A certain cube is composed of 1000 smaller cubes, arranged 1

Question

A certain cube is composed of 1000 smaller cubes, arranged 10 by 10 by 10. The top layer of cubes is removed from a face, then from the adjacent face above it, then from the adjacent face to the right of the first. The process is repeated on the same three faces in reverse order. Finally, a last layer is taken from the first face. How many smaller cubes have been removed from the larger cube?

(A) 488
(B) 552
(C) 612
(D) 722
(E) 900

(A) 488
(B) 552 
(C) 612 
(D) 722 
(E) 900

Bunuel · Accepted Answer

{width}*{length}*{height} = 10*10*10.

The top layer of cubes is removed from a face, we get 10*9*10;
Then from the adjacent face above it, we get 10*9*9
Then from the adjacent face to the right of the first, we get 9*9*9.

The process is repeated on the same three faces in reverse order, we get 8*8*8.

Finally, a last layer is taken from the first face, we get 8*7*8=448.

{# of removed cubes} = {original} - {final} = 1,000 - 448 = 552.

Answer: B.

Hope it's clear.

anairamitch1804 · Answer

We can answer this by keeping track of how many cubes are lopped off of each side as the cube is trimmed (10 x 10 + 10 x 9 + 9 x 9 + ...), but this approach is tedious and error prone. A more efficient method is to determine the final dimensions of the trimmed cube, then find the difference between the dimensions of the trimmed and original cubes.

Let's call the first face A, second face B, and third face C. By the end of the operation, we will have removed 2 layers each from faces B and C, and 3 layers from face A. So B now is 8 cubes long, C is 8 cubes long, and A is 7 cubes long. The resulting solid has dimensions 8 x 8 x 7 cubes or 448 cubes. We began with 1000 cubes, so 1000 - 448 = 552. Thus, 552 cubes have been removed.

The correct answer is B

WillEconomistGMAT · Answer

Hint: Once you see what's happening with the first few operations, this might be a good candidate for ballparking.

WholeLottaLove · Answer

Are there any more problems similar to this to practice? I got the steps right but it took me a loooooooong time.

And why does 7x8x8 represent the number of cubes removed? Isn't that the number of cubes remaining of the larger cube?

Never mind, I got it - I misread the question.

MarkusKarl · Answer

The cube that remains is 7*8*8 (we took three layers from one side, and two from the other two sides, order does not matter)
(10-3)(10-2)(10-)2=7*8*8=448
1000-448=552

Posted from my mobile device

JimminyCricket · Answer

I rushed it, it's definitely easier to do it the way mentioned above. I removed them and slowly added them to one another, wasted time doing so.

disenapati · Answer

Understanding this question itself will take around 2 mins, plus 30-40 sec for solving, shall these be attempted or should be guessed and moved over in real test scenarios ?

kornn · Answer

Dear IanStewart , I completely cannot understand what the question is saying. I'm lost

This may not be a great question, but could you please explain how do we know which side that the question is referring to?

IanStewart · Answer

I don't know the source, but it's clearly not an official problem. It's not worded the way an official question would be. For one thing, it assumes an abstract cube has some particular orientation (when it takes about the face "to the right" of another), which is not the case - there are four faces "to the right" of another face depending how you look at a cube. There's no value in expending effort decoding the wording of questions that aren't written the way official questions are written.

Nikhil30 · Answer

i got your point 10*10*10.
as width , but every face is a square that means 100=10*10*10.
but if you remove top face its equivalent to removing top square isnt it which is 100??
thus didnt undertsand 10*10*9?

Pratham_Patil24 · Answer

Would these type of questions be tested on focus edition, given geometry is no more tested?

Bunuel · Answer

The wording itself is not very GMAT-like; however, the question does not involve specialized geometry knowledge, so something like this, with better wording, could still be tested.

P.S. Check these two topics:
 
  GMAT Syllabus for Focus Edition  
  Geometry Tested on GMAT Focus?

While specific geometry knowledge is not tested on GMAT Focus, not everything involving shapes, volumes, or areas requires specialized geometry knowledge. The area of a square or rectangle, the volume of a cube or rectangular solid, and the Pythagorean theorem are not considered specific geometry knowledge by the GMAT and can still be tested. Moreover, a question can involve shapes but test another area, such as combinations or other topics. There are several  questions involving these concepts in the GMAT Prep Focus mocks .

The chapter on coordinate geometry, including planes and slopes, is still present in the recent Official Guides. That said, it is tested to a much smaller extent. For example, you might see some questions involving graphs, either in Problem Solving or in Data Insights graph-based questions. However, those usually fall under the functions category rather than pure coordinate geometry, so they typically won’t involve distance calculations, angles, or similar topics.

A certain cube is composed of 1000 smaller cubes, arranged 1

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