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

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New post 26 Apr 2019, 06:57
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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



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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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New post 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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New post 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



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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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New post 15 May 2019, 04:03
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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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New post 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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New post 17 May 2019, 15:44
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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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New post 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



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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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New post 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.
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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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New post 21 May 2019, 10:08
[quote="Bunuel"]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



Here is my take ....

The question is asking,what is the area of the base of the vat= a*b (a=length; b=breath)

Let's say total capacity of the vat= x
2x/3= 60 gallon
x= 90 gallon (total capacity)

If 15/2g of water occupies 1 cubic foot of space
then, 90g of water will occupy= 90*2/15 = 12 cubic foot of space in the vat (Total volume)

We can also write:
a*b*c= 12 cubic foot (c=depth; C=3 feet)
a*b*3= 12
a*b= 4 (which is length * breath= area of the base)

The answer 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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New post 23 May 2019, 17:15
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



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Quantitative Review 2020 NEW QUESTION



Since the vat is 3 feet deep and water is filled to 2/3 of its capacity, the water is ⅔ x 3 = 2 feet deep. In cubic feet, the water is 60/7.5 = 8 cubic feet in volume. Since the water is 2 feet deep, the base of the vat must be 8/2 = 4 square feet.

Answer: A
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Re: When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap   [#permalink] 23 May 2019, 17:15
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