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gmat prep question

by yvonne12 » Sun Apr 15, 2007 5:32 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 co workers would have to contribute, so the cost of the lunch paid?

1. x/t
2. x/t-s
3. sx/t-s
4. sx/t(t-s)
5.x(t-s)/t
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Re: gmat prep question

by jayhawk2001 » Sun Apr 15, 2007 8:30 pm
yvonne12 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 co workers would have to contribute, so the cost of the lunch paid?

1. x/t
2. x/t-s
3. sx/t-s
4. sx/t(t-s)
5.x(t-s)/t
X/T is the original amount
X/(T-S) is the new amount

X/(T-S) - X/T
= (XT - XT + XS) / T(T-S)
= XS / T(T-S)

Is D the answer ?
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by Cybermusings » Mon Apr 16, 2007 2:51 am
Total workers = t
Total money to be contributed = x
Therefore each worker should have contributed = x/t
Workers who did not contribute = s
Therefore shortfall in contribution = x*s/t
Now this additional amount (i.e. xs/t) to be contributed by t-s members.
Hence additional amount to be contributed = (xs/t)/t-s = xs/ t (t-s).
Hence Choice D
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yes

by yvonne12 » Mon Apr 16, 2007 4:18 pm
d is the answer. It just made sense to me for the answer to be x/t-s. can you explain why this wouldnt work??

total money is x
and total worker is t

workers that fail to pay s

so wouldnt I get the same answer ?? x/t-s

how should I approach this type of question?
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Re: yes

by jayhawk2001 » Mon Apr 16, 2007 7:22 pm
yvonne12 wrote:d is the answer. It just made sense to me for the answer to be x/t-s. can you explain why this wouldnt work??

total money is x
and total worker is t

workers that fail to pay s

so wouldnt I get the same answer ?? x/t-s

how should I approach this type of question?
x/t-s is just the new amount. The question asks for the difference between
the old and the new amount. The old amount (i.e. if everyone paid) is
x/t. So, you will have to subtract x/t from x/t-s
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by trumpet1184 » Mon Jul 27, 2009 6:54 pm
I misinterpreted "remaining co-workers" as those who still have not yet paid (S) instead of the poor co-workers who have already paid (T-S). Therefore, I ran a huge circle and ended up choosing A, which of course represents the misinterpreted answer...

I hope the GMAT test makers write their current problems more unambiguously. If you've read this far, thank you for putting up with my rant - I feel much better now.
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by ghacker » Tue Jul 28, 2009 6:25 am
The answer is D

To find the additional amount we have to simplify x{(T-[T-S])}/(t(T-S))

When simplified the answer is D
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by imhimanshu » Fri Jul 31, 2009 12:52 am
Assume the values and plug in...D would satisfy. hardly took 30 secs
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by FullerGMat » Mon Jul 11, 2011 2:20 pm
imhimanshu wrote:Assume the values and plug in...D would satisfy. hardly took 30 secs
See, when I assumed values, the values I chose were yielding the same valued answers for equations in choice A and choice D, and I wrongly chose choice A. My values: T=10, S=5, x=$100. Perhaps these were not the smartest values to pick as t is then a factor of x, but I'm still stuck on how, then, to choose smarter values for this kind of question. Any advice?
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by GMATGuruNY » Mon Jul 11, 2011 6:59 pm
yvonne12 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 co workers would have to contribute, so the cost of the lunch paid?

1. x/t
2. x/t-s
3. sx/t-s
4. sx/t(t-s)
5.x(t-s)/t
Let X = 6.
Let T = 6.
Share per worker = 6/6 = 1.
Let S = 5.
Remaining workers = 6-5 = 1.
Share per worker = 6/1 = 6.
Increase in share per worker = 6-1 = 5. This is our target.

Now we plug X=6, T=6 and S=5 into the answers to which yields our target of 5.

Only answer choice D works:
sx/t(t-s) = (5*6)/ 6*(6-5) = 5.

The correct answer is D.
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by kumadil2011 » Sun Dec 04, 2011 11:07 pm
Hi Mitch..

Could you please give us a tips on how to pick the right numbers..

I picked
x=100
t=10
s=5

got a wrong answer...
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by GMATGuruNY » Mon Dec 05, 2011 4:40 am
kumadil2011 wrote:Hi Mitch..

Could you please give us a tips on how to pick the right numbers..

I picked
x=100
t=10
s=5

got a wrong answer...
With your numbers:
Original amount per worker - 100/10 = 10.
Target = increase if 5 workers fail to contribute = 100/5 - 10 = 10.

An important rule when plugging in: CHECK ALL 5 ANSWER CHOICES.
When your numbers are plugged into the answer choices, more than one answer choice yields the target.
To determine the correct answer, plug a different set of numbers into the remaining answer choices.
Eliminate any remaining answer choice that doesn't work with the new set of numbers.

The issue with your numbers is that the original amount and the target are equal.
If we assign the same number to different values in the problem, we increase the risk that more than one answer choice will yield the target.
To avoid this issue, choose numbers so that every value in the problem is represented by a different number.
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by Anaira Mitch » Sat Jan 14, 2017 1:38 pm
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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by Brent@GMATPrepNow » Sat Jan 14, 2017 2:06 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
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

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by Jeff@TargetTestPrep » Thu Jan 19, 2017 5:00 pm
yvonne12 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 co workers would have to contribute, so the cost of the lunch paid?

1. x/t
2. x/t-s
3. sx/t-s
4. sx/t(t-s)
5.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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