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# Four big sandwiches are divided among m students (m>4).

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Four big sandwiches are divided among m students (m>4). [#permalink]  24 Nov 2005, 01:16
Four big sandwiches are divided among m students (m>4). First three are divided among m and the last one divided among (m-4). 4 of the students are full and want none of sandwiches and one of them likes the taste of the sandwich very much and eats a piece of all four sandwiches. What portion of the four sandwiches did he eat?

A. (m-4)/(m(m-4))
B. (4m-4)/(m(m-4))
C. (m-3)/(m(m-4))
D. (m-8)/(m(m-4))
E. (4m-12)/(m(m-4))
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Four big sandwiches are divided among m students (m>4). First three are divided among m and the last one divided among (m-4). 4 of the students are full and want none of sandwiches and one of them likes the taste of the sandwich very much and eats a piece of all four sandwiches. What portion of the four sandwiches did he eat?

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

***********************************************

There are 4 sandwiches.

3 sandwiches are divided by m pieces, and one piece is 3/m.
1 sandwich is divided by (m-4) pieces, and one piece is 1/(m-4).

One student eats a piece of all FOUR sandwiches.

Therefore, he eats total of 4 pieces !

If so, the OA should be 3 * (3/m) + 1 * ( 1/(m-4) ) !

At what point am I mistaken here?
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i am clueless here.
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Re: Sandwiches [#permalink]  24 Nov 2005, 02:55
getzgetzu wrote:
Four big sandwiches are divided among m students (m>4). First three are divided among m and the last one divided among (m-4). 4 of the students are full and want none of sandwiches and one of them likes the taste of the sandwich very much and eats a piece of all four sandwiches. What portion of the four sandwiches did he eat?

A. (m-4)/(m(m-4))
B. (4m-4)/(m(m-4))
C. (m-3)/(m(m-4))
D. (m-8)/(m(m-4))
E. (4m-12)/(m(m-4))

uhm, really this question is not clear at all
I understand this way : since the one who eats a piece of 4 sandwiches---> he must eat 3 pieces of the 3 sandwiches divided among m(call it sandwich A) and 1 piece of the sandwich divided among m-4( call this sandwhich B)
each piece of sandwich A is 1/m
each piece of sandwich B is 1/(m-4)
since the person eats 3 pieces of A and 1 piece of B, the portion he eats is : 3*1/m - 1/(m-4) = (4m-12)/[m(m-4)]
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Re: Sandwiches [#permalink]  24 Nov 2005, 03:10
laxieqv wrote:
getzgetzu wrote:
Four big sandwiches are divided among m students (m>4). First three are divided among m and the last one divided among (m-4). 4 of the students are full and want none of sandwiches and one of them likes the taste of the sandwich very much and eats a piece of all four sandwiches. What portion of the four sandwiches did he eat?

A. (m-4)/(m(m-4))
B. (4m-4)/(m(m-4))
C. (m-3)/(m(m-4))
D. (m-8)/(m(m-4))
E. (4m-12)/(m(m-4))

uhm, really this question is not clear at all
I understand this way : since the one who eats a piece of 4 sandwiches---> he must eat 3 pieces of the 3 sandwiches divided among m(call it sandwich A) and 1 piece of the sandwich divided among m-4( call this sandwhich B)
each piece of sandwich A is 1/m
each piece of sandwich B is 1/(m-4)
since the person eats 3 pieces of A and 1 piece of B, the portion he eats is : 3*1/m - 1/(m-4) = (4m-12)/[m(m-4)]

3 sandwiches are divided by m pieces, and so one piece is 3/m.
As one piece is 3/m, three pieces are 9/m.

Or...?
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Re: Sandwiches [#permalink]  24 Nov 2005, 05:35
gamjatang wrote:
laxieqv wrote:
getzgetzu wrote:
Four big sandwiches are divided among m students (m>4). First three are divided among m and the last one divided among (m-4). 4 of the students are full and want none of sandwiches and one of them likes the taste of the sandwich very much and eats a piece of all four sandwiches. What portion of the four sandwiches did he eat?

A. (m-4)/(m(m-4))
B. (4m-4)/(m(m-4))
C. (m-3)/(m(m-4))
D. (m-8)/(m(m-4))
E. (4m-12)/(m(m-4))

uhm, really this question is not clear at all
I understand this way : since the one who eats a piece of 4 sandwiches---> he must eat 3 pieces of the 3 sandwiches divided among m(call it sandwich A) and 1 piece of the sandwich divided among m-4( call this sandwhich B)
each piece of sandwich A is 1/m
each piece of sandwich B is 1/(m-4)
since the person eats 3 pieces of A and 1 piece of B, the portion he eats is : 3*1/m - 1/(m-4) = (4m-12)/[m(m-4)]

3 sandwiches are divided by m pieces, and so one piece is 3/m.
As one piece is 3/m, three pieces are 9/m.

Or...?

each sandwich is divided into m pieces...3 sandwich we have 3/m pieces.
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Re: Sandwiches [#permalink]  24 Nov 2005, 05:44
laxieqv wrote:
gamjatang wrote:
laxieqv wrote:
getzgetzu wrote:
Four big sandwiches are divided among m students (m>4). First three are divided among m and the last one divided among (m-4). 4 of the students are full and want none of sandwiches and one of them likes the taste of the sandwich very much and eats a piece of all four sandwiches. What portion of the four sandwiches did he eat?

A. (m-4)/(m(m-4))
B. (4m-4)/(m(m-4))
C. (m-3)/(m(m-4))
D. (m-8)/(m(m-4))
E. (4m-12)/(m(m-4))

uhm, really this question is not clear at all
I understand this way : since the one who eats a piece of 4 sandwiches---> he must eat 3 pieces of the 3 sandwiches divided among m(call it sandwich A) and 1 piece of the sandwich divided among m-4( call this sandwhich B)
each piece of sandwich A is 1/m
each piece of sandwich B is 1/(m-4)
since the person eats 3 pieces of A and 1 piece of B, the portion he eats is : 3*1/m - 1/(m-4) = (4m-12)/[m(m-4)]

3 sandwiches are divided by m pieces, and so one piece is 3/m.
As one piece is 3/m, three pieces are 9/m.

Or...?

each sandwich is divided into m pieces...3 sandwich we have 3/m pieces.

First three are divided among m.

Not that each of the first three is divided among m.

...
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uhm, we can understand in the two ways ....IMO, since four sandwiches have 4 different tastes ( that's why that person want to taste a piece of all 4 sandwiches) ..so the sandwiches should be divided one by one ...so that everyone has the same amount of a certain kind of sandwich .....Anyway, this problem is very obscure.
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