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# GMATPrep question

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GMATPrep question [#permalink]  07 Mar 2010, 23:42
00:00

Difficulty:

(N/A)

Question Stats:

75% (01:43) correct 25% (00:30) wrong based on 19 sessions
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!

[Reveal] Spoiler:
D
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Re: GMATPrep question [#permalink]  07 Mar 2010, 23:52
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!

[Reveal] 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

Hope this helps !!!
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Last edited by mustdoit on 08 Mar 2010, 00:06, edited 2 times in total.
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Re: GMATPrep question [#permalink]  08 Mar 2010, 00:00
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.
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Re: GMATPrep question [#permalink]  12 Mar 2010, 08:31
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!

[Reveal] 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.
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Re: GMATPrep question [#permalink]  12 Mar 2010, 22:14
1
KUDOS
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)}
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Re: GMATPrep question [#permalink]  15 Mar 2010, 07:35
1
KUDOS
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)
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My debrief: done-and-dusted-730-q49-v40

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Re: GMATPrep question [#permalink]  23 Jun 2010, 09:01
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
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Re: GMATPrep question [#permalink]  23 Jun 2010, 10:46
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.
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My debrief: done-and-dusted-730-q49-v40

Re: GMATPrep question   [#permalink] 23 Jun 2010, 10:46
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