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Four extra-large sandwiches of exactly the same size were ordered for

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Re: Four extra-large sandwiches of exactly the same size were ordered for  [#permalink]

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New post 15 Jun 2018, 08:38
Hi all,

I don't mean to bump an old post but this leads me to think I am really over-thinking problems. I took the same approach as many of you, picking numbers, but I got lost in the question stem. I kept thinking "is Carol included in M? is she an outsider that eats them after they've been divided evenly among the M students?" This seems to be a common error I make. Any tips for getting over this?
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Re: Four extra-large sandwiches of exactly the same size were ordered for  [#permalink]

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New post 17 Jun 2018, 01:17
Bunuel 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?

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)]

Kudos for a correct solution.



Let X be the area of each sandwich.

Given 3 sandwiches are evenly divided among m students. Hence each student received one piece of area 3X/m

Now the 4th sandwich is refused by 4 students & is evenly divided among the rest of the students. Hence each of these students received a X/(m-4) area a piece of this sandwich.

Carol ate one piece from each sandwich, hence total area of sandwich consumed by carol = 3X/m + X/(m-4) = X(4m-12)/[m(m-4)]

Hence Carol ate (4m-12)/[m(m-4)] fraction of the extra large sandwich.

Answer E.


Thanks,
GyM
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Re: Four extra-large sandwiches of exactly the same size were ordered for  [#permalink]

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New post 17 Jun 2018, 03:13
Bunuel 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?

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)]

Let m=5, implying that there are 5 students.
Let each sandwich = 5 units, implying that 3 sandwiches = 3*5 = 15 units.

Since 3 sandwiches are distributed among all 5 students -- including Carol -- the number of units received by Carol from these 3 sandwiches = 15/5 = 3 units.

Since 4 of the 5 students do not share in the last sandwich, and Carol eats a portion of EVERY sandwich, all 5 units of the last sandwich must be given to Carol.
Thus, total units for Carol = 3+5 = 8 units.

Resulting fraction:
(Carol's units)/(units per sandwich) = 8/5. This is our target.
Now plug m=5 into the answer choices to see which yields our target of 8/5.

Every answer choice has the same denominator:
m(m-4) = 5(5-4) = 5.
To yield our target of 8/5, the correct answer choice must have a numerator of 8.
Only E works:
4m-12 = (4*5) - 12 = 8.


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Re: Four extra-large sandwiches of exactly the same size were ordered for  [#permalink]

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New post 27 Jun 2018, 10:53
I feel that this question could be best solved by substituting some value to m.
Let m = 12.

Scenario 1:
3 sandwiches --- 12 students
? --- 1 student
\(= \frac{3}{12} = \frac{1}{4}\)

Scenario 2:
1 sandwich --- 8 students
? --- 1 student
\(= \frac{1}{8}\)

\(Total : \frac{1}{4}+ \frac{1}{8} = \frac{3}{8}\)

When substituted m=12 in all of the options, only E gives the correct value.
E is the correct answer.
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Re: Four extra-large sandwiches of exactly the same size were ordered for &nbs [#permalink] 27 Jun 2018, 10:53

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