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February 5th, 2013, 02:52 AM   #1
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A few math questions...

Hi! I was studying for my next olympiad, and came across these two question -

A cube is painted blue on all sides. It is then cut into 125 smaller equal cubes. How many cubes will be there in which no face is colored?

a) 27 b) 8 c) 16 d) 24

-------------------------------------------------------------------------------------and-------------------------------------------------------------------------------------

The smallest number which when divided by 20, 25, 35 and 40 and leaves a remainder of 14, 19, 29 and 34 respectively is -

a) 1394 b) 1404 c) 1664 d) 1406



Thank you for your time. Please answer with an explanation, so questions like these can use the same principle.

Warm regards,
Cadence
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February 5th, 2013, 05:56 AM   #2
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Re: A few math questions

First question. When you remove all the outer blocks of a 5󬊅 cube, you are left with a 3󫢫 cube.

Second question. Use inspection. Only one of the four given numbers is divisible by 20 when you subtract 14. Which is it? (NB: If you were not given choices for this question, you could use the Chinese-remainder theorem.)
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March 20th, 2013, 11:07 PM   #3
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Re: A few math questions...

Question 1 Answer is 27.
Question 1 Answer is 1394.
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