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# Four extra-large sandwiches of exactly the same size were

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Manager
Joined: 10 Oct 2005
Posts: 113
Location: Hollywood
Four extra-large sandwiches of exactly the same size were  [#permalink]

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31 Jan 2007, 06:17
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Four extra-large sandwiches of exactly the same size were ordered for m students, where m > 4. Three of the sandwiches were evenly divided among the students. Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carol ate one piece from each of the four sandwiches, the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich?

(A) m+4/m(m-4)

(B) 2m-4/m(m-4)

(C) 4m-4/m(m-4)

(D) 4m-8/m(m-4)

(E) 4m-12/m(m-4)

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Director
Joined: 28 Dec 2005
Posts: 900
Re: Four extra-large sandwiches of exactly the same size were  [#permalink]

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31 Jan 2007, 06:25
1
3 sandwiches divided like this: 3/m
The last 1 sadwich divided like this: 1/(m-4)

If carol had one piece from each sandwich, that means she had (or at least I hope she did..):
(3/m+1/m-4) = 4m-12/m(m-4)
Senior Manager
Joined: 04 Jan 2006
Posts: 276
Re: Four extra-large sandwiches of exactly the same size were  [#permalink]

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31 Jan 2007, 07:09
TOUGH GUY wrote:
Four extra-large sandwiches of exactly the same size were ordered for m students, where m > 4. Three of the sandwiches were evenly divided among the students. Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carol ate one piece from each of the four sandwiches, the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich?

Good word problem!

There are total m students

Three of the sandwiches were evenly divided among the students
=> 3/m sandwich/student

4 students did not want any of the fourth sandwich
=> (m - 4) students still want the 4th sandwich (you greedy pigs!)

the 4th sandwich was evenly divided among the remaining students
=> 1/(m-4) sandwich/student

Carol got every piece that was divided (one of all the pigs from the group )
=> (3/m) + (1/(m-4))

the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich
=> [(3/m) + (1/(m-4)] / 1
=> (3*(m-4) + 1*m)/(m*(m-4))
=> (3m - 12 + m)/(m*(m-4)
=> (4m - 12)/m(m-4)

Director
Joined: 24 Aug 2006
Posts: 695
Location: Dallas, Texas
Re: Four extra-large sandwiches of exactly the same size were  [#permalink]

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02 Feb 2007, 00:25
Tough is a relative term but I think this one is really easy in absolute sense

3/m +1/(m-4)
=(3m-12+m)/m*(m-4)

(E)
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Re: Four extra-large sandwiches of exactly the same size were  [#permalink]

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02 Apr 2017, 09:51
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Re: Four extra-large sandwiches of exactly the same size were &nbs [#permalink] 02 Apr 2017, 09:51
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