Some Math Problems

Enough Thinking Done

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13 Replies - 991 Views - Last Post: 18 March 2009 - 10:37 AM

#1 trotski  Icon User is offline

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Some Math Problems

Posted 12 March 2009 - 12:41 AM

Please, this is not homework, help me out with them

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

??

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Replies To: Some Math Problems

#2 no2pencil  Icon User is online

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Re: Some Math Problems

Posted 12 March 2009 - 12:43 AM

If they are not homework, why are there multiple choices?
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#3 NeoTifa  Icon User is offline

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Re: Some Math Problems

Posted 12 March 2009 - 02:07 PM

And aren't they supposed to have like diagrams or something?
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#4 BigAnt  Icon User is offline

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Re: Some Math Problems

Posted 12 March 2009 - 03:23 PM

and why do you have ii instead of b?
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#5 mostyfriedman  Icon User is offline

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Re: Some Math Problems

Posted 12 March 2009 - 06:23 PM

these are all very easy problems...you can solve em with a bit of cleverness even if you suck at math
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#6 AdamSpeight2008  Icon User is offline

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Re: Some Math Problems

Posted 12 March 2009 - 06:40 PM

Like that the first question's answer can't odd.
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#7 atik97  Icon User is offline

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Re: Some Math Problems

Posted 12 March 2009 - 06:43 PM

>>> (10**2002+2)/(10**1001)
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000L
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#8 AdamSpeight2008  Icon User is offline

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Re: Some Math Problems

Posted 12 March 2009 - 07:03 PM

View Postshadhin, on 13 Mar, 2009 - 12:43 AM, said:

>>> (10 ^ 2002+2)/(10 ^ 1001)

The +2 makes the result have a fractional part.
Which is 1/(5 * 10^1000)

This post has been edited by AdamSpeight2008: 12 March 2009 - 07:15 PM

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#9 trotski  Icon User is offline

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Re: Some Math Problems

Posted 13 March 2009 - 03:29 AM

Has shadhin really used 2002 zeros? And I don't understand your and AdamSpeight2008 's response. What is the answer then? We can't just cancel out because the +2 is not with the power. it is being added with the 10 (power 2002.). I have used ii because B)/> was giving a smilie

And wat about the second question?
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#10 AdamSpeight2008  Icon User is offline

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Re: Some Math Problems

Posted 13 March 2009 - 04:06 AM

Why the answer can't be odd.

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

"You will not apply my precept," he said, shaking his head. "How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth? We know that he did not come through the door, the window, or the chimney. We also know that he could not have been concealed in the room, as there is no concealment possible. When, then, did he come?"
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

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#11 trotski  Icon User is offline

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Re: Some Math Problems

Posted 18 March 2009 - 03:30 AM

Ingenious AdamSpeight2008! Wonderful. And Thanks a lot.
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#12 trotski  Icon User is offline

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Re: Some Math Problems

Posted 18 March 2009 - 03:40 AM

Quote

O^E+E=E

Have to look into that one!

And where did he come from into the room? I haven't read The Sign of the Four!
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#13 AdamSpeight2008  Icon User is offline

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Re: Some Math Problems

Posted 18 March 2009 - 07:31 AM

View Posttrotski, on 18 Mar, 2009 - 09:40 AM, said:

Quote

O^E+E=E

Have to look into that one!

That was as test to see anyone reading & checking.:rolleyes:/>

Another Correction: E^E+O=O
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#14 trotski  Icon User is offline

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Re: Some Math Problems

Posted 18 March 2009 - 10:37 AM

Should I throw another question here or start a new post? What about my second question, i.e, that plane and line l, etc?
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