To celebrate a colleague's retirement, the T coworkers in an office ag : Problem Solving (PS)

vakuts

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To celebrate a colleague's retirement, the T coworkers in an office ag [#permalink]

08 Mar 2010, 00:42

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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

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sidhu4u

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Re: To celebrate a colleague's retirement, the T coworkers in an office ag [#permalink]

15 Mar 2010, 08:35

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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)

Igor010

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Re: To celebrate a colleague's retirement, the T coworkers in an office ag [#permalink]

12 Mar 2010, 23:14

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$T$ - 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:

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BrentGMATPrepNow

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Re: To celebrate a colleague's retirement, the T coworkers in an office ag [#permalink]

11 Dec 2021, 07:36

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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

The PLAN was for T coworkers to share the cost of lunch, which costs x dollars
So, each coworker was supposed to pay x/T dollars

In REALITY, S coworkers failed to pay, which means the total number of coworkers who are paying = T - S
So, in reality, each of the T - S coworkers had to pay x/(T-S) dollars

So, the ADDITIONAL amount each coworker paid = x/(T-S) - x/T
Check the answer choices..... x/(T-S) - x/T is not among them.

Looks like we need to combine the two fractions by first rewriting them with a common denominator as follows:
x/(T-S) - x/T = (x)(T)/(T-S)(T) - (x)(T-S)/(T-S)(T)
= xT/(T-S)(T) - (xT - xS)/(T-S)(T)
= xS/(T-S)(T)

Answer: D

mustdoit

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Re: To celebrate a colleague's retirement, the T coworkers in an office ag [#permalink]

Updated on: 08 Mar 2010, 01:06

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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!

Show Spoiler

D

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 !!!

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.

aiyedh

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Re: To celebrate a colleague's retirement, the T coworkers in an office ag [#permalink]

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.

bangalorian2000

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Re: To celebrate a colleague's retirement, the T coworkers in an office ag [#permalink]

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!

Show Spoiler

D

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.

MrFriendship

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Re: To celebrate a colleague's retirement, the T coworkers in an office ag [#permalink]

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

sidhu4u

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Re: To celebrate a colleague's retirement, the T coworkers in an office ag [#permalink]

23 Jun 2010, 11:46

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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.

mbaiseasy

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Re: To celebrate a colleague's retirement, the T coworkers in an office ag [#permalink]

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

S

Marcab

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Re: To celebrate a colleague's retirement, the T coworkers in an office ag [#permalink]

07 Dec 2012, 20:51

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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.

shanmugamgsn

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Re: To celebrate a colleague's retirement, the T coworkers in an office ag [#permalink]

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..

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Bunuel

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Re: To celebrate a colleague's retirement, the T coworkers in an office ag [#permalink]

08 Dec 2012, 05:51

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Expert Reply

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.
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Re: To celebrate a colleague's retirement, the T coworkers in an office ag [#permalink]

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)

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JeffTargetTestPrep

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Re: To celebrate a colleague's retirement, the T coworkers in an office ag [#permalink]

11 Dec 2017, 11:59

Expert Reply

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
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Re: To celebrate a colleague's retirement, the T coworkers in an office ag [#permalink]

06 Oct 2020, 08:55

OFFICIAL GMAT EXPLANATION

If the T coworkers equally shared the cost of x dollars, each would pay x÷T dollars. However, if S coworkers fail to pay their share, then the cost of x dollars would be equally shared by the remaining T – S coworkers and each would pay x÷T-S dollars. The difference in the two amounts is Sx/T(T-S).

The correct answer is (D).

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Basshead

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Re: To celebrate a colleague's retirement, the T coworkers in an office ag [#permalink]

23 Oct 2020, 17:54

Lunch costs a total of x dollars, which is split between T coworkers:

$Original plan = \frac{X}{T}$

A few coworkers didn't pay, resulting in more of a burden for the rest of the co-workers:

$New plan = \frac{X}{T-S}$

How do we determine the additional amount the remaining co-workers had to contribute? We subtract the original plan from the new plan (since it was more expensive per person in the new plan)

$\frac{X}{T-S} - \frac{X}{T} = \frac{XT - XT - XS}{T(T-S)} = \frac{XS}{T(T-S)}$

Answer is D.
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RastogiSarthak99

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Re: To celebrate a colleague's retirement, the T coworkers in an office ag [#permalink]

11 Jul 2022, 10:35

My 2 cents on this:

I like to take numbers instead of variables. It takes maybe 30 seconds more, but it works for me.

10 coworkers, 50 dinner bill, 3 did not pay

original 50/10 = 5 per person --> means 5 * 3 = 15 not paid. Remainder covered by 7 employees, therefore 15/7

To arrive at 15/7 --> (S * X/T)/T-S Gives us SX/T(T-S)

D.

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Re: To celebrate a colleague's retirement, the T coworkers in an office ag [#permalink]

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Re: To celebrate a colleague's retirement, the T coworkers in an office ag [#permalink]

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