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

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by Brent@GMATPrepNow » Wed Feb 15, 2017 9:07 am
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


Source: GMAT Prep Now
Difficulty level: 650 - 700

Answer: A
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by DavidG@VeritasPrep » Wed Feb 15, 2017 10:12 am
Brent@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


Source: GMAT Prep Now
Difficulty level: 650 - 700

Answer: A
If the original 5-liter conner is 3/4 full, that means 1/4 of the container, or 5/4 liters will have been poured out. If a total of 5/4 liters is poured into 2 glasses, then each glass will contain (5/4)/2, or 5/8 liters. If that 5/8 liters represents 3/4 of the capacity of the glass, then 5/8 = (3/4)x; x = 20/24 = 5/6. The answer is A
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by Brent@GMATPrepNow » Wed Feb 15, 2017 5:06 pm
Brent@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
My original solution was identical to David's so here's another approach:

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

Cheers,
Brent
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by Matt@VeritasPrep » Wed Feb 15, 2017 5:40 pm
If each of the glasses has capacity x, then we know that

(3/4)*5 + (3/4)*x + (3/4)*x = 5

(3/4)*2x = (1/4)*5

x = 5/6
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by Matt@VeritasPrep » Wed Feb 15, 2017 5:41 pm
Did this one score as 65th+ percentile in testing? I'd be surprised, especially given the scale of difficulty on the quant section these days.
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by Brent@GMATPrepNow » Wed Feb 15, 2017 5:42 pm
Matt@VeritasPrep wrote:If each of the glasses has capacity x, then we know that

(3/4)*5 + (3/4)*x + (3/4)*x = 5

(3/4)*2x = (1/4)*5

x = 5/6
NICE!
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by Brent@GMATPrepNow » Wed Feb 15, 2017 5:47 pm
Matt@VeritasPrep wrote:Did this one score as 65th+ percentile in testing? I'd be surprised, especially given the scale of difficulty on the quant section these days.
That question first went through several phases of psychometric testing, and then the staff (here at GMAT Prep Now world headquarters) held several meetings to tweek the question to maximize awesomeness.

I then consulted various astrological charts and a fortune cookie to arrive at the 650-700 figure :-)

What level of difficulty would you give the question?
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by Matt@VeritasPrep » Wed Feb 15, 2017 6:39 pm
Brent@GMATPrepNow wrote: I then consulted various astrological charts and a fortune cookie to arrive at the 650-700 figure :-)

What level of difficulty would you give the question?
I doubt I'd outperform the fortune cookies! I'd have to turn to a psychic octopus or a magic 8-ball, I'm afraid.

Ashamed to admit it, but I asked more because I'm curious - I've gotten worse and worse at predicting the difficulty rating of questions.
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