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# When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap

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Math Expert
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When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap  [#permalink]

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26 Apr 2019, 06:57
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Difficulty:

45% (medium)

Question Stats:

72% (02:26) correct 28% (02:22) wrong based on 67 sessions

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When a rectangular vat that is 3 feet deep is filled to 2/3 of its capacity, it contains 60 gallons of water. If $$7\frac{1}{2}$$ gallons of water occupies 1 cubic foot of space, what is the area, in square feet, of the base of the vat?

A.  4
B.  8
C.  12
D. 150
E. 225

PS95602.01
Quantitative Review 2020 NEW QUESTION

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Re: When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap  [#permalink]

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26 Apr 2019, 08:45
IMO A

volume = area of base *height

let the area be A

then volume = A*3

now this is filled to 2/3 of its capacity

so volume of water = 2/3*(A*3)

now the volume of water = 60(15/2)= 8 cubic feet

so 2/3*(A*3)= 8

So A = 8/2 = 4

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Re: When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap  [#permalink]

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28 Apr 2019, 05:24
total fill in feet ; 3*2/3 = 2feet
and 60 gallons in feet have 60*2/15 = 8 ft^3 of water
so base has 8ft^3/2feet = 4ft^2
IMO A

Bunuel wrote:
When a rectangular vat that is 3 feet deep is filled to 2/3 of its capacity, it contains 60 gallons of water. If $$7\frac{1}{2}$$ gallons of water occupies 1 cubic foot of space, what is the area, in square feet, of the base of the vat?

A.  4
B.  8
C.  12
D. 150
E. 225

PS95602.01
Quantitative Review 2020 NEW QUESTION

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Re: When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap  [#permalink]

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15 May 2019, 04:03
1
Let's assume V as the volume of our vat. 2/3*X=60 so we can find V=60*3/2=90.
Volume=width*length*height, width*length= area of our base and width*length*3=90 => width*length=90/3=30
Our answer is 30*2/15=4, which is A.
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Re: When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap  [#permalink]

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17 May 2019, 14:32
Snezanelle wrote:
Let's assume V as the volume of our vat. 2/3*X=60 so we can find V=60*3/2=90.
Volume=width*length*height, width*length= area of our base and width*length*3=90 => width*length=90/3=30
Our answer is 30*2/15=4, which is A.

Hello! Snezanelle,

Where does the 15 comes from?

Kind regards!
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Re: When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap  [#permalink]

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17 May 2019, 15:44
Unitary method can be applied to this :

If, 2/3 is 60 gallons then 3/3(1) = 90 gallons
As 1 cubic feet = 15/2 ,
12 cubic feet = 15/2*12 (multiplying both sides by 12)
12 cubic = 90 gallons (total volume)

total area = 3*X = 12
Therefore, x = 4
A
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Re: When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap  [#permalink]

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17 May 2019, 18:28
Bunuel wrote:
When a rectangular vat that is 3 feet deep is filled to 2/3 of its capacity, it contains 60 gallons of water. If $$7\frac{1}{2}$$ gallons of water occupies 1 cubic foot of space, what is the area, in square feet, of the base of the vat?

A.  4
B.  8
C.  12
D. 150
E. 225

PS95602.01
Quantitative Review 2020 NEW QUESTION

Let x be the area sq. foot of base. Volume of the water= x*2 ....(Height of tank filled id 2 ft.)

Now form the proportion 15/2 : 1 :: 60 : 2x
x=4.
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Re: When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap  [#permalink]

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18 May 2019, 08:24
jfranciscocuencag wrote:
Snezanelle wrote:
Let's assume V as the volume of our vat. 2/3*X=60 so we can find V=60*3/2=90.
Volume=width*length*height, width*length= area of our base and width*length*3=90 => width*length=90/3=30
Our answer is 30*2/15=4, which is A.

Hello! Snezanelle,

Where does the 15 comes from?

Kind regards!

Hi,
15/2 = 7*(1/2), which is mentioned in the problem.
Re: When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap   [#permalink] 18 May 2019, 08:24
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