GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 04 Aug 2020, 04:02 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Four extra-large sandwiches of exactly the same size were ordered for

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 65785
Four extra-large sandwiches of exactly the same size were ordered for  [#permalink]

### Show Tags

15
127 00:00

Difficulty:   55% (hard)

Question Stats: 73% (02:47) correct 27% (02:52) wrong based on 1924 sessions

### HideShow timer Statistics

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.

_________________
GMAT Club Legend  V
Status: GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator l A learner forever :)
Joined: 08 Jul 2010
Posts: 4512
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Re: Four extra-large sandwiches of exactly the same size were ordered for  [#permalink]

### Show Tags

14
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)]

Kudos for a correct solution.

Three of the sandwiches were evenly divided among the students
i.e. Amount of Sandwiches with each students = 3/m

Amount of 4th Sandwich with remaining (m-4) students = 1/(m-4)

The amount of Sandwich that carol ate = 3/m + 1/(m-4) = (3m-12+m)/[m(m-4)] = (4m-12)/[m(m-4)]

_________________
Prepare with PERFECTION to claim Q≥50 and V≥40 !!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
One-on-One Skype classes l Classroom Coaching l On-demand Quant course l Admissions Consulting

Most affordable l Comprehensive l 2000+ Qn ALL with Video explanations l LINK: Courses and Pricing
Our SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
FREE GMAT Resource: 22 FREE (FULL LENGTH) GMAT CATs LINKS l NEW OG QUANT 50 Qn+VIDEO Sol.
Manager  B
Joined: 25 Jun 2016
Posts: 60
GMAT 1: 780 Q51 V46
Four extra-large sandwiches of exactly the same size were ordered for  [#permalink]

### Show Tags

27
6
Yep, picking numbers works nicely here. Here's a video that goes over a value substitution solution for this question:

Algebra also works well:

Originally posted by GMATAcademy on 06 Jul 2016, 05:38.
Last edited by GMATAcademy on 06 Jul 2016, 06:13, edited 1 time in total.
##### General Discussion
Verbal Forum Moderator V
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2445
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
Re: Four extra-large sandwiches of exactly the same size were ordered for  [#permalink]

### Show Tags

1
Since first three sandwiches were equally divided among m students , Carol ate = 3/m
Fourth sandwhich was divided equally among m-4 students , carol ate = 1/(m-4)
Amount of sandwhich Carol ate = 3/ m + 1/(m-4) = 4m-12/m(m-4)

_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
Retired Moderator Joined: 29 Apr 2015
Posts: 748
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
Four extra-large sandwiches of exactly the same size were ordered for  [#permalink]

### Show Tags

4
1
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.

I feel most comfortable to plug in a number for m since the question does allow so.

We have 4 sandwiches to share among m students. m>4. Let m = 6.

3 of the 4 sandwiches are shared equally among 6 students. Therefore we have 3/4 of the 4 sandwiches to share among 6. $$\frac{3}{4}$$/6 = $$\frac{1}{8}$$. So we know that one piece is 1/8 of the 4 sandwiches.

Finally, the fourth sandwich is divided among the remaining students. In our case this will be 2 students. We have $$\frac{1}{4}$$/2 = $$\frac{1}{8}$$

Now hungry Carol eats from each one piece. Hence she eats 1/4 of the 4 sandwiches which is a whole sandwich (1 = Target Value) in total.

Plug in 6 in the equations below. Answer D will provide you with a 1 as a result.
Intern  Joined: 29 Mar 2015
Posts: 19
Re: Four extra-large sandwiches of exactly the same size were ordered for  [#permalink]

### Show Tags

6
Let's assume $$m=10$$

Then Carol ate

$$\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{6}=\frac{28}{60}$$ of the sandwhich.

The nominator needs to equal 28 when 10 is plugged in for m. Obviously, only E satisfies the condition.
Intern  Joined: 23 Jun 2014
Posts: 13
Re: Four extra-large sandwiches of exactly the same size were ordered for  [#permalink]

### Show Tags

reto wrote:
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.

I feel most comfortable to plug in a number for m since the question does allow so.

We have 4 sandwiches to share among m students. m>4. Let m = 6.

3 of the 4 sandwiches are shared equally among 6 students. Therefore we have 3/4 of the 4 sandwiches to share among 6. $$\frac{3}{4}$$/6 = $$\frac{1}{8}$$. So we know that one piece is 1/8 of the 4 sandwiches.

Finally, the fourth sandwich is divided among the remaining students. In our case this will be 2 students. We have $$\frac{1}{4}$$/2 = $$\frac{1}{8}$$

Now hungry Carol eats from each one piece. Hence she eats 1/4 of the 4 sandwiches which is a whole sandwich (1 = Target Value) in total.

Plug in 6 in the equations below. Answer D will provide you with a 1 as a result.

I think you are having some mistakes here.
First of all, the first 3 sandwiches are shared equally among 6 students. So each one will eat: 3/6 = 0.5 (sandwich)
Then 4 students do not eat the fourth one, so there are only two members eating including Carol so carol will eat: 1/2 = 0.5 (sandwich)
So totally, Carol will eat exactly 1 sandwich, using m = 6, the answer must be E where as your answer D will be that Carol eats 4/3 sandwich (not correct)
Using m as a variable or using a particular figure, the answer still must be E.
Retired Moderator Joined: 29 Oct 2013
Posts: 245
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Four extra-large sandwiches of exactly the same size were ordered for  [#permalink]

### Show Tags

1
the moment I see the answer choices ‘all variables’ I know I can plug in numbers

Let m=6 so a pie eaten by Carol from 3 sandwiches is 3/6= ½
A pie eaten by Carol from the fourth sandwich = ½
So she had 1 whole sandwich
M(m-4)= 6*2=12 so we want 12 in the numerator only E gives the numerator of 12 as (4m-12)=(4*6-12)=12
Ans E
_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876
Intern  B
Joined: 16 Dec 2013
Posts: 32
Location: United States
GPA: 3.7
Re: Four extra-large sandwiches of exactly the same size were ordered for  [#permalink]

### Show Tags

[quote="NoHalfMeasures"]the moment I see the answer choices ‘all variables’ I know I can plug in numbers

Let m=6 so a pie eaten by Carol from 3 sandwiches is 3/6= ½
A pie eaten by Carol from the fourth sandwich = ½
So she had 1 whole sandwich
M(m-4)= 6*2=12 so we want 12 in the numerator only E gives the numerator of 12 as (4m-12)=(4*6-12)=12
Ans E[/quote

I have a question here... Here's my calculation. Please let me know what I'm doing wrong.

Let m=6. so each of the student gets 3/6 or 1/2 of the sandwich.
4th sandwich is shared by only 2 students equaling 1/2 sandwich each.
Carol's bite from sandwiches is (1/2)*3+1/4=2.

Where am i going wrong?
Manager  Joined: 29 Nov 2011
Posts: 87
Re: Four extra-large sandwiches of exactly the same size were ordered for  [#permalink]

### Show Tags

Flexxice 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)]

I get what I have to do and more or less know how to do it, but in the solution, the OG makes a really weird calculation. Unfortunately, this weird step is needed and I hope someone can explain this step to me. Carol ate [/m] of the first three sandwiches and [/m - 4] of the last sandwich. Thus, I have to add both fractions. The following is the OG's way:

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

I have no idea what has been done in the second step. Could someone please explain this to me? The rest is clear.

it took me some time to understand the solution,but can help you little bit.

there are 4 sandwiches and no of students m , whatever the value may be.

3 sandwiches divided amount student each will get 3/m part.
now the 4th sandwich is divided amount m-4 student because 4 student dont want to eat now no of students pending is m-4

carol is among those student who was in both groups
so first group got 3/m + second grp got 1/m-4 , becauase only 1 sanwich is left to divide among m-4 students
Board of Directors P
Joined: 17 Jul 2014
Posts: 2420
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
WE: General Management (Transportation)
Re: Four extra-large sandwiches of exactly the same size were ordered for  [#permalink]

### Show Tags

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)]

i put m=6.
3 sandwiches were divided among 6 people. thus, each ate half.
last one - 4 refused, and 2 ate half of the fourth.
so last 2 ate in total 1 "whole" (by size) sandwich

since we have same denominator, we must find a value for numerator to be equal with it.
m(m-4)=6*2=12. so numerator must be 12.
only E works.
Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2800
Re: Four extra-large sandwiches of exactly the same size were ordered for  [#permalink]

### Show Tags

1
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.

We are originally given that 4 sandwiches were ordered and that 3 of those sandwiches were divided by m students. Thus, each student had 3/m sandwiches.

However, since 4 students did not want any of the 4th sandwich, the 4th sandwich was actually divided amongst the remaining students, or m – 4 students. Thus, each of the remaining students received 1/(m-4) sandwiches.

We are given that Carol actually ate one piece from each of the four sandwiches. Thus, Carol ate:

3/m + 1/(m- 4)

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

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

Since a whole sandwich is equal to 1, Carol had (4m-12)/[m(m-4)] of a full sandwich.

_________________

# Jeffrey Miller | Head of GMAT Instruction | Jeff@TargetTestPrep.com

250 REVIEWS

5-STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE

NOW WITH GMAT VERBAL (BETA)

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

SVP  B
Joined: 06 Nov 2014
Posts: 1856
Re: Four extra-large sandwiches of exactly the same size were ordered for  [#permalink]

### Show Tags

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.

3 sandwiches divided among m students.
Hence each student gets 3/m sandwiches

For the last one, 4 students do not want to eat, hence remaining students = m - 4
Each student gets 1/ (m-4) sandwiches

Total sandwiches eaten by Carol = 3/m + 1/(m-4) = 3m - 12 + m / m(m-4) = 4m-12/m(m-4)

Correct Option: E
Manager  S
Joined: 03 Jan 2017
Posts: 131
Re: Four extra-large sandwiches of exactly the same size were ordered for  [#permalink]

### Show Tags

took me a little longer because of tuff wording:
smart numbers technique
let's 6 be the total number of students
students ordered 4 sandwiches, 3 ones were divideded between 6 students, each got 3/6
then the left sandwich were divided between 2 (6-4) students. hence 1/2 got each student

that chick Carol ate one piece in each party: 3/6+1/2=1
question asks what was her fraction of a sandwich: 1/1=1

Let's put 6 in each answer choice and test

E is one that works
Intern  B
Joined: 03 Jul 2016
Posts: 30
Re: Four extra-large sandwiches of exactly the same size were ordered for  [#permalink]

### Show Tags

JeffTargetTestPrep wrote:
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.

We are originally given that 4 sandwiches were ordered and that 3 of those sandwiches were divided by m students. Thus, each student had 3/m sandwiches.

However, since 4 students did not want any of the 4th sandwich, the 4th sandwich was actually divided amongst the remaining students, or m – 4 students. Thus, each of the remaining students received 1/(m-4) sandwiches.

We are given that Carol actually ate one piece from each of the four sandwiches. Thus, Carol ate:

3/m + 1/(m- 4)

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

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

Since a whole sandwich is equal to 1, Carol had (4m-12)/[m(m-4)] of a full sandwich.

can you please explain, all the students would have had 4m-12/(m(m-4)) pieces except 4 students who refused?
because if each student gets 3/m portion - it is similar to 1/m + 1/m + 1/m
am i right?
Marshall & McDonough Moderator D
Joined: 13 Apr 2015
Posts: 1664
Location: India
Re: Four extra-large sandwiches of exactly the same size were ordered for  [#permalink]

### Show Tags

Avinash_R1 wrote:

can you please explain, all the students would have had 4m-12/(m(m-4)) pieces except 4 students who refused?
because if each student gets 3/m portion - it is similar to 1/m + 1/m + 1/m
am i right?

Hi,

I think you haven't understood the question correctly. Since Carol ate a piece from all the 4 cakes she belongs to the category of people who did not refuse to eat the 4th cake.

In the first 3 cakes she could eat 3/m
In the 4th cake she ate 1/(m - 4)
Current Student B
Joined: 25 Feb 2017
Posts: 34
Location: Korea, Republic of
Schools: LBS '19 (A)
GMAT 1: 720 Q50 V38
GPA: 3.67
Re: Four extra-large sandwiches of exactly the same size were ordered for  [#permalink]

### Show Tags

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)]

This is my 2 cents.
I plugged m = 12
Then, 3 breads / 12 equally gives = 1/4
As 4 didn't want anymore, 1 bread / 8 gives = 1/8
So, Carol ate (1/4) + (1/8) = 3/8.
(3/8) of bread divide by 4 breads gives = 3/24 <--this is the fraction of the bread Carol ate.

What this means is that the numerator needs to be a factor of 3.
Only E is --> (4*12)-12 = 36
Intern  B
Joined: 01 May 2017
Posts: 33
Re: Four extra-large sandwiches of exactly the same size were ordered for  [#permalink]

### Show Tags

1
2
Method - 1 (number picking).

Let us pick a number which is more than 4 and gets divided by 4. The first such number is 8, so let m = 8

so Carol will have $$\frac{1}{8}$$ from 1st sandwich, $$\frac{1}{8}$$from 2nd sandwich, and $$\frac{1}{8}$$ from 3rd sandwich - total = $$\frac{3}{8}$$

The 4th sandwich will be divided into 4 less part; so it will be divided into 4 parts, of which Carol will have 1/4

So Carol will have a total of $$\frac{3}{8}$$ + $$\frac{1}{4}$$= $$\frac{3}{8}$$+ $$\frac{2}{8}$$ = $$\frac{5}{8}$$

Now let us apply m = 8 in each of the 5 options to see, which one gives us $$\frac{5}{8}$$, the answer will be option E

Method - 2 (algebra).

Carol will have $$\frac{1}{m}$$ of a sandwich from 1st, 2nd, and 3rd sandwich, and $$\frac{1}{(m-4)}$$ from the 4th sandwich

So Carol will have a total of 3 * $$\frac{1}{m}$$ + $$\frac{1}{(m-4)}$$, which will lead to option E
VP  D
Joined: 09 Mar 2016
Posts: 1261
Four extra-large sandwiches of exactly the same size were ordered for  [#permalink]

### Show Tags

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.

hey everyone here is my solution, nothing UNordinary this time just a boring algebra:)

Let number of students be $$m$$

Three of the sandwiches were evenly divided among the students. $$\frac{3}{m}$$

Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. $$\frac{1}{m-4}$$

Now sum up $$\frac{3}{m}$$ + $$\frac{1}{m-4}$$ = $$\frac{3m-12+m}{m(m-4)}$$ = $$\frac{4m-12}{m(m-4)}$$

hey niks18 this was my aproach, but what i dont understand is this question

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?

how can this answer $$\frac{4m-12}{m(m-4)}$$ represent the amount of sandwich that she ate i mean If Carol ate one piece from each of the four sandwiches $$\frac{4m-12}{m(m-4)}$$ this answer rather represents all four pizzas distrubuted among all students ... please explain i got correct answer but this Carol makes things complicated Retired Moderator D
Joined: 25 Feb 2013
Posts: 1122
Location: India
GPA: 3.82
Four extra-large sandwiches of exactly the same size were ordered for  [#permalink]

### Show Tags

1
dave13 wrote:
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.

hey everyone here is my solution, nothing UNordinary this time just a boring algebra:)

Let number of students be $$m$$

Three of the sandwiches were evenly divided among the students. $$\frac{3}{m}$$

Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. $$\frac{1}{m-4}$$

Now sum up $$\frac{3}{m}$$ + $$\frac{1}{m-4}$$ = $$\frac{3m-12+m}{m(m-4)}$$ = $$\frac{4m-12}{m(m-4)}$$

hey niks18 this was my aproach, but what i dont understand is this question

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?

how can this answer $$\frac{4m-12}{m(m-4)}$$ represent the amount of sandwich that she ate i mean If Carol ate one piece from each of the four sandwiches $$\frac{4m-12}{m(m-4)}$$ this answer rather represents all four pizzas distrubuted among all students ... please explain i got correct answer but this Carol makes things complicated Hi dave13

As per the question Carol ate one piece from each of the four pizzas. Now 3 pizzas were divided equally among m students. Hence each piece from one pizza equals =1/m

the fourth pizza was divided equally among (m-4) students. hence each piece of the 4th pizza equals = 1/(m-4)

So in total Carol ate 1/m+1/m+1/m+1/(m-4) = $$\frac{4m-12}{m(m-4)}$$, This is the number of pieces eaten by all those students who ate one piece from all the 4 pizzas.

Other simplified method will be through substitution. Refer solutions above to understand how substitution can solve this problem easily. Four extra-large sandwiches of exactly the same size were ordered for   [#permalink] 08 May 2018, 10:34

Go to page    1   2    Next  [ 37 posts ]

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