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Water is poured from a full 5-liter jug into two identical

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BrentGMATPrepNow
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Water is poured from a full 5-liter jug into two identical [#permalink] New post   15 Feb 2017, 10:06
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Water is poured from a full 5-liter jug into two identical glasses until all three containers are each 3/4 full. What is the capacity, in liters, of one glass?

A) 5/6
B) 8/9
C) 9/8
D) 6/5
E) 5/3

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Re: Water is poured from a full 5-liter jug into two identical [#permalink] New post   15 Feb 2017, 18:07
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GMATPrepNow wrote:
Water is poured from a full 5-liter jug into two identical glasses until all three containers are each 3/4 full. What is the capacity, in liters, of one glass?

A) 5/6
B) 8/9
C) 9/8
D) 6/5
E) 5/3


Let x = the capacity of each glass (in liters)
So, if the glass is 3/4 full, then (3/4)x = the amount of water in one glass
So, (2)(3/4)x = the amount of water in TWO glasses

IMPORTANT: the volume of water IN the TWO glasses is equal to the volume of water that was poured OUT of the 5-liter jug.
Since the 5-liter jug ends up being 3/4 full, we can conclude that 1/4 of the water was poured OUT of the 5-liter jug.
So, (1/4)(5) = the volume of water that was poured OUT of the 5-liter jug.

Now we'll set up a "word equation"
Volume of water IN the TWO glasses = volume of water poured OUT of the 5-liter jug
We get: (2)(3/4)x = (1/4)(5)
Simplify: 6x/4 = 5/4
Multiply both sides by 4 to get: 6x = 5
Solve: x = 5/6

Answer: A

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Re: Water is poured from a full 5-liter jug into two identical [#permalink] New post   15 Feb 2017, 18:15
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GMATPrepNow wrote:
Water is poured from a full 5-liter jug into two identical glasses until all three containers are each 3/4 full. What is the capacity, in liters, of one glass?

A) 5/6
B) 8/9
C) 9/8
D) 6/5
E) 5/3


Another approach:

Since the 5-liter jug ends up being 3/4 full, we can conclude that 1/4 of the water was poured OUT of the 5-liter jug.
1/4 of 5 liters = (1/4)(5) = 5/4 liters

Equal amounts of those 5/4 liters were poured into EACH of the two glasses.
So, (1/2)5/4 liters = volume of water poured into ONE glass
Simplify to get: 5/8 liters = volume of water poured into ONE glass

That volume of 5/8 liters represents 3/4 of the capacity of the glass.
So, if we let c = the capacity of the glass, then 3/4 of c = 5/8 liters
In other words, (3/4)c = 5/8
To solve, multiply both sides by 4/3 to get: c = (4/3)5/8)
= 20/24
= 5/6

Answer: A
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Re: Water is poured from a full 5-liter jug into two identical [#permalink] New post   15 Feb 2017, 23:00
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GMATPrepNow wrote:
Water is poured from a full 5-liter jug into two identical glasses until all three containers are each 3/4 full. What is the capacity, in liters, of one glass?

A) 5/6
B) 8/9
C) 9/8
D) 6/5
E) 5/3

*Kudos for all correct solutions


    • Since all three containers are \(\frac{3}{4}\)th full at the end.

    • We can infer that from the jug, we poured \((1-\frac{3}{4})*5\) litre in the identical glasses.

    • Therefore in each glass, water poured would be \(\frac{1}{2}\) of \((1 - \frac{3}{4})*5\)

    • If the capacity of the glass is \(G\), then -
      • \(\frac{3}{4} * G =\frac{1}{2} * (1-\frac{3}{4})*5\)

      • \(G = \frac{4}{3} *\frac{1}{2} * \frac{1}{4} *5 = \frac{5}{6} litres\)

Hence the correct answer is Option A

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Water is poured from a full 5-liter jug into two identical [#permalink] New post   15 Feb 2017, 14:49
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GMATPrepNow wrote:
Water is poured from a full 5-liter jug into two identical glasses until all three containers are each 3/4 full. What is the capacity, in liters, of one glass?

A) 5/6
B) 8/9
C) 9/8
D) 6/5
E) 5/3

*Kudos for all correct solutions


1/4*5=5/4 liter
(5/4)/2=5/8 liter
let g=glass capacity
5/8 liter=3/4*g
g=5/6 liter
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Re: Water is poured from a full 5-liter jug into two identical [#permalink] New post   17 Feb 2017, 02:47
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(1/4)*5 = (3/4)*2x
X = 5/6.
Option D.....

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Water is poured from a full 5-liter jug into two identical [#permalink] New post   15 Feb 2017, 10:24
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First jug --> Full quantity = 5

Let x be the quantity of each identical glass.

5 - (3/4)*(2x) = (3/4)*5
20 - 6x = 15
x = 5/6

Answer: A
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Re: Water is poured from a full 5-liter jug into two identical [#permalink] New post   23 Aug 2018, 06:02
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GMATPrepNow wrote:
Water is poured from a full 5-liter jug into two identical glasses until all three containers are each 3/4 full. What is the capacity, in liters, of one glass?

A) 5/6
B) 8/9
C) 9/8
D) 6/5
E) 5/3

*Kudos for all correct solutions


This is how i solved

after the glasses were pored the jar was left 3/4 full = 3/4* 5 = 3.75 Ltrs
Which means 1.25 ltrs was poured in total to both the glasses combined
perglass = 1.25 /2 = .625 ltrs =

.625 ltrs 3/4full so
full would be by unitry method
625/1000 = 3/4X ( Here X is the full capacity of the glass )
cross multiply and get 125/150 = 5/6 = ANS A
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Re: Water is poured from a full 5-liter jug into two identical [#permalink] New post   09 Mar 2022, 13:15
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CyrilT22 wrote:
Hi Brent. In the related video that you posted for this question you performed an equation with Curly, Moe and Larry's age. I just wanted to ask how did you go from 2M+10 to 4M+15. Before that you did 2*M= 2M and 2*5=10 which I understand but I don't see how we went from it to 4M+15

Thank you


Here's the section of the my solution you're referring to:


The calculation of 2(M + 5) is just one small part of that equation.
The original equation is: M + (M +5) + 2(M + 5) = 95
Once we expand 2(M + 5)to get 2M + 10, the equation becomes: M + (M +5) + 2M + 10 = 95
At this point, we can simplify M + M + 2M to get 4M, which means the equation becomes: 4M + 5 + 10 = 95
Now we can simplify 5 + 10 to get 15, which means the equation becomes: 4M + 15 = 95

Does that help?
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Water is poured from a full 5-liter jug into two identical [#permalink] New post   14 Mar 2022, 05:19
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BrentGMATPrepNow wrote:
Water is poured from a full 5-liter jug into two identical glasses until all three containers are each 3/4 full. What is the capacity, in liters, of one glass?

A) 5/6
B) 8/9
C) 9/8
D) 6/5
E) 5/3

*Kudos for all correct solutions


Answer:

Volume of water poured from 5 liter jug = 1/4*5 = 5/4 ( 1/4 because the 5 liter jug is only 3/4 of its volume now, as are the other two containers as given in the question)
5/4th of a liter is poured in the two identical containers. That means, each container was filled with half of 5/4 liters, which is 1/2*5/4 = 5/8

5/8th of a liter fills 3/4th of each of the identical containers.
Therefore, 3/4*x = 5/8
multiply 4/3 on both sides, x = 5/8*4/3 = 20/24
which is simplified to 5/6
Answer is Option (A) 5/6
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Re: Water is poured from a full 5-liter jug into two identical [#permalink] New post   28 Jan 2019, 00:55
Since the 5 liter jug ends up remaining filled to 3/4th of its capacity after the water is removed from it, we can say the following:

3/4x + 3/4x = 1/4*5 (assuming x to be the total volume of each of the two glasses into which water is filled)
3/4 (2x) = 5/4
x = 5/6 (Option A)
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Re: Water is poured from a full 5-liter jug into two identical [#permalink] New post   23 Mar 2020, 22:01
3x/4 + 3x/4 =5/4
So 6x=5
X=5/6

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Re: Water is poured from a full 5-liter jug into two identical [#permalink] New post   24 Mar 2020, 12:15
the container itself will be 15/4 rest 5/4 will be divided into two part each

5/8 is 3/4th of a container

thus 5/6 will be 1 (100%) of that container
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Re: Water is poured from a full 5-liter jug into two identical [#permalink] New post   24 Mar 2020, 12:51
first things first:

A) 5/6 = 80+%
B) 8/9 = 80++%
C) 9/8 = over 100%
D) 6/5 = over 100%
E) 5/3 = over 100%

So, is the answer closer to 90% or to 80%?

Let's see. Everything is 3/4 of their totals.

5L - 1/4 ...
that 1/4 is = 1.25L

1.25L / 2 cups = 0.6125 per cup

solve:
0.6125 = 3/4X

solve for X
X= ~0.24/3
X= ~0.8
Now convert decimal to fraction.
Choices A and B are both in the 0.8.. region, but B is too close to 0.9. Therefore, A fits the best because 16.66*5 = 83.33
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Re: Water is poured from a full 5-liter jug into two identical [#permalink] New post   09 Mar 2022, 11:23
Hi Brent. In the related video that you posted for this question you performed an equation with Curly, Moe and Larry's age. I just wanted to ask how did you go from 2M+10 to 4M+15. Before that you did 2*M= 2M and 2*5=10 which I understand but I don't see how we went from it to 4M+15

Thank you


BrentGMATPrepNow wrote:
GMATPrepNow wrote:
Water is poured from a full 5-liter jug into two identical glasses until all three containers are each 3/4 full. What is the capacity, in liters, of one glass?

A) 5/6
B) 8/9
C) 9/8
D) 6/5
E) 5/3


Let x = the capacity of each glass (in liters)
So, if the glass is 3/4 full, then (3/4)x = the amount of water in one glass
So, (2)(3/4)x = the amount of water in TWO glasses

IMPORTANT: the volume of water IN the TWO glasses is equal to the volume of water that was poured OUT of the 5-liter jug.
Since the 5-liter jug ends up being 3/4 full, we can conclude that 1/4 of the water was poured OUT of the 5-liter jug.
So, (1/4)(5) = the volume of water that was poured OUT of the 5-liter jug.

Now we'll set up a "word equation"
Volume of water IN the TWO glasses = volume of water poured OUT of the 5-liter jug
We get: (2)(3/4)x = (1/4)(5)
Simplify: 6x/4 = 5/4
Multiply both sides by 4 to get: 6x = 5
Solve: x = 5/6

Answer: A

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Re: Water is poured from a full 5-liter jug into two identical [#permalink] New post   09 Mar 2022, 13:59
Hi Brent. Yes that helps thank you!

BrentGMATPrepNow wrote:
CyrilT22 wrote:
Hi Brent. In the related video that you posted for this question you performed an equation with Curly, Moe and Larry's age. I just wanted to ask how did you go from 2M+10 to 4M+15. Before that you did 2*M= 2M and 2*5=10 which I understand but I don't see how we went from it to 4M+15

Thank you


Here's the section of the my solution you're referring to:


The calculation of 2(M + 5) is just one small part of that equation.
The original equation is: M + (M +5) + 2(M + 5) = 95
Once we expand 2(M + 5)to get 2M + 10, the equation becomes: M + (M +5) + 2M + 10 = 95
At this point, we can simplify M + M + 2M to get 4M, which means the equation becomes: 4M + 5 + 10 = 95
Now we can simplify 5 + 10 to get 15, which means the equation becomes: 4M + 15 = 95

Does that help?
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Re: Water is poured from a full 5-liter jug into two identical [#permalink] New post   27 Mar 2023, 12:13
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