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Math Expert V
Joined: 02 Sep 2009
Posts: 58427
Jar X is 16 full of water. Jar Y, which has half the capacity of Jar X  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 73% (01:25) correct 27% (01:43) wrong based on 199 sessions

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Jar X is 1/6 full of water. Jar Y, which has half the capacity of Jar X, is 1/2 full of water. If the contents of Jar X is poured into Jar Y, Jar Y will be filled to what fraction of its capacity?

A. 5/12
B. 2/3
C. 7/9
D. 5/6
E. 7/8

Kudos for a correct solution.

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Math Expert V
Joined: 02 Aug 2009
Posts: 8011
Re: Jar X is 16 full of water. Jar Y, which has half the capacity of Jar X  [#permalink]

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Bunuel wrote:
Jar X is 1/6 full of water. Jar Y, which has half the capacity of Jar X, is 1/2 full of water. If the contents of Jar X is poured into Jar Y, Jar Y will be filled to what fraction of its capacity?

A. 5/12
B. 2/3
C. 7/9
D. 5/6
E. 7/8

Kudos for a correct solution.

jar Y is half the capacity of Jar X.. so 1/2 of jar Y=1/4 of Jar X..
when contents of jar Y are poured into Jar X, which is already 1/6 full, the jar X is filled upto 1/4+1/6=5/12..
just realized, the contents are being poured in Y....
so jar Y is half the capacity of Jar X.. so 1/3 of jar Y=1/6 of Jar X..
when contents of jar X are poured into Jar Y, which is already 1/2 full, the jar X is filled upto 1/2+1/3=5/6.. ans D
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Re: Jar X is 16 full of water. Jar Y, which has half the capacity of Jar X  [#permalink]

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my thought was:

let 12 be jar X capacity and 6 (half of that) be jar Y capacity.

since jar X is 1/6 filled = 2

jar Y is half filled = 3

if we pour from jar X to jar Y we gaet it will be filled 5/6 of its capacity. answer D for me.
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Re: Jar X is 16 full of water. Jar Y, which has half the capacity of Jar X  [#permalink]

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Bunuel wrote:
Jar X is 1/6 full of water. Jar Y, which has half the capacity of Jar X, is 1/2 full of water. If the contents of Jar X is poured into Jar Y, Jar Y will be filled to what fraction of its capacity?

A. 5/12
B. 2/3
C. 7/9
D. 5/6
E. 7/8

Kudos for a correct solution.

I think that the fastest way to solve this problem might be to assign values (numbers) for Jar X and Jar Y. So we can let Jar X have a capacity of 6 litres and Jar Y (which has half the capacity of Jar X) have the capacity of 3 litres of water. Jar X is a 1/6 full - so it contains 1 litre of water and Jar Y is 1/2 full so it contains 1.5 litres of water. Therefore if the contents of Jar X are transferred to Jar Y, that means that Jar Y will now be (1 + 1.5) = 2.5 Litres full. Thus Jar Y would be filled till 2.5/3 litres of its capacity which is equivalent to (5/2)/3 = 5/6.

I think the answer is D!

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Re: Jar X is 16 full of water. Jar Y, which has half the capacity of Jar X  [#permalink]

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kdatt1991 wrote:
Bunuel wrote:
Jar X is 1/6 full of water. Jar Y, which has half the capacity of Jar X, is 1/2 full of water. If the contents of Jar X is poured into Jar Y, Jar Y will be filled to what fraction of its capacity?

A. 5/12
B. 2/3
C. 7/9
D. 5/6
E. 7/8

Kudos for a correct solution.

I think that the fastest way to solve this problem might be to assign values (numbers) for Jar X and Jar Y. So we can let Jar X have a capacity of 6 litres and Jar Y (which has half the capacity of Jar X) have the capacity of 3 litres of water. Jar X is a 1/6 full - so it contains 1 litre of water and Jar Y is 1/2 full so it contains 1.5 litres of water. Therefore if the contents of Jar X are transferred to Jar Y, that means that Jar Y will now be (1 + 1.5) = 2.5 Litres full. Thus Jar Y would be filled till 2.5/3 litres of its capacity which is equivalent to (5/2)/3 = 5/6.

I think the answer is D!

Please consider giving me KUDOS if you felt this post was helpful! Thanks. Hi kdatt,
you could have made it more easier and safer by taking values which dont get you decimals....
decimals can unknowingly lead to wrong ans while solving...
so value of X could have been 12, and Y,6....
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Re: Jar X is 16 full of water. Jar Y, which has half the capacity of Jar X  [#permalink]

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Bunuel wrote:
Jar X is 1/6 full of water. Jar Y, which has half the capacity of Jar X, is 1/2 full of water. If the contents of Jar X is poured into Jar Y, Jar Y will be filled to what fraction of its capacity?

A. 5/12
B. 2/3
C. 7/9
D. 5/6
E. 7/8

Kudos for a correct solution.

Let Jar X capacity = 12 units
Let Jar Y capacity = 6 units

Jar X currently contains 2 units (12 multiplied by 1/6)
Jar Y currently contains 3 units (6 multiplied by 1/2)

pouring X into Y results in 2+3=5

5/6

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Re: Jar X is 16 full of water. Jar Y, which has half the capacity of Jar X  [#permalink]

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Answer = D = 5/6

Let the size of Jar X = 1, then size of Jar Y $$= \frac{1}{2}$$

Water in Jar X $$= \frac{1}{6}$$

Water in Jar Y $$= \frac{1}{2*2} = \frac{1}{4}$$

Jar X water added in Jar Y $$= \frac{1}{4} + \frac{1}{6} = \frac{5}{12}$$

Required fraction for Jar Y $$= \frac{\frac{5}{12}}{\frac{1}{2}} = \frac{5}{6}$$
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Re: Jar X is 16 full of water. Jar Y, which has half the capacity of Jar X  [#permalink]

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Bunuel wrote:
Jar X is 1/6 full of water. Jar Y, which has half the capacity of Jar X, is 1/2 full of water. If the contents of Jar X is poured into Jar Y, Jar Y will be filled to what fraction of its capacity?

A. 5/12
B. 2/3
C. 7/9
D. 5/6
E. 7/8

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Plug in values for Jar X and Jar Y. To find a good number, multiply together the denominators of the two fractions in the problem; this will ensure that our calculations work nicely. If Jar X is 12 gallons, Jar Y would be 6 gallons. If Jar X is 1/6 full, it would contain 2 gallons of water. If Jar Y is 1/2 full, it would contain 3 gallons of water. Thus, when Jar X is poured into Jar Y, Jar Y would then have 5 gallons in it, which is 5/6 of its capacity, and the correct answer is (D).

To solve this problem algebraically, note that Jar X is 1/6 full, and Jar Y is 1/2 full. Because Jar Y is half as large as Jar X, Jar X is twice as large as Jar Y, so X = 2Y. 1/6 X must then equal 1/3 Y. Pouring Jar X into Jar Y means adding 1/3 Y (Jar X) to 1/2 Y (Jar Y), for a total of 5/6 Y.
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Re: Jar X is 16 full of water. Jar Y, which has half the capacity of Jar X  [#permalink]

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Bunuel wrote:
Jar X is 1/6 full of water. Jar Y, which has half the capacity of Jar X, is 1/2 full of water. If the contents of Jar X is poured into Jar Y, Jar Y will be filled to what fraction of its capacity?

A. 5/12
B. 2/3
C. 7/9
D. 5/6
E. 7/8

We can let the capacity of Jar X = 12 and the the capacity of jar Y = 6.

So Jar X has 2 and Jar Y has 3.

If all of Jar X is poured into Jar Y, then Jar Y will be filled to 5/6 of capacity.

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Re: Jar X is 16 full of water. Jar Y, which has half the capacity of Jar X  [#permalink]

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Assign a smart number for this problem. Let assign 12 ml of water to X and 6 ml of water to Y. So X is having 2 ml and Y is having 3 ml. if the contents of Jar X is poured into Jar Y,then jar Y is having total 3+2 i.e 5 ml of water which is 5/6 of it capacity.

Answer should be D.
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Re: Jar X is 16 full of water. Jar Y, which has half the capacity of Jar X  [#permalink]

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_________________ Re: Jar X is 16 full of water. Jar Y, which has half the capacity of Jar X   [#permalink] 27 May 2019, 02:47
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