13 Replies  1041 Views  Last Post: 18 March 2009  10:37 AM
#1
Some Math Problems
Posted 12 March 2009  12:41 AM
The number 10^2002 + 2 is divisible by
a) 4
ii) 5
c) 6
d) 9
e) 10^1001
??
On a plane, figure F consists of 2002 points. Line l is a line of symetry of figure F. Exactly k points of figure F belong to line l. Which can not be the value of k?
a) 2002
ii) 0
c) 1001
d) 2000
e) 2
??
Replies To: Some Math Problems
#2
Re: Some Math Problems
Posted 12 March 2009  12:43 AM
#3
Re: Some Math Problems
Posted 12 March 2009  02:07 PM
#4
Re: Some Math Problems
Posted 12 March 2009  03:23 PM
#5
Re: Some Math Problems
Posted 12 March 2009  06:23 PM
#6
Re: Some Math Problems
Posted 12 March 2009  06:40 PM
#7
Re: Some Math Problems
Posted 12 March 2009  06:43 PM
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#8
Re: Some Math Problems
Posted 12 March 2009  07:03 PM
#9
Re: Some Math Problems
Posted 13 March 2009  03:29 AM
And wat about the second question?
#10
Re: Some Math Problems
Posted 13 March 2009  04:06 AM
O = Positive Odd Number
E = Positive Even Number
O^O+O=E
O^O+E=O
O^E+O=O
O^E+E=E
E^O+O=O
E^O+E=E
E^E+O=E
E^E+E=E
So we have the number;
10 ^ 2002 + 2 =? => E ^ E + E = E
Red Numbers ruled out
4
5
6
9
10^1001
Why it can't be 10^1001
The result of 10^2002 + 2 ends in the digit 2.
So imagine shift that number, 1001 decimals places the right.
After you done that the 2 is 1001 places to the right of the decimal point.
<Integer Part>.<Fractional Part>
Now the list is;
4
5
6
9
10^1001
Why can't it be 4
Dividing the number by 2, the result ends with a 1
Dividing this answer by 2 result in a fractional part of .5
Now the list is;
4
5
6
9
10^1001
Why it must be 6
If I may quote Sherlock Holmes
Quote
The Sign of the Four, ch. 6 (1890)
Sherlock Holmes in The Sign of the Four (Doubleday p. 111)
Explanation
Quick to see if a number is divisible by 3.
The sum of all the digits is a multiple of 3.
2000 x 0
1 x 1
1 x 2
0+1+2=3
3/3=1
Add any number that is both a multiple of 2 and 3, must also be a multiple of 6.
Not as hard as it first looks.
This post has been edited by AdamSpeight2008: 13 March 2009  04:10 AM
#11
Re: Some Math Problems
Posted 18 March 2009  03:30 AM
#12
Re: Some Math Problems
Posted 18 March 2009  03:40 AM
Quote
Have to look into that one!
And where did he come from into the room? I haven't read The Sign of the Four!
#13
Re: Some Math Problems
Posted 18 March 2009  07:31 AM
#14
Re: Some Math Problems
Posted 18 March 2009  10:37 AM
