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Vial V is 2/3 full of a certain solution and vial W, which has 50%

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Vial V is 2/3 full of a certain solution and vial W, which has 50%  [#permalink]

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08 Mar 2013, 10:16
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Difficulty:

45% (medium)

Question Stats:

79% (02:30) correct 21% (02:44) wrong based on 184 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?

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Re: Vial V is 2/3 full of a certain solution and vial W, which has 50%  [#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

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?
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Re: Vial V is 2/3 full of a certain solution and vial W, which has 50%  [#permalink]

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09 Mar 2013, 01:24
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let the capacity of V = 6, then the capacity of W = 6+0.5*6=9

the amount of solution in V = (2/3)*6=4 and the half of it is 2 (4/2 )
the amount of solution in W = (3/4)*9=27/4

(half of solution in V + the amount of solution in W )/ capacity of W = (2+27/4)/9 =35/36
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Re: Vial V is 2/3 full of a certain solution and vial W, which has 50%  [#permalink]

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09 Mar 2013, 03:21
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?

Similar questions to practice:
equal-amount-of-water-were-poured-into-two-empty-jars-of-98962.html
a-glucose-solution-contains-15-grams-of-glucose-per-140243.html
two-equally-sized-jugs-full-of-water-are-each-emptied-into-t-143944.html

Hope it helps.
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Re: Vial V is 2/3 full of a certain solution and vial W, which has 50%  [#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

Ans:E
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Re: Vial V is 2/3 full of a certain solution and vial W, which has 50%  [#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

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Re: Vial V is 2/3 full of a certain solution and vial W, which has 50%  [#permalink]

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26 Sep 2016, 05:57
i worked with 24 and 36, as it seemed easier to work with...
24*2/3 = 16.
36*3/4 = 27

16/2 = 8
8+27 = 35.
we have 35/36
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Re: Vial V is 2/3 full of a certain solution and vial W, which has 50%  [#permalink]

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25 Dec 2017, 20:04
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Re: Vial V is 2/3 full of a certain solution and vial W, which has 50%   [#permalink] 25 Dec 2017, 20:04
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