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Noob88


Member


Joined: 23 Nov 2005
Posts: 239

Posted: 09 Oct 2008 08:23:04 pm    Post subject:

Each day Chris is chided for not cleaning up his room, so he picks up approximately 10% of the
items on the floor in the morning. (He always rounds off to the nearest whole number if his
calculations result in a fraction.) However during the course of each day, 10 new items somehow
end up on the floor. If he has a clean floor on Sunday morning, how many items will be on the
floor by the end of the week on Saturday night?

a) 14 B) 42 c) 52 d) 63 e) None of these


Ok I worked this out like this
Sun morn: 0
Mon morn: 10
Tue morn: 19
Wed morn: 26
Thur Morn: 32
Fri Morn: 39
Sat morn: 44

Each of my friends is getting a different answer... none of us getting a, b, c, or d... Can anyone give me a for sure answer?


Last edited by Guest on 09 Oct 2008 08:23:17 pm; edited 1 time in total
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bananaman
Indestructible


Calc Guru


Joined: 12 Sep 2005
Posts: 1124

Posted: 09 Oct 2008 08:53:40 pm    Post subject:

The correct answer is 52. He cleans his room every morning and 10 items get added throughout the day. The breakdown looks like this...

Sun 0 -> 10
Mon 9 -> 19
Tues 17 -> 27
Wed 24 -> 34
Thurs 31 -> 41
Fri 37 -> 47
Sat 42 -> 52

There will be 52 items on his floor on Saturday in the evening.
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Weregoose
Authentic INTJ


Super Elite (Last Title)


Joined: 25 Nov 2004
Posts: 3976

Posted: 10 Oct 2008 04:02:57 am    Post subject:

0→nMin
0→u(nMin)
"10+round(.9u(n-1),0→u

u(n will return the number of items after the nth day. Plugging in u(7 yields 52.

This series has a limit – in precisely four weeks' time, he will have accumulated 96 items, at which point both his room and efforts will be in equilibrium with one another. Assuming he doesn't either pick up the slack or slack off. :P

C is the right answer. Smile


Last edited by Guest on 25 Jul 2010 05:15:00 am; edited 1 time in total
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MSR5


Newbie


Joined: 22 Jun 2008
Posts: 49

Posted: 15 Oct 2008 02:19:28 am    Post subject:

Wait, how is it possible to even get a clean floor on Sunday. Each day 10% of the mess in the morning is cleaned, so suppose there is 50 items not regarding the +10 items per day. The first day 5 items is picked up, the seconds day 4.5 rounded up, the third day 4.05 rounded down, etc. It is impossible to get the floor clean this way. I'm not very good at English so I probably missed something.
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Weregoose
Authentic INTJ


Super Elite (Last Title)


Joined: 25 Nov 2004
Posts: 3976

Posted: 15 Oct 2008 06:44:26 am    Post subject:

MSR5 wrote:
Wait, how is it possible to even get a clean floor on Sunday.  Each day 10% of the mess in the morning is cleaned, so suppose there is 50 items not regarding the +10 items per day. The first day 5 items is picked up, the seconds day 4.5 rounded up, the third day 4.05 rounded down, etc.  It is impossible to get the floor clean this way.  I'm not very good at English so I probably missed something.
You misread the problem starts us out with a clean floor and asks us how dirty it will become by the end of the time period. Wink
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DarkerLine
ceci n'est pas une |


Super Elite (Last Title)


Joined: 04 Nov 2003
Posts: 8328

Posted: 15 Oct 2008 08:05:00 am    Post subject:

It's possible to have a clean floor if there were -11 items on the floor the previous day. Wink
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darkstone knight


Advanced Member


Joined: 07 Sep 2008
Posts: 438

Posted: 15 Oct 2008 09:38:46 am    Post subject:

you "clean" 10% of the floor by adding more junk???

0x5
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Noob88


Member


Joined: 23 Nov 2005
Posts: 239

Posted: 15 Oct 2008 02:32:45 pm    Post subject:

Yeah it was a stupid problem... We were all just misinterpreting the wording. After seeing what you guys did the wording makes more sense to me, we just couldn't figure out precisely what the question was asking Neutral
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