GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Oct 2018, 07:57

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

A number of people shared a meal, intending to divide the cost evenly

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
B
Joined: 09 Jan 2017
Posts: 22
Location: Germany
Concentration: International Business, General Management
GPA: 3.7
A number of people shared a meal, intending to divide the cost evenly  [#permalink]

Show Tags

New post 27 Jan 2017, 06:18
7
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

50% (02:22) correct 50% (02:41) wrong based on 106 sessions

HideShow timer Statistics

A number of people shared a meal, intending to divide the cost evenly among themselves. However, several of the diners left without paying. When the cost was divided evenly among the remaining diners, each remaining person paid $12 more than he or she would have if all diners had contributed equally. Was the total cost of the meal, in dollars, an integer?

(1) Four people left without paying.

(2) Ten people in total shared the meal.

_________________

Kudos for correct answers or good questions!

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6976
Re: A number of people shared a meal, intending to divide the cost evenly  [#permalink]

Show Tags

New post 27 Jan 2017, 06:48
lmuenzel wrote:
A number of people shared a meal, intending to divide the cost evenly among themselves. However, several of the diners left without paying. When the cost was divided evenly among the remaining diners, each remaining person paid $12 more than he or she would have if all diners had contributed equally. Was the total cost of the meal, in dollars, an integer?

(1) Four people left without paying.

(2) Ten people in total shared the meal.


Hi,

A GOOD Q..

Info from Q
1) Rs 12 extra was paid by remaining people.
so the Q asks us if \(\frac{12*r}{l}\) is integer.
It will be possible ONLY if l is factor 12*r....
r is remaining people and I is people who left w/o paying


Let's see the statements..
1) l is 4..
So \(\frac{12*r}{l}=\frac{12*r}{4}=3*r\)
Now r is integer so 3*r will be integer. This is what each pays.
When this is multiplied by TOTAL number of persons, it will still be integer.
Suff

2) r is 10..
12*10/l will depend on l whether it is integer or not..
If l is a factor of 120 such as 10,12,2,3,4,6,30,60, it will be integer.
If it is 7,9,50etc it will not be an integer.
Insufficient

A
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 3024
Location: Canada
Re: A number of people shared a meal, intending to divide the cost evenly  [#permalink]

Show Tags

New post 27 Jan 2017, 08:53
1
Top Contributor
lmuenzel wrote:
A number of people shared a meal, intending to divide the cost evenly among themselves. However, several of the diners left without paying. When the cost was divided evenly among the remaining diners, each remaining person paid $12 more than he or she would have if all diners had contributed equally. Was the total cost of the meal, in dollars, an integer?

(1) Four people left without paying.
(2) Ten people in total shared the meal.


Target question: Was the total cost of the meal, in dollars, an integer?
This is a great candidate for rephrasing the target question

Given: A number of people shared a meal, intending to divide the cost evenly among themselves. However, several of the diners left without paying. When the cost was divided evenly among the remaining diners, each remaining person paid $12 more than he or she would have if all diners had contributed equally.

Let c = TOTAL cost of the meal
Let n = number of people who SHARED the meal
Let d = the number of deadbeats who left before paying
So, n - d = number of people who PAID for the meal

Cost per person with all n people = c/n
Cost per person with n-d people = c/(n - d)

Word equation: (cost per person with original diners) + 12 = cost per person with reduced number of diners
Equation: c/n + 12 = c/(n - d)
Eliminate fractions by multiplying both sides by (n)(n - d) to get: c(n - d) + 12(n)(n - d) = cn
Expand: cn - cd + 12n² - 12nd = cn
Subtract cn from both sides: -cd + 12n² - 12nd = 0
Add cd to both sides: 12n² - 12nd = cd
Divide both sides by d to get: 12n²/d - 12n = c
Factor: n(12n/d - 12) = c

Since n(12n/d - 12) equals the total cost of the meal, we can REPHRASE the target question....
REPHRASED target question: Is n(12n/d - 12) an integer?

Statement 1: Four people left without paying
In other words, statement 1 tells us that d = 4
Plug d = 4 into the REPHRASED target question to get: Is n(12n/4 - 12) an integer?
n(12n/4 - 12) = n(3n - 12), and n(3n - 12) is definitely an integer.
How do we know this?
Well, we know that n is an integer.
So, 3n is an integer, which means 3n - 12 is an integer, which means n(3n - 12) is an integer.
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: Ten people in total shared the meal
In other words, statement 2 tells us that n = 10
Plug n = 10 into the REPHRASED target question to get: Is (10)(120/d - 12) an integer?
There are several values of d that yield conflicting answers to the target question. Here are two:
Case a: if d = 2, then (10)(120/d - 12) = (10)(120/2 - 12) = 480, and 480 IS an integer
Case b: if d = 7, then (10)(120/d - 12) = (10)(120/7 - 12), and this does NOT evaluate to be an integer
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

RELATED VIDEO

_________________

Brent Hanneson – GMATPrepNow.com
Image
Sign up for our free Question of the Day emails

Senior SC Moderator
User avatar
V
Joined: 14 Nov 2016
Posts: 1314
Location: Malaysia
GMAT ToolKit User Premium Member CAT Tests
A number of people shared a meal, intending to divide the cost evenly  [#permalink]

Show Tags

New post 07 Feb 2017, 19:24
lmuenzel wrote:
A number of people shared a meal, intending to divide the cost evenly among themselves. However, several of the diners left without paying. When the cost was divided evenly among the remaining diners, each remaining person paid \($12\) more than he or she would have if all diners had contributed equally. Was the total cost of the meal, in dollars, an integer?

(1) Four people left without paying.

(2) Ten people in total shared the meal.


Official solution from Veritas Prep.

Following our normal approach to word problems, we want to label our unknowns and then translate the statements in the problem to algebra. What makes this problem feel more difficult is simply the sheer number of unknowns. But don’t panic – it’s fine to have statements containing mostly unknowns, and the algebra will always work itself out in the end.

Let’s call the total cost of the meal \(C\). The number of diners who ended up paying will be \(P\), and then number who left without paying will be \(L\). The total number of diners is therefore \(P+L\). (We chose the variables in this way to match the information provided in the two additional premises, but we’re better off not actually plugging in those premises until much later.)

The price that each diner “should have paid” for the meal is \(\frac{C}{(P+L)}\). The price that each remaining diner actually paid, however, is \(\frac{C}{P}\). The difference can be expressed as

\(\frac{C}{P}−\frac{C}{(P+L)}=12\)

Taking the common denominator gives

\(\frac{C*(P+L)}{P*(P+L)}−\frac{CP}{P*(P+L)}=12\)

\(\frac{(CP+CL–CP)}{P(P+L)}=12\)

\(CL=12P(P+L)\)

Since the question asks whether the total cost was an integer, we’ll solve for that:

\(C=\frac{12P(P+L)}{L}\)

At this point, we can see that whether the total cost \(C\) is an integer depends most of all on \(L\) – whether the number of people who left divides evenly into \(12\), \(P\), and/or \(P+L\). Since statement 1 answers this question in the affirmative (4 divides evenly into \(12\), making \(C\) an integer), this statement is sufficient alone. Since statement \(2\) provides no information of relevance, that statement is insufficient. The answer is \(A\).
_________________

"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Rules for posting in verbal forum | Please DO NOT post short answer in your post!

Advanced Search : https://gmatclub.com/forum/advanced-search/

Intern
Intern
avatar
B
Joined: 15 Aug 2012
Posts: 42
Schools: AGSM '19
GMAT ToolKit User
A number of people shared a meal, intending to divide the cost evenly  [#permalink]

Show Tags

New post 07 Jun 2018, 22:05
Bunuel or chetan2u

Trying to understand if my reasoning (Especially for statement 2) is correct. Would appreciate if you can provide come feedback.

Statement 1:
Let's say N is the original number of people and P is the original price they shared.

Total=NP

Now we have 4 people who left us. So remaining number of people is (N-4). New price shared among people is (P+12)

Total = (N-4)(P+12)

Total in both cases the total paid remains the same so
-> NP=(N-4)(P+12)
-> NP= NP+12N-4P-48
-> 48=12N-4P
-> 48=4(3N-P)
-> 12=3N-P
-> (12+P)/3=N
-> 4 + P/3 = N

N has to be an integer because it's the number of people. For N to be an integer, P has to be an integer and a multiple of 3. This means that both N and P are integers so our total amount paid NP must also equals an integer.

Statement 2: We only know that the number of people is 10. Total amount paid is 10(12+x) where x was the original amount everyone would've shared if no one left.
-> Total Amount = 120 + 10*x

The result can be an integer or it might not (if x was a decimal i.e. 1.75?)

So B is Insufficient
GMAT Club Bot
A number of people shared a meal, intending to divide the cost evenly &nbs [#permalink] 07 Jun 2018, 22:05
Display posts from previous: Sort by

A number of people shared a meal, intending to divide the cost evenly

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.