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

Question

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

BrentGMATPrepNow · Accepted Answer

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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Kurtosis · Answer

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

gracie · Answer

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

BrentGMATPrepNow · Answer

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

EgmatQuantExpert · Answer

• 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 Thanks, Saquib Quant Expert e-GMAT Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

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Jayeshvekariya · Answer

(1/4)*5 = (3/4)*2x
X = 5/6.
Option D.....

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mimajit · Answer

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

Pritishd · Answer

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)

Saiharish98 · Answer

3x/4 + 3x/4 =5/4
So 6x=5
X=5/6

Posted from my mobile device

Vidhi96 · Answer

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

gerikso · Answer

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

CyrilT22 · Answer

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

Thank you

BrentGMATPrepNow · Answer

Here's the section of the my solution you're referring to:
 https://i.imgur.com/vgO6dlh.png

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?

CyrilT22 · Answer

Hi Brent. Yes that helps thank you!

nkr037 · Answer

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

bumpbot · Answer

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