To celebrate a colleague's retirement, the T coworkers : GMAT Problem Solving (PS)
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# To celebrate a colleague's retirement, the T coworkers

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

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07 Mar 2010, 23:42
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55% (hard)

Question Stats:

58% (02:18) correct 42% (01:12) wrong based on 340 sessions

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

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15 Mar 2010, 07:35
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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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Re: To celebrate a colleague's retirement, the T coworkers in an office [#permalink]

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07 Mar 2010, 23:52
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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!

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

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12 Mar 2010, 22:14
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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: $$\frac{\frac{X}{T}*S}{T-S}=\frac{XS}{T}*\frac{1}{(T-S)}$$ Intern Joined: 26 Sep 2009 Posts: 10 Followers: 0 Kudos [?]: 0 [0], given: 1 Re: To celebrate a colleague's retirement, the T coworkers in an office [#permalink] ### Show Tags 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. Senior Manager Joined: 01 Feb 2010 Posts: 267 Followers: 1 Kudos [?]: 57 [0], given: 2 Re: To celebrate a colleague's retirement, the T coworkers in an office [#permalink] ### Show Tags 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. Intern Joined: 16 Mar 2010 Posts: 42 Followers: 0 Kudos [?]: 8 [0], given: 39 Re: To celebrate a colleague's retirement, the T coworkers in an office [#permalink] ### Show Tags 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 Senior Manager Joined: 13 Dec 2009 Posts: 263 Followers: 10 Kudos [?]: 186 [0], given: 13 Re: To celebrate a colleague's retirement, the T coworkers in an office [#permalink] ### Show Tags 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. _________________ My debrief: done-and-dusted-730-q49-v40 Intern Joined: 30 Jun 2012 Posts: 13 Followers: 0 Kudos [?]: 26 [0], given: 4 To celebrate a colleague's retirement, the T coworkers [#permalink] ### Show Tags 07 Dec 2012, 19:33 1 This post was BOOKMARKED 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 Senior Manager Joined: 13 Aug 2012 Posts: 464 Concentration: Marketing, Finance GMAT 1: Q V0 GPA: 3.23 Followers: 26 Kudos [?]: 443 [0], given: 11 Re: To celebrate a colleague's retirement, the T coworkers [#permalink] ### Show Tags 07 Dec 2012, 19:45 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 Status: Been a long time guys... Joined: 03 Feb 2011 Posts: 1420 Location: United States (NY) Concentration: Finance, Marketing GPA: 3.75 Followers: 177 Kudos [?]: 1365 [0], given: 62 Re: To celebrate a colleague's retirement, the T coworkers [#permalink] ### Show Tags 07 Dec 2012, 19:51 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 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. _________________ Manager Joined: 04 Oct 2011 Posts: 224 Location: India Concentration: Entrepreneurship, International Business GMAT 1: 440 Q33 V13 GMAT 2: 0 Q0 V0 GPA: 3 Followers: 0 Kudos [?]: 50 [0], given: 44 Re: To celebrate a colleague's retirement, the T coworkers [#permalink] ### Show Tags 08 Dec 2012, 04:18 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 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 Joined: 02 Sep 2009 Posts: 37108 Followers: 7252 Kudos [?]: 96513 [0], given: 10753 Re: To celebrate a colleague's retirement, the T coworkers [#permalink] ### Show Tags 08 Dec 2012, 04:51 Expert's post 1 This post was BOOKMARKED 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.

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

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14 Jan 2017, 13:38
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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Re: To celebrate a colleague's retirement, the T coworkers   [#permalink] 14 Jan 2017, 13:38
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