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Difficult Math Problem #105 - Mixtures

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by 800guy » Mon Mar 05, 2007 12:19 pm
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

from diff math doc, oa coming when some people answer with explanations.
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by jayhawk2001 » Mon Mar 05, 2007 9:19 pm
Let x be the fraction

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

So cups of milk to be poured into the 4-cup bottle = 4 * 2/3 = 8/3

(D) looks like the correct answer
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OA

by 800guy » Wed Mar 07, 2007 10:09 am
OA - you got it, jayhawk

x + y = 4
x = 4 - y

x/2 = y/4
4x = 2y
4(4-y) = 2y
16 = 6y
y = 8/3 (D)
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by artistocrat » Thu May 26, 2011 6:52 pm
This is a great example of picking numbers. Half of 4 is 2, as per question, and half of 2 and 2/3 is 1 and 1/3, which add up to 4 (cups added).
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by cans » Thu May 26, 2011 7:35 pm
IMO D
2x+4x=4 => 4x=8/3
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by SoCan » Thu May 26, 2011 7:43 pm
jayhawk2001 wrote:Let x be the fraction

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

So cups of milk to be poured into the 4-cup bottle = 4 * 2/3 = 8/3

(D) looks like the correct answer
Great example of keeping it simple. No need to introduce an extra variable.
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by thestartupguy » Thu Sep 08, 2011 3:45 am
Is this a tough question? It doesn't seem so. :|
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by navami » Thu Sep 08, 2011 6:13 am
4 cups
lets assume fraction X is filled in both the cups.
- - - -
so 4*X is full for 4 cup bottle


- -
and 2*X is full for 2 cup bottle



now 4*X + 2*X = 4
X = 2/3

And is D
This time no looking back!!!
Navami
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by GMATGuruNY » Thu Sep 08, 2011 6:36 am
800guy 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

from diff math doc, oa coming when some people answer with explanations.
The 4-cup container is twice the size of the 2-cup container, so the 4-cup container must be given twice the amount of milk.
Thus, the ratio of the amounts for the two containers = 2:1.
Since 2+1=3, out of every 3 cups, 2 must be given to the 4-cup container.
Thus, the 4-cup container must be given 2/3 of the total amount.
(2/3)*4 = 8/3.

The correct answer is D.
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by knight247 » Thu Sep 08, 2011 7:25 am
Let 1 cup=150ml
4cups=600ml ....2cups=300ml

So we have,

600 ml to be poured in a 300 ml bottle and 600 ml bottle
x be the quantity poured in the 300ml bottle and y be the quantity poured in the 600ml bottle. We have x+y=600.....(1)

Also since the fractions are equal we have,
x/300=y/600

x=0.5y
Putting this value of x in statement (1)

0.5y+y=600



1.5y=600

y=400

x=200

400/150=40/15=8/3 Hence [spoiler]D[/spoiler]
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