12
Hi All,

This question can be approached in a number of different ways (depending on how you prefer to 'do the math'). Some ways are faster than others though...

We're told to pour 4 cups of milk into 6 cups of 'space' - this means that 2/3 of the space will be 'filled'....

We're told that the same fraction of each bottle will be filled, so we'll fill 2/3 of the 2-cup bottle and 2/3 of the 4-cup bottle.

We're asked for the amount of milk that is put in the 4-cup bottle: (2/3)(4) = 8/3

[Reveal] Spoiler:
D

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

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03 Oct 2015, 15:34
I went by this approach

If it was 3 cups we would divide it in a way that is : 1 cup in the first one and 2 cups in the 2nd one.. so the ratio in both of them are same.. i.e 1/2 full..

now take the 4th cup..since we have 4 cups and divide it in similar ratio..i.e 1:2.. so 1/3rd of that cup goes into first bottle and 2/3rd goes into 2nd bottle.. so the 2nd cup..i.e 4 cup bottle now has 2 and 2/3 cups.. which is 3/8 cups..

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Re: Four cups of milk are to be poured into a 2-cup bottle and [#permalink]

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11 Jul 2016, 21:42
Vavali 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

Given: 4 litres of milk and two empty bottles. One of 2 litres and another of 4 litres.

Total milk = 4 litres.
Total space = 6 litres.

Hence each bottle will be filled to 2/3rd capacity.
Quantity of milk in 4 litres bottle = 4*(2/3) = 8/3 litres

Correct option: D
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Re: Four cups of milk are to be poured into a 2-cup bottle and   [#permalink] 11 Jul 2016, 21:42
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