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Vial V is 2/3 full of a certain solution and vial W, which [#permalink]

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08 Mar 2013, 10:16

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E

Difficulty:

45% (medium)

Question Stats:

68% (03:08) correct
32% (02:37) wrong based on 120 sessions

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Vial V is \(\frac{2}{3}\) full of a certain solution and vial W, which has 50% more capacity than vial V, is \(\frac{3}{4}\) full of the same solution. If half of the solution in vial V is poured into vial W, vial W will be filled to what fraction of its capacity?

(A)\(\frac{27}{36}\)

(B)\(\frac{10}{11}\)

(C)\(\frac{11}{12}\)

(D)\(\frac{23}{24}\)

(E)\(\frac{35}{36}\)

I was able to solve it in under 2 mins, but curious to know if there is a 10-sec approach?

Re: Vial V is 2/3 full of a certain solution and vial W, which [#permalink]

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08 Mar 2013, 12:32

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Hello,

Let me try helping you with this one.

It is mentioned in the question that the volume of W is 50% larger than the volume of V. Hence, W=\(\frac{3}{2}\)*V This implies that V=\(\frac{2}{3}\)*W Now, V is filled with 2/3 with the solution and W is filled 3/4 with the solution. Half of the solution in V is filled into W. We need to find the fraction of W that is filled. So, we have to express everything in terms of W.

Half of the solution in V in terms of W is 1/3. When we express that in terms of W, it becomes

half the volume of solution in V=\(\frac{1}{3}\)*\(\frac{2}{3}\)*W This is added to 3/4 of the volume W. The total volume is (\(\frac{1}{3}\)*\(\frac{2}{3}\)*W)+(\(\frac{3}{4}\)*W)=\(\frac{35}{36}\)*W

Hence, the answer is E.

Hope this helps! Let me know if I could help you any further.

megafan wrote:

Vial V is \(\frac{2}{3}\) full of a certain solution and vial W, which has 50% more capacity than vial V, is \(\frac{3}{4}\) full of the same solution. If half of the solution in vial V is poured into vial W, vial W will be filled to what fraction of its capacity?

(A)\(\frac{27}{36}\)

(B)\(\frac{10}{11}\)

(C)\(\frac{11}{12}\)

(D)\(\frac{23}{24}\)

(E)\(\frac{35}{36}\)

I was able to solve it in under 2 mins, but curious to know if there is a 10-sec approach?

Vial V is \(\frac{2}{3}\) full of a certain solution and vial W, which has 50% more capacity than vial V, is \(\frac{3}{4}\) full of the same solution. If half of the solution in vial V is poured into vial W, vial W will be filled to what fraction of its capacity?

(A)\(\frac{27}{36}\)

(B)\(\frac{10}{11}\)

(C)\(\frac{11}{12}\)

(D)\(\frac{23}{24}\)

(E)\(\frac{35}{36}\)

I was able to solve it in under 2 mins, but curious to know if there is a 10-sec approach?

Re: Vial V is 2/3 full of a certain solution and vial W, which [#permalink]

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12 Aug 2013, 05:47

Let capacity be denoted by "C"

V = C ===> currently filled = 2/3 C Given : Capacity of W is 50% more than V

W = C + 0.5 C = 1.5 C ===> currently filled = 3/4(1.5C)

half of contents of V ==> 2/3C * 1/2 = 2/6C are then poured in W Required to calculate the fraction to which W will be filled after half of contents of V are filled in W 2/6C +3/4(1.5C)/1.5C Solving, we get 35/36

Re: Vial V is 2/3 full of a certain solution and vial W, which [#permalink]

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12 Aug 2013, 09:20

megafan wrote:

Vial V is \(\frac{2}{3}\) full of a certain solution and vial W, which has 50% more capacity than vial V, is \(\frac{3}{4}\) full of the same solution. If half of the solution in vial V is poured into vial W, vial W will be filled to what fraction of its capacity?

(A)\(\frac{27}{36}\)

(B)\(\frac{10}{11}\)

(C)\(\frac{11}{12}\)

(D)\(\frac{23}{24}\)

(E)\(\frac{35}{36}\)

I was able to solve it in under 2 mins, but curious to know if there is a 10-sec approach?

........... just 30 seconds to solve with this techniques:

Attachments

volume and ratio own.png [ 33.83 KiB | Viewed 1262 times ]

Re: Vial V is 2/3 full of a certain solution and vial W, which [#permalink]

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