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Math Expert V
Joined: 02 Sep 2009
Posts: 59587
Barney is forming two large cubes, A and B, with small identical cubes  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 64% (02:29) correct 36% (02:38) wrong based on 72 sessions

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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

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 59587
Re: Barney is forming two large cubes, A and B, with small identical cubes  [#permalink]

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Bunuel wrote:

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

Check other 3-D Geometry Questions in our Special Questions Directory.
_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 59587
Re: Barney is forming two large cubes, A and B, with small identical cubes  [#permalink]

### Show Tags

Bunuel wrote:

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

_________________
NUS School Moderator V
Joined: 18 Jul 2018
Posts: 1024
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: Barney is forming two large cubes, A and B, with small identical cubes  [#permalink]

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1
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

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GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5428
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Barney is forming two large cubes, A and B, with small identical cubes  [#permalink]

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1
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 wrote:

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
Director  P
Joined: 24 Nov 2016
Posts: 926
Location: United States
Re: Barney is forming two large cubes, A and B, with small identical cubes  [#permalink]

### Show Tags

Bunuel wrote:

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

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: [1,8,27,64,125,216,343…];
x=125, y=64, x-y=61… x+y=169

Ans (C) Re: Barney is forming two large cubes, A and B, with small identical cubes   [#permalink] 08 Nov 2019, 08:32
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