M37-01

Question

Barney is forming two large cubes, A and B, with small identical cubes. He used  x  small cubes to form cube A and  y  small cubes to form cube B. If  x - y = 61 , then what is the value of  x + y ?

A.  64 
B.  125 
C.  169 
D.  189 
E.  216

Bunuel · Accepted Answer

To form a larger cube using small identical cubes, you need an n by n by n arrangement. So if the number of small cubes used is x, then x = n^3 for some integer n. That’s why x and y must be perfect cubes. You can’t form a cube with, say, 10 unit cubes, only numbers like 1, 8, 27, 64, etc. (which are perfect cubes).

Bunuel · Answer

Official Solution:

Barney is forming two large cubes, A and B, with small identical cubes. He used  x  small cubes to form cube A and  y  small cubes to form cube B. If  x - y = 61 , then what is the value of  x + y ?

A.  64 
B.  125 
C.  169 
D.  189 
E.  216

Notice that since large cubes are made from small identical cubes, then both  x  and  y  must be perfect cubes (a perfect cube is a cube of an integer). So,  x  and  y  can be: 1, 8, 27, 64, 125, 216, ... 
 
We are given that  x-y=61 , so  x  and  y  are 125 and 64, respectively.
 
Thus,  x+y=189 .
 
Note that while this question uses basic knowledge of lines and figures, it is actually not a Geometry question. There are 8 questions within GMAT Prep Focus Edition that use similar principles.  Here is one example .

Answer: D

miag · Answer

Hi  Bunuel , sorry but how did you infer that x, and y must be perfect cubes - didnt connect the two while solving? thank you!

avellanjc · Answer

Bunuel ,  Bunuel ,

Couldnt there be an extra variable between your x and your n in x = n^3

I mean could it be x=p n^3

or does n takes care of everything ( each individual smaller side* number of smaller cubes) and this must be a cube itself?

Regards,

Juan C. Avellan

Bunuel · Answer

No, x itself must be a perfect cube. If the big cube is n by n by n, then the total number of small cubes is exactly n^3. So x = n^3, nothing extra.

Usernamevisible · Answer

Is this not a geometry problem which is not part of GMAT FOCUS, there were 2-3 questions on geometry in mock and it ruined the experience.

Other question in the same mock

https://gmatclub.com/forum/m23-184334.html
https://gmatclub.com/forum/m47-456878.html

bb Bunuel - please look into this

Bunuel · Answer

No.

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.

M37-01

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