Each of 64 white 1-centimeter cubes will have exactly one

You almost got it right. Look at the explanation provided in my previous post. 64 is wrong. It should be 96 = 6 sides x (4*4).

Each of 64 white 1-centimeter cubes will have exactly one face painted blue. If these 64 cubes are joined together to form one large cube, as shown above, what is the greatest possible fraction of the surface area that could be blue?

The question said there are 64 cubes with 1 face painted blue, so the total number of faces painted blue would be 64 only.

nick1816 and TheNightKing, try this question adapted from OG Quant 2020. +1 Kudo to the question is appreciated

There are 64 cubes with 1 face painted------> Then we joined them together to form one large cube------> Whatever we do, the Max. painted sides cannot be greater than 64-------> It will be 56.


I still don't get your point.

The question did NOT ask what is the fraction of the "black" surface area that can be exposed in the larger, 4x4x4 cubes (which is 56 out of available 64 black sides).

The question rather asks what is the greatest possible fraction of the surface area of larger 4x4x4 cubes that COULD be black. So, there must sensically be a mixture of black and white faces in the surface of larger 4x4x4 cubes.

Ah! Correct. Now I get it. It has to be 56 out of 96.
7/12 is the answer.
Thanks.

I got this OG question correct but got your's wrong as usual.
https://gmatclub.com/forum/each-of-27-w ... l#p2266240

chondro48

You again came up with a spin-off of original question and the situation didn't change as far as your question is concerned. Why do you do so?

Greatest possible fraction confused me.

However, this time i solved the original with ease since it was easier.

Hi lnm87, glad that you solved the OG2020 version with ease . This question (4*4*4 cube) is the one that appeared in real test I took in 2018, but the color was red, not blue/black (I decided to change the color due to copyright issue). I was in the same boat like you at that time.

Comparing this question with the OG Quant Review 2020 version, you will find that both match word-to-word. I did so as to eliminate any ambiguity (as in the case of all my previous questions), for example: both precisely say `greatest possible fraction...'. Despite that, this question still somewhat confuses some people (including me in actual test).

Perhaps one possible cause is a subconscious tension of 'seemingly harder' calculation of 4*4*4 cube (3*3*3 cube seems much more humane to me than 4*4*4 cube) ?

Perhaps our current PS method (i.e. getting final answer precisely; plugging smart number to evaluate choice) may not deliver good time-efficiency for such case (with a mere increase/decrease in the cube dimensionality).

As for me (after reflection), I realised that the latter is the 60% factor while the former 40% one.

Given: Each of 64 white 1-centimeter cubes will have exactly one face painted black.

Asked: If these 64 cubes are joined together to form one large cube, as shown above, what is the greatest possible fraction of the surface area that could be black?

We will have 6 faces with 16 1 cm squares. Total 16*6 = 96 squares

For all 6 faces middle 2*2 squares may be painted black, total 4*6=24 squares

All 8 corners will have 8 squares painted black out of 24 squares.

Remaining squares (96-24-24=48) along the edges may be painted black on one side only = 24 squares more

Total maximum possible squares that may be painted black = 24+8+24= 56 squares

Greatest possible fraction of surface area that may be painted black = 56/96= 7/12

IMO D

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chondro48 please see the solution to your problem

Your question just amplified the calculations(mental) and thus tension.
I will put one question which got in my gmat.

number of the cubes in the core= (n-2)^3= (4-2)^3=8
Hence maximum fraction of surface that could be black= (64-8)/16*6= 56/96= 7/12