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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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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

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

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

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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

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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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)
_________________

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

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07 Dec 2012, 19:51

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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.
_________________

Concentration: Entrepreneurship, International Business

GMAT 1: 440 Q33 V13

GPA: 3

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

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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

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.

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)
_________________

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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