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Four extra-large sandwiches

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ska7945 Master | Next Rank: 500 Posts Default Avatar
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Four extra-large sandwiches

Post Mon Sep 08, 2008 5:23 pm
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?

1. m+4/m(m-4)
2. 2m-4/m(m-4)
3. 4m-4/m(m-4)
4. 4m-8/m(m-4)
5. 4m-12/m(m-4)

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Danny@GMATAcademy Junior | Next Rank: 30 Posts Default Avatar
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Post Tue Jul 05, 2016 5:19 pm
Two ways to solve this question:

Value Substitution: https://www.youtube.com/watch?v=L-fqOMzmglM

Algebra: https://www.youtube.com/watch?v=usxNJ89lAZs

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jiana90 Newbie | Next Rank: 10 Posts
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Post Sun Jan 22, 2017 11:38 am
Hi everyone, I searched online for a better explanation for this question. even though I understand it now, how can the gmat test makers expect from someone to think and answer these type of questions under 2 mints. I have been studying for 3 months now and whenever I face such questions i feel helpless but i really wanna do well in the exam, so if someone sees this please let me know how do you think and answer such tough questions under 2 mints.

thanks

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GMAT/MBA Expert

Post Fri Jan 27, 2017 9:57 am
ska7945 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)
We are given that four extra-large sandwiches of exactly the same size were ordered for m students and m > 4.

Three sandwiches were divided among all the students, so each student (including Carol) ate 3/m sandwiches.

Furthermore, since 4 students didn’t want the last (4th) sandwich, that sandwich was divided among m - 4 students. So each of the remaining m - 4 students (including Carol) had 1/(m-4) of the sandwich.

So, Carol ate:

3/m + 1/(m-4)

Getting a common denominator of m(m-4), we have:

3(m-4)/[m(m-4)] + m/[m(m-4)] = (3m - 12 + m)/[m(m-4)] = (4m - 12)/[m(m-4)]

Answer: E

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krutik Junior | Next Rank: 30 Posts Default Avatar
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Post Thu Sep 10, 2015 11:26 am
thanks a ton. You are the best Smile

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GMAT/MBA Expert

Post Thu Sep 10, 2015 9:09 am
ska7945 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?

1. m+4/m(m-4)
2. 2m-4/m(m-4)
3. 4m-4/m(m-4)
4. 4m-8/m(m-4)
5. 4m-12/m(m-4)
I received a PM requesting that I solve this problem.

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.

Each 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.

The correct answer is E.

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cramya Legendary Member Default Avatar
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Post Fri Oct 24, 2008 10:31 pm
Let x be the size of each sandwich

Carol ate x/m+x/m+x/m + x/m-4 (first 3 divided equally among m students and the 4th among m-4 students so each part would be x/m in the first 3 and x/m-4 for the 4th)

=3x/m + x/m-4

Fraction Carol ate per whole large sandwich(size x)

(3x/m + x/m-4 ) / x


(3x(m-4)+ mx / m(m-4) ) *1/x

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

x cancels out

4m-12/m(m-4) is the fraction she ate of a whole extra-large sandwich

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vishubn Legendary Member Default Avatar
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Post Fri Oct 24, 2008 8:35 pm
can any one elaborate on this more plzzzzzz

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just_do_it Senior | Next Rank: 100 Posts Default Avatar
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Post Mon Sep 08, 2008 5:35 pm
IMO E,

each of the 3 sandwiches is divided among m students. Each one gets 1/m
the 4th sandwich is divided among (m-4) studetns . each one gets 1/(m-4)

since carol ate parts of each of the 4 sandwiches, she would have eaten

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

hope this helps.

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