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Drum x is 1/2 full of oil and drum y, which has twice the capacity of

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Drum x is 1/2 full of oil and drum y, which has twice the capacity of  [#permalink]

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New post Updated on: 13 Feb 2015, 04:09
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Drum x is 1/2 full of oil and drum y, which has twice the capacity of drum x is 2/3 full of oil. if all of the oil in drum x is poured into drum y, then drum y will be filled to what capacity?

A. 3/4
B. 5/6
C. 11/12
D. 7/6
E. 11/6

why not:
drum x capacity = x
drum y capacity = 2x

drum y contains 2/3(2x) = 4/3x oil
drum x + y = 4/3x + 1/2x = 11/6x
answer E ... this is wrong.

Originally posted by ggarr on 27 Mar 2007, 20:10.
Last edited by Bunuel on 13 Feb 2015, 04:09, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: Drum x is 1/2 full of oil and drum y, which has twice the capacity of  [#permalink]

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New post 27 Mar 2007, 20:16
1
pick numbers -

drum A capacity 3 units
drum B capacity 6 units

drum A contains 1.5 units.
drum B contains4 units.

drum B gets filled 5.5 after pouring 1.5 from A to B.

Hence drum B is full 5.5/6 of its capacity. i.e. 11/12
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Re: Drum x is 1/2 full of oil and drum y, which has twice the capacity of  [#permalink]

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New post 27 Mar 2007, 20:29
1
1
ggarr wrote:
Drum x is 1/2 full of oil and drum y, which has twice the capacity of drum x is 2/3 full of oil. if all of the oil in drum x is poured into drum y, then drum y will be filled to what capacity?

3/4
5/6
11/12
7/6
11/6

why not:
drum x capacity = x
drum y capacity = 2x

drum y contains 2/3(2x) = 4/3x oil
drum x + y = 4/3x + 1/2x = 11/6x
answer E ... this is wrong.


its correct except ... you need to divide by the actual capacity of the drum to get the fraction so
(11x/6)/(2x) = 11/12
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Re: Drum x is 1/2 full of oil and drum y, which has twice the capacity of  [#permalink]

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New post 27 Mar 2007, 20:43
1
1
ggarr wrote:
Drum x is 1/2 full of oil and drum y, which has twice the capacity of drum x is 2/3 full of oil. if all of the oil in drum x is poured into drum y, then drum y will be filled to what capacity?

3/4
5/6
11/12
7/6
11/6

why not:
drum x capacity = x
drum y capacity = 2x

drum y contains 2/3(2x) = 4/3x oil
drum x + y = 4/3x + 1/2x = 11/6x
answer E ... this is wrong.


The answer is in terms of Drum Y, so I did the calc in terms of Y...

So...

X is 1/2 the size of Y and is 1/2 full... so in terms of Y, X is 1/4

Y as we already know is 2/3 full...

therefore, when you add the two drums together...

2/3 + 1/4 = (8+3)/12 = 11/12
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Re: Drum x is 1/2 full of oil and drum y, which has twice the capacity of  [#permalink]

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New post 26 May 2007, 13:53
ggarr wrote:
Drum x is 1/2 full of oil and drum y, which has twice the capacity of drum x is 2/3 full of oil. if all of the oil in drum x is poured into drum y, then drum y will be filled to what capacity?

3/4
5/6
11/12
7/6
11/6



There is a variation of this question. How do i set this one up?

Drum x is 1/2 full of oil and drum y, which has twice the capacity of drum x is 2/J full of oil. if all of the oil in drum x is poured into drum y, then drum y will be filled to what capacity?

3/4
5/6
11/12
7/6
11/6
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Re: Drum x is 1/2 full of oil and drum y, which has twice the capacity of  [#permalink]

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New post 26 May 2007, 14:39
[quote="bmwhype2"][quote="ggarr"]Drum x is 1/2 full of oil and drum y, which has twice the capacity of drum x is 2/3 full of oil. if all of the oil in drum x is poured into drum y, then drum y will be filled to what capacity?

3/4
5/6
11/12
7/6
11/6

[/quote]

There is a variation of this question. How do i set this one up?

Drum x is 1/2 full of oil and drum y, which has twice the capacity of drum x is 2/J full of oil. if all of the oil in drum x is poured into drum y, then drum y will be filled to what capacity?

3/4
5/6
11/12
7/6
11/6[/quote]


Let C be the capacity of oil drum X
then the capacity of drum Y is 2C

if 1/2 of X is filled, then it is filled to C/2
similarly, if 2/J of Y is filled, it is filled to 4C/J

now, all of X is poured into Y, the total in Y is C/2 + 4C/J
this equals to (CJ + 8C)/2J = C(J+8)/2J
Now, Y is filled to (C(J+8)/2J)/2C = (J+8)/4J

I hope this is what you were looking for. I was a little confused with J in the question and none of the answer choices lending themselves as being correct.
cheers
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Re: Drum x is 1/2 full of oil and drum y, which has twice the capacity of  [#permalink]

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New post 01 Jun 2007, 23:17
saurster wrote:
bmwhype2 wrote:
ggarr wrote:
Drum x is 1/2 full of oil and drum y, which has twice the capacity of drum x is 2/3 full of oil. if all of the oil in drum x is poured into drum y, then drum y will be filled to what capacity?

3/4
5/6
11/12
7/6
11/6



There is a variation of this question. How do i set this one up?

Drum x is 1/2 full of oil and drum y, which has twice the capacity of drum x is 2/J full of oil. if all of the oil in drum x is poured into drum y, then drum y will be filled to what capacity?

3/4
5/6
11/12
7/6
11/6



Let C be the capacity of oil drum X
then the capacity of drum Y is 2C

if 1/2 of X is filled, then it is filled to C/2
similarly, if 2/J of Y is filled, it is filled to 4C/J

now, all of X is poured into Y, the total in Y is C/2 + 4C/J
this equals to (CJ + 8C)/2J = C(J+8)/2J
Now, Y is filled to (C(J+8)/2J)/2C = (J+8)/4J

I hope this is what you were looking for. I was a little confused with J in the question and none of the answer choices lending themselves as being correct.
cheers


PS1000 has many many many typos and errata? this being one of them.
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Re: Drum x is 1/2 full of oil and drum y, which has twice the capacity of  [#permalink]

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New post 02 Jun 2007, 00:42
Love the solutions here. Thx.

Heres how I solved it.

Drum x is 1/2 of y or 2x=y

Pick numbers:

x=50, y=100 Holds true to the equations above.

2/3 of y = 66.66666... 1/2 of x = 25.

Add 25+66.66666 = 91.6666666... Now just find an answer choice that has this percentage :-D and its C.
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Re: Drum x is 1/2 full of oil and drum y, which has twice the capacity of  [#permalink]

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New post 02 Nov 2011, 12:25
Picking smart numbers like 6 or 100 will give the answer.

Lets say Drum x capacity is 100. Drum Y capacity will be 200.

Oil in drum x is 50
Oil in drum y is 100* 2/3 = 400/3

Fraction of oil in y after x is emptied into y is = (50 + 400/3) / 200
= 550/600
= 11/12
Answer is c
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Re: Drum x is 1/2 full of oil and drum y, which has twice the capacity of  [#permalink]

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New post 11 Mar 2015, 18:30
1
[quote="ggarr"]Drum x is 1/2 full of oil and drum y, which has twice the capacity of drum x is 2/3 full of oil. if all of the oil in drum x is poured into drum y, then drum y will be filled to what capacity?

A. 3/4
B. 5/6
C. 11/12
D. 7/6
E. 11/6

Hello All,

I took the exact approach as others to solve this problem.

Let's say drum X has a capacity of 2, which means drum Y will have a capacity of 4 (twice the capacity of drum x) . if Drum x is 1/2 full then 2.1/2=1 If drum y is 2/3 full then 4.2/3=8/3. If all the oil is poured from x to y then we can add 1+8/3 = 11/3. Now to see the what drum y's capacity will be filled to we can do 11/3 divided by four, which is equal to 11/12 (c)
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Re: Drum x is 1/2 full of oil and drum y, which has twice the capacity of  [#permalink]

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New post 12 Mar 2015, 03:34
ggarr wrote:
Drum x is 1/2 full of oil and drum y, which has twice the capacity of drum x is 2/3 full of oil. if all of the oil in drum x is poured into drum y, then drum y will be filled to what capacity?

A. 3/4
B. 5/6
C. 11/12
D. 7/6
E. 11/6

why not:
drum x capacity = x
drum y capacity = 2x

drum y contains 2/3(2x) = 4/3x oil
drum x + y = 4/3x + 1/2x = 11/6x
answer E ... this is wrong.


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Re: Drum X is 1/2 full of oil and drum Y, which has twice the capacity of  [#permalink]

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New post 07 Dec 2017, 00:03
Bunuel wrote:
Drum X is 1/2 full of oil and drum Y, which has twice the capacity of drum X, is 2/3 full of oil. If all of the oil in drum X is poured into drum Y, then drum Y will be filled to what fraction of its capacity?

(A) 3/4
(B) 5/6
(C) 11/12
(D) 7/6
(E) 11/6

2/3+1/4 = 11/12

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Re: Drum X is 1/2 full of oil and drum Y, which has twice the capacity of  [#permalink]

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New post 07 Dec 2017, 01:36
Bunuel wrote:
Drum X is 1/2 full of oil and drum Y, which has twice the capacity of drum X, is 2/3 full of oil. If all of the oil in drum X is poured into drum Y, then drum Y will be filled to what fraction of its capacity?

(A) 3/4
(B) 5/6
(C) 11/12
(D) 7/6
(E) 11/6


Assume Drum X capacity to be 300 and Drum Y capacity to be 600
Drum X has 150 lltrs and Drum Y has 400 ltrs
After pouring Drum y will be 550/600 = 11/12
C
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Drum X is 1/2 full of oil and drum Y, which has twice the capacity of  [#permalink]

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New post 07 Dec 2017, 17:54
Bunuel wrote:
Drum X is 1/2 full of oil and drum Y, which has twice the capacity of drum X, is 2/3 full of oil. If all of the oil in drum X is poured into drum Y, then drum Y will be filled to what fraction of its capacity?

(A) 3/4
(B) 5/6
(C) 11/12
(D) 7/6
(E) 11/6

Algebra

\(X = \frac{1}{2}Y\)

\(X\) is half full of oil. Its oil amount constitutes:

\(\frac{1}{2}\) of \(\frac{1}{2}Y\)

\(\frac{1}{2} * \frac{1}{2}Y=\frac{1}{4}Y\)

\(Y\) is \(\frac{2}{3}\) full of oil = \(\frac{2}{3}Y\)

Contents of X are poured into Y:
\(\frac{1}{4}Y + \frac{2}{3}Y=\frac{(3 + 8)}{12}=\frac{11}{12}Y\)

Answer C

Pick numbers. For Y, do not go smaller than any denominator in answer choices

Let X's capacity = 6 gallons
Y's capacity = (2 * X) = 12 gallons

X is 1/2 full of oil:
6 * 1/2 = 3 gallons inside

Y is 2/3 full
12 * 2/3 = 8 gallons inside

X's oil is poured into Y:
3 + 8 = 11

\(\frac{FillAmt}{CapacityY} = \frac{11}{12}\)

Answer C
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Re: Drum x is 1/2 full of oil and drum y, which has twice the capacity of  [#permalink]

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New post 19 Mar 2018, 11:06
Hi All,

TESTing Values will work great on this question. Based on what the question asks for and the answer choices, a great number to pick for Drum Y's capacity is 12. That number is based on the common denominator of the 5 options.

Now, we just need to follow the facts in this question and create a little table:

We're told that Drum Y is 2/3 full of oil:

Drum Y = capacity of 12; has 8 in it

We're also told that Drum Y has twice the capacity of Drum X and that Drumb X is 1/2 full of oil:

Drum X = capacity of 6; has 3 in it

Finally, we're told to pour the oil from Drum X into Drum Y….

Drum Y = 8+3 = 11
Drum Y is 11/12 full

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Re: Drum x is 1/2 full of oil and drum y, which has twice the capacity of  [#permalink]

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New post 20 Mar 2018, 15:08
Hi,

I figured a faster approach here:

As we know that the capacity of y = 2x, and 1/2 of x is filled with oil, hence, when you pour from x to y, 1/4 part of y is filled with oil( Refer to y= 2x)

So (1/4 + 2/3)y = 11/12y
Ans: C
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Re: Drum x is 1/2 full of oil and drum y, which has twice the capacity of &nbs [#permalink] 20 Mar 2018, 15:08
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