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

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:

In this case, the volume = 20 x 20 x 10 = 4000


Case b:

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:


In this case, the volume = 20 x 20 x 10 = 4000


Case b:

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

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

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

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

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

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

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)

Answer: Option C

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