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 February 5th, 2013, 02:52 AM #1 Newbie   Joined: Feb 2013 Posts: 1 Thanks: 0 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
 February 5th, 2013, 05:56 AM #2 Member   Joined: Jan 2013 Posts: 93 Thanks: 0 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.)
 March 20th, 2013, 11:07 PM #3 Newbie   Joined: Mar 2013 Posts: 14 Thanks: 0 Re: A few math questions... Question 1 Answer is 27. Question 1 Answer is 1394.

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