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505-555 Level|   Geometry|            
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gmatt1476
If all of the six faces of a concrete block are rectangular, what is the volume of the block?

(1) Each of the four lateral faces of the block has an area of 200 square inches.
(2) The top of the block is square and has an area of 400 square inches.

DS15650.02

a 6 sided block can be cube or rectangular block
#1
Each of the four lateral faces of the block has an area of 200 square inches.
a*b = 200
can be 10*20 ; but top and bottom surface area not know
dimensions of a,b,c not know insufficient
#2
The top of the block is square and has an area of 400 square inches
i.e a=b=20
but third side not know insufficient
from 1 &2
we can say that area of block ; 10*20*20 ; 4000
OPTION C
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gmatt1476
If all of the six faces of a concrete block are rectangular, what is the volume of the block?

(1) Each of the four lateral faces of the block has an area of 200 square inches.
(2) The top of the block is square and has an area of 400 square inches.

DS15650.02

STRAIGHT to POINT:

1)Area of lateral alone >>insuff.
2)Area of Top n bottom alone>>> a2 =400>>a=20 >>insuff.


Now C: if a=side of square=one side of rectangle(L)=20>>>> other side of rectangle =200/20=10(given area of=200)

Now volume can be calculated

Therefore C


HOPE THIS HELPS

THANKS :thumbsup:
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BrentGMATPrepNow
I have a doubt. How can we say that the block is cuboid? It can be a cube.
As Square is a type of Rectangle and it is not mentioned anywhere in the question that the block is cuboid.
So, I think with that in mind we can say that Option B is correct.

Please correct me if I am wrong.
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BrentGMATPrepNow
I have a doubt. How can we say that the block is cuboid? It can be a cube.
As Square is a type of Rectangle and it is not mentioned anywhere in the question that the block is cuboid.
So, I think with that in mind we can say that Option B is correct.

Please correct me if I am wrong.

We know that the block is a cuboid, because we're told that all six faces are rectangular
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gmatt1476
If all of the six faces of a concrete block are rectangular, what is the volume of the block?

(1) Each of the four lateral faces of the block has an area of 200 square inches.
(2) The top of the block is square and has an area of 400 square inches.

DS15650.02

CONCEPT: Volume of a rectangular solid = Length*Width*Height

Question: FInd volume of rectangular block?

Statement 1: Each of the four lateral faces of the block has an area of 200 square inches.
ie. \(L*H = B*H = 200\)
i.e. L = B

Case 1: L = B = 20 and H = 10 Volume = 4000
Case 2: L = B = 5 and H = 40 Volume = 1000

but we don't know the height and Length individual values

NOT SUFFICIENT

STatement 2: The top of the block is square and has an area of 400 square inches
Top = L*B = 400
i.e L = B = 20 (square so L=B)
H is unknown hence

NOT SUFFICIENT

COmbining the statements

Case 1: L = B = 20 and H = 10 Volume = 4000

SUFFICIENT

ANswer: Option C

Genoa2000 Please check the explanation and two cases in statement 1
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Solution:

A new Og 2021 question

Let the dimensions of the concrete block be l, b, h for length, breadth and height respectively.

The volume of a cube = l.b.h

St(1):- Please let us know as and when you have queries in future.

The lateral faces are the four sides of the block.(You can imagine the four "walls" of a room)

Given, l h =200 and b h=200

=> l h=b h

=> l = b
However we do not know the third side to determine the value of the volume. (Insufficient)

St(2):- The top of the block is square and has an area of 400 square inches.

Let the dimension of the top square face be a units.

=> a^2 = 400

=> a = 20
Even though two of the dimensions are 20 each, we still do not know the third dimension needed for the volume.(Insufficient)

On combining both:-

l = b

l h = 200 and hence 20 * h =200 (20 is obtained as data from the second statement. You can also use b h=20)

Hence volume = lbh = 20*20*10 (Sufficient) option(C)

Hope this helps :thumbsup:
Devmitra Sen(GMAT Quant Expert)
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gmatt1476
If all of the six faces of a concrete block are rectangular, what is the volume of the block?

(1) Each of the four lateral faces of the block has an area of 200 square inches.
(2) The top of the block is square and has an area of 400 square inches.

DS15650.02



Answer: Option C

Video solution by GMATinsight

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