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There are two cubes of different sizes. One of these is coloured red on all the faces, while other is coloured green on all the faces except one which is coloured red. The one which is red on all faces is cut into 27 equal cubes, while the other one is cut into 64 equal cubes which are mixed up with other cubes.

How many cubes are coloured red only on one face?
(a) 10
(b) 16
(c) 20
(d) 22


The answer is given as (b) i.e. 16.

But, when I tried I got it as
cube I :
6 cubes with only one red face
cube II:
4 cubes with only one red face
8 cubes with one red and one green face
4 cubes with one red faceand two green faces

So, it should be either 22 (if I take it as "How many cubes are coloured red, only on one face?") or 10 (if I take it as "How many cubes are coloured red only, on one face?")

So can you tell me whether the answer in the book is correct, or the answer I got (which one? first or second?) is correct?

Help me !! I am having exam tomorrow!

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I think that from your interpretations, your answers are right. I would say 22. I don't get why the problem says: "which are mixed up with other cubes." ¿Why is that relevant? –  MyUserIsThis Feb 14 '13 at 14:15
    
Agree, the answer is 22 to me too. I still don't get what is meant by which are mixed up with other cubes though –  AndreasT Feb 14 '13 at 14:19
    
I also am confused. Please ignore it –  chndn Feb 14 '13 at 14:22
    
I think Ross Millikan is correct –  chndn Feb 14 '13 at 14:29
1  
I guess the "which are mixed..." is just to mix up matters ;-) –  vonbrand Feb 14 '13 at 15:15
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1 Answer

I agree with your logic and can read the question either way to get 10 or 22. I think the mixed up with the other cubes is just supposed to tell you to count small cubes from both big cubes, which you are doing.

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So the answer is 10 or 22? –  chndn Feb 14 '13 at 14:27
2  
@chndn: I don't think the question is clearly written. Your logic resulting in each of 10 and 22 is correct. I think I would go with 22, but without conviction. –  Ross Millikan Feb 14 '13 at 14:31
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