To celebrate a colleague's retirement, the T coworkers in an

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

To celebrate a colleague's retirement, the T coworkers in an

by BTGmoderatorDC » Mon Jun 10, 2019 8:40 pm

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

OA D

Source: GMAT Prep

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Source: Beat The GMAT — Problem Solving | Mon Jun 10, 2019 8:40 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Mon Jun 10, 2019 9:24 pm

BTGmoderatorDC 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

OA D

Source: GMAT Prep

Desired share from each = X/T;

The actual share of (T - S) coworkers = X/(T - S)

Additional amount by each coworker = X/(T - S) - X/T = SX/T(T - S)

The correct answer: D

Hope this helps!

-Jay
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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Tue Jun 11, 2019 3:09 am

BTGmoderatorDC 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 T coworkers in an office agreed to share equally the cost of a catered lunch.
The lunch costs a total of X dollars.
Let X=5 and T=5, implying that the original cost per worker = 5/5 = $1.

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?
Let S=4, with the result that the 1 remaining worker must pay the entire $5.
Since the share for the 1 remaining worker increases from $1 to $5 -- an increase of $4 -- the correct answer must yield 4 when X=5, T=5 and S=4.

Only D works:
SX/T(T-S) = (4*5)/(5 * 5-4) = 4

The correct answer is D.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Jun 14, 2019 9:42 am

BTGmoderatorDC 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

OA D

Source: GMAT Prep

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/(T-S) - (T-S)/(T-S) * (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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