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explanation plzzz..

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by raptor84 » Sat Feb 14, 2009 11:20 am
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 ammount, 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 is D why not A

i picked numbers as below for this

X=100
T=10
S=5

Initially cost/head = 100/10 = 10

After 5 i.e. S people drop out cost/head = 100/5 = 20

therefore additional cost/head = 20-10 = 10

using this in the answer choices i get both A & D right!!!

please explain where i am going wrong. Thanks!
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by cjb » Sat Feb 14, 2009 12:13 pm
I would have solved this algebraically, but using numbers is fine.

Randomly picked numbers may sometimes give you an ambiguous answer. If that happens, just pick another set!
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by earth@work » Sat Feb 14, 2009 12:32 pm
i usually do not pick numbers when we have to answer in given variables, i.e. i pick up variables only when the answer is either % or ratio or fraction.
Here, Initial cost per person = X/T
Cost after S failed to pay = X/(T-S)
Difference =>X/(T-S)- X/T = SX/T(T-S) ...Ans: D
i picked numbers as below for this

X=100
T=10
S=5

If we use A: X/T --- now this gives us the cost per head if everyone payed i.e no one failed to pay!

Also if u pick different digits Say, X=30, T=10, S=3
X/T=30/10 =3 per head
Drop out cost = 30/(10-3)=30/7
Additional cost = 30/7 - 3 = 9/7
A: x/T=30/10=3 ...incorrect
D:SX/T(T-S) = 3*30/(10*(10-3) = 3*30/(10*7)=9/7 CORRECT

the problem was with the numbers u picked: in that S was equal to T-S.... which when put in choice D) SX/T(T-S) = SX/T*S ...(since T-S =S )=SX/TS=X/T = choice A
So your method would be correct is it was given that out of total T half the coworkers(=S) were not able to pay... infact in this situation mentioning S was not important as we would have worked with half of T = T/2
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by semidevil » Sat Feb 14, 2009 12:37 pm
The question asks the remaining dollars that each of the coworkers has to contribute.

the total of the lunch was X, so X/T would be the amount each person had to contribute.

But since S people bailed out on it, the total amount would be divided among T-S people. so the equation is now X/(T-S).

So you can do X/T - X/(T-S) and you will get the difference that each T person had to contribute now.
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by Brent@GMATPrepNow » Thu Oct 24, 2019 12:35 pm
raptor84 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 ammount, 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
Originally, T people were to pay total cost of x dollars.
So, each person pays x/T each.

After S people drop out, there are T-S people to pay total cost of x dollars.
So, each person pays x/(T-S) each.

The additional amount that each must pay = New cost per person - original cost per person
= x/(T-S) - x/T
Check the answer choices . . . not there. It looks like they want us to combine the two fractions.

So, rewrite with common denominator: x/(T-S) - x/T = xT/[T(T-S)] - [x(T-S)]/[T(T-S)]
= xT/[T(T-S)] - [xT-xS)]/[T(T-S)]
= xS/[T(T-S)]
= D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Scott@TargetTestPrep » Tue Oct 29, 2019 6:42 pm
raptor84 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 ammount, 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/(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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