A 5 × 5 × 5 cube is built using unit cu

Question

GMATBusters’ Quant Quiz Question -9 
A 5 × 5 × 5 cube is built using unit cubes. How many cuboids can be formed using the same set of unit cubes?
A. 1000
B. 1728
C. 2730
D. 3375
E. 4096

GMATBusters · Accepted Answer

Official Explanation : To understand the concept, let us take an example of 2-D Rectangle first: https://gmatclub.com/forum/download/file.php?id=53753 Solcube.JPG

Raxit85 · Answer

Again one more tricky one, still let me try. 
A 5×5×5 cube is made up of 125 unit cubes. 
Therefore we can make cubes using each side as 1 unit or 2 unit or 3 unit or 4 unit or 5 units.
With 1 unit the number of cubes will be 1.
With 2 units the number of cubes will be 6.
With 3 units the number of cubes will be 27
With 4 unit the number of cubes will be 64
With 5 units the number of cubes will be 125.
So, i think to get max unit cubes, answer may be multiple of 125, i.e. 1000/3375.
I'd like to guess 3375.
Ans. D

techwave · Answer

Answer: D

From the prompt, the cube is built out of 125 unit cubes.
Selecting 1, 2, 3, 4 or 5 cubes at a time, taken
length, breadth and height wise. 
Total number of cuboids =
(1+2+3+4+5) ^3 =3375

ashwini2k6jha · Answer

we have to find different solution of x+y+z=125
which is (125+3-1)C(3-1)=127C2

Archit3110 · Answer

giving a try
for cube of side 5*5*5 ; 
now to make a non identical cube we need to get sum of total cubes which can be made 
in this case for each side = 5*6/2 ; 15
and for three such sides we have 15^3 ; 3375
IMO D

A 5 × 5 × 5 cube is built using unit cubes. How many different non identical cuboids
can be formed using the same number of unit cubes?
A. 1000
B. 1728
C. 2730
D. 3375
E. 4096

shameekv1989 · Answer

GMATBusters  :- Could you please provide an explanation for this problem. Thanks

shameekv1989 · Answer

GMATBusters  :- 
Let's take the 6 lines as 1st, 2nd, 3rd, 4th, 5th and 6th

When we take  6_C_2  -

Let's take 1st and 2nd of each L, W and H - This will form 1*1*1 cube

If we choose 5th and 6th of each L, W, and H - This will also form 1*1*1 cube

Aren't we considering identical cuboids in such case? How are we eliminating identical ones when we take  6_C_2 ?

GMATBusters · Answer

You are right, there was a typo in the question, I have revised the same to avoid confusion. 
Thank you.

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A 5 × 5 × 5 cube is built using unit cu

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