Barney is forming two large cubes, A and B, with small identical cubes

Question

Fresh GMAT Club Tests' 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

M37-01

Archit3110 · Accepted Answer

only way to solve this question is by using plug in technique

given x-y=61
x=61+y
and value of x+y answer choices

put x+y= 189

we get 61+2y=189
y=64 and x=125
both x& y are perfect cube of 4 & 5 .
so sufficient IMO D

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 .

Answer: D

Bunuel · Answer

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

Bunuel · Answer

Par of  GMAT CLUB'S New Year's Quantitative Challenge Set

Chethan92 · Answer

Given x-y = 61.

Lets try out the options.

From 1) x+y = 64.
Then 2x = 125.
x has to be an integer. Hence 1 is wrong.

From 2) x+y = 125.
Then 2x = 186.
x = 93 and y = 32.
Since x and y are cubes. Using 93 smaller cubes, a bigger cube cannot be made. Hence option 2 is wrong.

Similarly checking the rest of the options. From 4, we get x = 125 and y = 64.

x = 125 = 5*5*5
y = 64 = 4*4*4.

Hence D is the correct option

Posted from my mobile device

exc4libur · Answer

If a large cube is made of small cubes, then the number of small cubes is the cube of a side of the large cube;
For instance: Large cube with side 2 can be made of 2^3=8 smaller cubes;

so x-y=61 is the difference between two perfect cubes;
perfect cubes:  ;
x=125, y=64, x-y=61… x+y=169

Ans (C)

kgmat12 · Answer

As the large cubes are made up of smaller cubes, the number of smaller cubes x and y must be one of these integers:
2^3 = 8
3^3 = 27
4^3 = 64
5^3 = 125
from here we see that x-y = 125-64 = 61 and x+y = 125+64 = 189.

Aks111 · Answer

In order to form a Cube the numbers x and y have to be perfect cubes.
Let  x = a^3  and  y = b^3 
Given  a^3 - b^3 = 61 
 (a-b) (a^2+ ab + b^2) = 61  
The above equation is a product of two integers and as 61 is a prime number we can conclude
 (a-b) = 1   i.e.  a = b+1  
and  (a^2+ ab + b^2) = 61  
Substituting a = b+1,
 (b+1)^2 + (b+1)*b + b^2 = 61 
 b^2 + 2b + 1 + b^2 + b + b^2 = 61 
 3b^2 + 3b + 1 = 61 
 b^2 + b - 20 = 0 
=> b = 4 or -5
Because b should be positive b = 4 and a = 5
  x= a^3 = 125   and  y = b^3 = 64

Therefore, x+y = 125+64 = 189

Answer: D 
Alternatively, substituting the answer choices is quicker.

bumpbot · Answer

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Barney is forming two large cubes, A and B, with small identical cubes

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