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

It is currently 14 Aug 2018, 15:00

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

To celebrate a colleague's retirement, the T coworkers

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

Hide Tags

Intern
Intern
avatar
Joined: 27 Feb 2010
Posts: 12
To celebrate a colleague's retirement, the T coworkers in an office  [#permalink]

Show Tags

New post 08 Mar 2010, 00:42
1
7
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

64% (01:23) correct 36% (01:11) wrong based on 526 sessions

HideShow timer Statistics

To celebrate a colleague's retirement, the T coworkers in an office agreed to share equally the cost of a catered lunch. If the lunch costs a total of x dollars and S of the coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of the lunch is completely paid?

A. x/T
B. x/(T-S)
C. Sx/(T-S)
D. Sx/T(T-S)
E. X(T-S)/T
Manager
Manager
User avatar
Joined: 18 Feb 2010
Posts: 160
Schools: ISB
Re: To celebrate a colleague's retirement, the T coworkers in an office  [#permalink]

Show Tags

New post Updated on: 08 Mar 2010, 01:06
1
vakuts wrote:
Hi everyone,

I am struggling with this problem from GMATPrep test:

To celebrate a colleauge's retirement, T coworkers in an office agreed to share equally the cost of catered lunch.
If lunch costs X dollars and S of coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of lunch is completely paid?

a) X/T
b) X/(T-S)
c) SX/(T-S)
d) SX/T(T-S)
e) X(T-S)/T

Thanks!



Since no absolute values are given in the question we can replace the given parameters with assumed numbers,

Let Total colleagues be 100 (T)
Let total contribution be 500 (X) (point to note is that its total cost not per person)
Those who dont pay are S (30)

Per person cost = X/T = 500/100 = 5

So cost for those who failed to pay = (X/T) * S = SX/T = 30*5=150

The equation for people who would bear the total cost after S people fail = (T-S)=70

There fore the solution is (SX/T)/ (T-S) = SX/T(T-S) = 150/70

Answer D

Hope this helps !!!
_________________

CONSIDER AWARDING KUDOS IF MY POST HELPS !!!


Originally posted by mustdoit on 08 Mar 2010, 00:52.
Last edited by mustdoit on 08 Mar 2010, 01:06, edited 2 times in total.
Intern
Intern
avatar
Joined: 26 Sep 2009
Posts: 8
Re: To celebrate a colleague's retirement, the T coworkers in an office  [#permalink]

Show Tags

New post 08 Mar 2010, 01:00
to save time you can pick number :

T=6 , x= 12 and s= 2

if we say that 2 worker will not pay , that mean we will divide their required payment on others(4 worker out of 6).

that mean each of the 4 remaining workers should pay 1 .

so by subistitution we will find that D is the only that will give us 1 answer.
Manager
Manager
avatar
Joined: 01 Feb 2010
Posts: 239
Re: To celebrate a colleague's retirement, the T coworkers in an office  [#permalink]

Show Tags

New post 12 Mar 2010, 09:31
vakuts wrote:
Hi everyone,

I am struggling with this problem from GMATPrep test:

To celebrate a colleauge's retirement, T coworkers in an office agreed to share equally the cost of catered lunch.
If lunch costs X dollars and S of coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of lunch is completely paid?

a) X/T
b) X/(T-S)
c) SX/(T-S)
d) SX/T(T-S)
e) X(T-S)/T

Thanks!



New amount paid by T-S = X/(T-S)
Extra amount by everybody = X(1/(T-S) - 1/T)
= SX/T(T-S) hence D.
Manager
Manager
User avatar
Joined: 14 Dec 2009
Posts: 71
Re: To celebrate a colleague's retirement, the T coworkers in an office  [#permalink]

Show Tags

New post 12 Mar 2010, 23:14
3
\(T\) - total number of people
\(S\)- number of people that left
\(X\) - total amount $

\(\frac{X}{T}\) - $ that 1 person had to pay at first.
\(\frac{X}{T}*S\) - $ that should be shared
\(T-S\) - people who should share \(\frac{X}{T}*S\)

\(\frac{\frac{X}{T}*S}{T-S}\) - aditional payment for 1 person

simplify: \(\frac{\frac{X}{T}*S}{T-S}=\frac{XS}{T}*\frac{1}{(T-S)}\)
:wink:
Manager
Manager
User avatar
Joined: 13 Dec 2009
Posts: 235
Reviews Badge
Re: To celebrate a colleague's retirement, the T coworkers in an office  [#permalink]

Show Tags

New post 15 Mar 2010, 08:35
4
Answer is D XS/T(T-S)
Originally everyone has to pay = X/T
when s people failed to pay each remaining person has to pay = X/(T-S)
so additional amt = X/(T-S) - X/T = XS/T(T-S)
_________________

My debrief: done-and-dusted-730-q49-v40

Intern
Intern
avatar
Joined: 16 Mar 2010
Posts: 42
Re: To celebrate a colleague's retirement, the T coworkers in an office  [#permalink]

Show Tags

New post 23 Jun 2010, 10:01
sidhu-

would you mind explaining how you simplify X/(T-S) - X/T = XS/T(T-S) ?

I got to the X/(T-S) - X/T but I cannot figure out how to get to the answer choice D.

Appreciate it!

-Sameer
Manager
Manager
User avatar
Joined: 13 Dec 2009
Posts: 235
Reviews Badge
Re: To celebrate a colleague's retirement, the T coworkers in an office  [#permalink]

Show Tags

New post 23 Jun 2010, 11:46
sameermunshi wrote:
sidhu-

would you mind explaining how you simplify X/(T-S) - X/T = XS/T(T-S) ?

I got to the X/(T-S) - X/T but I cannot figure out how to get to the answer choice D.

Appreciate it!

-Sameer


Sameer,

It's pretty simple.
We have => Additional amount to be paid by each = \(\frac{X}{(T-S)} - \frac{X}{T}\)

=> Take LCM => Denominator becomes \(T(T-S)\) and Numerator becomes \(XT - X(T-S)\)

=> So we have \(\frac{XT - X(T-S)}{T(T-S)}\)

=> \(\frac{XT -XT + XS}{T(T-S)}\)

=> \(XT\) gets cancelled in numerator => \(\frac{XS}{T(T-S)}\) => choice D.
_________________

My debrief: done-and-dusted-730-q49-v40

Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 441
Concentration: Marketing, Finance
GPA: 3.23
GMAT ToolKit User
Re: To celebrate a colleague's retirement, the T coworkers  [#permalink]

Show Tags

New post 07 Dec 2012, 20:45
Cost of lunch = x
Number of People = T

If all joined in to pay, each will pay \(\frac{x}{T}\)
But that did not happen, only T-S paid. Thus, each who paid contributed \(\frac{x}{T-S}\)

\(\frac{x}{T-S}-\frac{x}{T}\) --> extra amount they paid because S are stingy..
\(\frac{xT - xT + xS}{(T)(T-S)}\)
\(\frac{xS}{T(T-S)}\)

AnsweR: D
_________________

Impossible is nothing to God.

VP
VP
User avatar
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1252
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
GMAT ToolKit User Premium Member
Re: To celebrate a colleague's retirement, the T coworkers  [#permalink]

Show Tags

New post 07 Dec 2012, 20:51
1
apoorvarora wrote:
To celebrate a colleague's retirement, the T coworkers in an office agreed to share equally the cost of a catered lunch. If the lunch costs a total of x dollars and S of the coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of the lunch is completely paid?

A. x/T
B. x/T-S
C. Sx/T-S
D. Sx/T(T-S)
E. X(T-S)/T


Initial BURDEN on each coworker--->Total cost/ Number of Coworkers

or \(X/T\)

Now, when S coworkers are not paying their share, naturally the BURDEN on each coworker will increase in they have to raise their share in the total cost.
S are not paying their share, so # of coworkers who are willing to pay= T-S

Final BURDEN on each coworker----->Total cost/(T-S)

or \(X/(T-S)\)

Subtract the smaller from the larger.

\(X/(T-S) - X/T\) = \(XS/[T*(T-S)]\) .
Hope that helps.
_________________

Prepositional Phrases Clarified|Elimination of BEING| Absolute Phrases Clarified
Rules For Posting
www.Univ-Scholarships.com

Manager
Manager
User avatar
Joined: 04 Oct 2011
Posts: 199
Location: India
Concentration: Entrepreneurship, International Business
GMAT 1: 440 Q33 V13
GPA: 3
Re: To celebrate a colleague's retirement, the T coworkers  [#permalink]

Show Tags

New post 08 Dec 2012, 05:18
apoorvarora wrote:
To celebrate a colleague's retirement, the T coworkers in an office agreed to share equally the cost of a catered lunch. If the lunch costs a total of x dollars and S of the coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of the lunch is completely paid?

A. x/T
B. x/T-S
C. Sx/T-S
D. Sx/T(T-S)
E. X(T-S)/T


I went with substitution method...
I replaced variables with values for easy calculations :-D

let
T =10
X= 200
s =2

Actual each person share 200/10 = 20

But 2 members didnt pay , so 8 members (T-S) would have paid the balance...
200/8 =25

25-20 = 5 Only choice D gives value same value..
_________________

GMAT - Practice, Patience, Persistence
Kudos if u like :)

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47898
Re: To celebrate a colleague's retirement, the T coworkers  [#permalink]

Show Tags

New post 08 Dec 2012, 05:51
apoorvarora wrote:
To celebrate a colleague's retirement, the T coworkers in an office agreed to share equally the cost of a catered lunch. If the lunch costs a total of x dollars and S of the coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of the lunch is completely paid?

A. x/T
B. x/(T-S)
C. Sx/(T-S)
D. Sx/T(T-S)
E. X(T-S)/T


Pick some smart numbers.

Let T=3, x=$3 and S=2.

So, we'd have that originally 3 coworkers were to pay $1 each for $3 lunch but 2 coworkers fail to pay, thus the remaining worker should pay additional $2 to cover the cost of the lunch.

Now, substitute T=3, x=$3 and S=2 into the answers to see which yields $2. Only answer D works.

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Director
Director
User avatar
G
Joined: 26 Oct 2016
Posts: 656
Location: United States
Concentration: Marketing, International Business
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Re: To celebrate a colleague's retirement, the T coworkers  [#permalink]

Show Tags

New post 14 Jan 2017, 14:38
In the origin plan, each one should pay X/T.
Actually, each of the remaining coworkers paid X/(T-S).
Then, X/(T-S) - X/T = S*X / T(T-S)
_________________

Thanks & Regards,
Anaira Mitch

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2727
Re: To celebrate a colleague's retirement, the T coworkers  [#permalink]

Show Tags

New post 11 Dec 2017, 11:59
vakuts wrote:
To celebrate a colleague's retirement, the T coworkers in an office agreed to share equally the cost of a catered lunch. If the lunch costs a total of x dollars and S of the coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of the lunch is completely paid?

A. x/T
B. x/(T-S)
C. Sx/(T-S)
D. Sx/T(T-S)
E. X(T-S)/T


We are given that T coworkers agreed to equally split the payment for the cost of a lunch. We are also given that the lunch costs X dollars and S coworkers do not pay their share.

We need to determine the ADDITIONAL AMOUNT that each coworker has to pay now.

The original cost per person for the lunch would have been X/T. Since S coworkers did not pay, the actual cost was X/(T-S). Thus, the additional amount paid was:

X/(T-S) - X/T

Getting a common denominator, which is T(T-S), we have:

T/T x X/(T-S) - (T-S)/(T-S) x (X/T)

XT/[T(T-S)] - X(T-S)/[T(T-S)]

[XT - XT + XS]/[T(T-S)]

XS/[T(T-S)]

Answer: D
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: To celebrate a colleague's retirement, the T coworkers &nbs [#permalink] 11 Dec 2017, 11:59
Display posts from previous: Sort by

To celebrate a colleague's retirement, the T coworkers

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

Events & Promotions

PREV
NEXT


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®.