K is a rectangular solid. Find the volume of K

Question

(1) a diagonal line across the front face of K has a length of 40
(2) a diagonal line across the bottom face of K has a length of 25

Kudos for a correct  solution .

jaxndaxt145 · Answer

IMO E

By themselves insufficient and I am not sure how you would relate the two equations to find the necessary information.

ynaikavde · Answer

Both statement are independently insufficient

combined we can have several combinations

say a b c are sides

40^2=(24^2+32^) ; 25^2= (7^2+24^2) giving us a b c as(7,24,32)
40^2=(20^2+ 1200) ; 25^2= (15^2+20^2) giving us a b c as(17,20,sqrt(1200))
both give different volume.
hence answer is E

karan14 · Answer

easy one E.

Coz using both we can't get individual value of the sides or the product of the three sides.

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION:

So, the prompt gives us relatively little information. We are looking for the volume. Statement #1 tells us a diagonal line across the front face has a length of 40. If L is the length and H is the height, then this means: L^2 + H^2 = 40^2 = 1600. That’s one equation with two unknowns, and no way to solve for the volume.

Statement #1 by itself is insufficient.

Statement #2 tells us a diagonal line across the bottom face has a length of 25. If L is the length and W is the width, then this means: L^2 + W^2 = 25^2 = 625. Again, that’s one equation with two unknowns, and no way to solve for the volume. Statement #2 by itself is insufficient.

Combine the statements: we now know both L^2 + H^2 = 40^2 = 1600 and L^2 + W^2 = 25^2 = 625. We now have two equations but three unknowns: still not enough information to solve for the individual values, nor can we somehow rearrange to get the product of LWH. Even combined, the statements are insufficient.

Answer = E.

Bunuel · Answer

Check other  3-D Geometry Questions  in our  Special Questions Directory .

Abhishek009 · Answer

Rectangular solid refers to a Cuboid.

FROM STATEMENT - I   ( INSUFFICIENT )

We can not find the volume of the Cuboid from the dimension of one diagonal.

FROM STATEMENT - II   ( INSUFFICIENT )

Same as statement I , We can not find the volume of the Cuboid from the dimension of one diagonal.

FROM STATEMENT I AND II   ( INSUFFICIENT )

We can not find the volume of a cuboid from the dimension of 2 diagonals , because the Volume of a Cuboid given the 3 diagonals as a , b and c is -

Volume \ of \ Cuboid = \sqrt{a^2 + b^2 + c^2} 
  
Thus Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed , answer will be (E)

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K is a rectangular solid. Find the volume of K

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GMAT Data Sufficiency (DS) Questions

K is a rectangular solid. Find the volume of K

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