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For the 64 cubes in the figure above, there is an 8 on each of the fac

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Bunuel
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For the 64 cubes in the figure above, there is an 8 on each of the fac [#permalink] New post   22 May 2020, 10:58
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For the 64 cubes in the figure above, there is an 8 on each of the faces not shown. If horizontal layer L is rotated 90° so that its front appears on the left side of the figure and then vertical layer R is rotated 90° so that its top appears on the front of the figure, the sum of the numbers on the front of the figure will be

A. 86
B. 93
C. 97
D. 103
E. 106


PS20401



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E
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NitishJain
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Re: For the 64 cubes in the figure above, there is an 8 on each of the fac [#permalink] New post   24 May 2020, 00:47
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E?

After two rotations: the front would be like:
6 6 7 6
8 8 7 8
6 6 7 6
6 6 7 6

There are 9 6's = 54
There are 4 7's = 28
There are 3 8's = 24
Sum: 106
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Re: For the 64 cubes in the figure above, there is an 8 on each of the fac [#permalink] New post   22 May 2020, 11:17
First turn, sum of front face= 8x4 + 6x12 = 104
Second turn, sum of front face= 104- (8x1 + 6x3) + (7x4)

= 104-26+28= 106

Ans E

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Re: For the 64 cubes in the figure above, there is an 8 on each of the fac [#permalink] New post   22 May 2020, 19:22
visualise a cube and solve ; :)

after the rotation of the cube layer L to 90* horizontal and R to 90* vertical the front face will now be
{6*(9)} + {7*3+8} + {5*3+ 8} = 54+ 29+23 ; 106
OPTION E


Bunuel wrote:

For the 64 cubes in the figure above, there is an 8 on each of the faces not shown. If horizontal layer L is rotated 90° so that its front appears on the left side of the figure and then vertical layer R is rotated 90° so that its top appears on the front of the figure, the sum of the numbers on the front of the figure will be

A. 86
B. 93
C. 97
D. 103
E. 106


PS20401



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1.png
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Re: For the 64 cubes in the figure above, there is an 8 on each of the fac [#permalink] New post   24 May 2020, 01:08
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Bunuel wrote:

For the 64 cubes in the figure above, there is an 8 on each of the faces not shown. If horizontal layer L is rotated 90° so that its front appears on the left side of the figure and then vertical layer R is rotated 90° so that its top appears on the front of the figure, the sum of the numbers on the front of the figure will be

A. 86
B. 93
C. 97
D. 103
E. 106


PS20401
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Attachment:
The attachment 1.png is no longer available


Shortest explanation



Current Sum of numbers on front face = 16*6 = 96 (16 squaares with 6 on each square)

The figure after L is rotated 90º


The figure after R is rotated 90º


The total Increase in sum = 3*2+4*1 = 10

4*1 for four 6 becoming 7 increasing the sum by 1 at each place
3*2 for three 6 becoming 8 increasing the sum by 2 at each place

i.e. New Sum = 96+10 = 106

Answer: Option E
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Screenshot 2020-05-24 at 1.32.58 PM.png
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Re: For the 64 cubes in the figure above, there is an 8 on each of the fac [#permalink] New post   28 Nov 2020, 13:57
Bunuel wrote:

For the 64 cubes in the figure above, there is an 8 on each of the faces not shown. If horizontal layer L is rotated 90° so that its front appears on the left side of the figure and then vertical layer R is rotated 90° so that its top appears on the front of the figure, the sum of the numbers on the front of the figure will be

A. 86
B. 93
C. 97
D. 103
E. 106


PS20401

Show Spoiler
Attachment:
1.png


After the first rotation we have:

6 6 6 6
8 8 8 8
6 6 6 6
6 6 6 6

After the second rotation we have:

6 6 7 6
8 8 7 8
6 6 7 6
6 6 7 6

Total = 106.

Answer = E.
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Re: For the 64 cubes in the figure above, there is an 8 on each of the fac [#permalink] New post   27 Feb 2023, 17:59
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Re: For the 64 cubes in the figure above, there is an 8 on each of the fac [#permalink]
27 Feb 2023, 17:59
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