If all of the six faces of a concrete block are rectangular, what is

Question

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

BrentGMATPrepNow · Accepted Answer

Target question :    What is the volume of the block?

Statement 1 : Each of the four lateral faces of the block has an area of 200 square inches.   
There are many rectangular solids that satisfy statement 1. Here are two:

Case a : 
 https://i.imgur.com/JK4hUkN.png  
In this case,  the volume = 20 x 20 x 10 = 4000

Case b : 
 https://i.imgur.com/8d9wxQx.png 
In this case,  the volume = 40 x 40 x 5 = 8000

Since we can’t answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : The top of the block is square and has an area of 400 square inches. 
There are many rectangular solids that satisfy statement 2. Here are two:

https://i.imgur.com/AA6buof.png 
In this case,  the volume = 20 x 20 x 10 = 4000

Case b : 
 https://i.imgur.com/eG4a4h8.png 
In this case,  the volume = 20 x 20 x 30 = 12000

Since we can’t answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
Statement 2 tells us that the top face is SQUARE  and  has an area of 400 square inches.
This means the  length and width are both 20 inches long . 
The only thing we don't yet know is the  height  of the block

Statement 1 tells us that the lateral faces each have an area of 200
Since the length and width are both 20 inches, this means the  height must be 10  (since 20 x 10 = 200)

Now that we know the measurements of the length, width and height, we can be certain that  the volume = 20 x 20 x 10 = 4000

Since we can answer the  target question  with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

ZoltanBP · Answer

Let l and w be the dimensions of the base, or top, of the rectangular block and let h be the height of the rectangular block. The original question: V = lwh = ?

1)  The lateral faces are perpendicular to the base and top of the rectangular block. Two lateral faces have areas of lh, and two lateral faces have areas of wh.

lh = wh = 200  \implies  l = w

Thus, the base of the rectangular block is a square.

V = lwh = w(wh) = w(200)

Since w and consequently V can be any positive number, we can't get a unique value to answer the original question.  \implies   Insufficient

2)  We know that the top of the rectangular block is a square with an area of 400, so l = w = 20 because (20)(20) = 400. However, we don't know the height of the rectangular block. Thus, we can't get a unique value to answer the original question.  \implies   Insufficient

1&2)  Since h = 200/w = 200/20 = 10, the volume of the block is

V = lwh = (20)(20)(10) =4,000

Thus, the answer to the original question is a unique value.  \implies   Sufficient

Answer: C

Archit3110 · Answer

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

itspCv2 · Answer

STRAIGHT to POINT: 1)Area of lateral alone >>insuff. 2)Area of Top n bottom alone>>> a 2 =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

AkshayC95 · Answer

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.

BrentGMATPrepNow · Answer

We know that the block is a cuboid, because we're told that   all six faces are  rectangular

GMATinsight · Answer

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

CrackverbalGMAT · Answer

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

Devmitra Sen(GMAT Quant Expert)

GMATinsight · Answer

Answer: Option C

Video solution by  GMATinsight

https://www.youtube.com/watch?v=7rFYYbzjvtM

bumpbot · Answer

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If all of the six faces of a concrete block are rectangular, what is

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