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 but dont know why? I picked numbers and found the answer to be C.

This is how i approached it:
T=10, S=5, x=2. So total amount = 20 and if only 5 people have to contribute then they need to contribute totally 4 dollars. Additional amount paid by each coworker is 2.

Substituting these values in C gives 5*2/(10-5) = 2! Can someone explain why D is the OA?

If you approach this sequentially, it will just fall into place.
Cost per paying person if everyone had paid their share = Total Cost / Number of ppl i.e. x/T

Cost per paying person when S ppl dont pay => Number of ppl paying is T-S. Hence cost per paying person = x/(T-S). Also note this will be a larger amount than the one above (x/T).

Hence, the difference (additional amount everyone has to pay) is
x/(T-S) - x/T = xS/(T(T-S)) ie D

Thanks Grv! I realized my mistake - i wrongly considered x to be the cost/person rather than the total cost.

Grv, thanks for helping out - appreciate it!

accguy, because the answers choices contain variables, you could also try assigning real values. There are a lot of variables, so it might take a little extra time, but you are less likely to make the mistake you made if you use real numbers instead of variables.

eg, 10 coworkers agreed to share cost. Lunch costs $30. 2 fail to pay (therefore, 8 do pay... hmm, that means I'll have to divide 30 by 8, which won't come out even. What's another integer less than 10 that will divide into 30 evenly? 6 works.) Scratch that. 4 fail to pay, so 6 do pay. How much EXTRA do those 6 pay compared (above what they should've paid in the first place)?

T=10
x=30
S=2 (cross this out)
S=4

Originally 10 people and $30, so each were supposed to pay $3. Then 4 people weaseled out, and 6 got stuck with the tab. The 6 each paid $5, which was $2 more than they were supposed to pay. So the answer is 2.

A) 30/10 does not equal 2
B) 30/6 does not equal 2
C) (30*4)/6 = does not equal 2
D) (30*4)/(6*10) = (3*4)/(6*1) = 12/6 = 2 ding ding ding!
E) (30*6)/10 = 3*6 = does not equal 2

Notice, by the way, that I didn't find the numerical answer for all of the choices. Once I could tell that the number would not be what I wanted (2), I stopped and crossed it off. Notice also that I didn't immediately multiply everything out - I simplified before I multiplied. Make your life easy! Finally, make sure to cross off S=2 completely, so that you don't accidentally start using that number (as I did while typing this out because I couldn't cross off the S=2 on my screen!!).

_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT

I solved this one algebraically.

[(Number of people who didn't pay) * (the cost divided by each person)] / (Number of people who really paid)

In the variables of the problem:

[S(X/T)] / (T-S)

Reducing the improper fraction:

(SX) / (T^2 - ST)

This reduces to (SX) / [T(T-S)]

Which is D.

that works too.

remember, the most important thing to do in a situation like this one -- in which there are multiple ways to solve the same problem -- is to become familiar with ALL of those methods, not to spend time worrying about which is “better” or “easier”.

the more approaches you have to these problems, the better off you will be on test day.

Hi Ron, I felt into a deadly trap with this one.
t=10
per person=10$
x=10*10 = 100
let s=5. therefore the remaining 5 need to give 10$ / person extra.
I dive in the answer choices with 3 pieces of info:
x=100
t=10
s=5

a>x/t = 100/10 = 10 bingo.


while reviewing i realize that D also satisfies my variables. I pulled out my dusted MGMAT VICS guide that I had shelved 2 months back and realized the root cause. In the past 2 months I have never fallen into such trap.


Problem is even if I had realized this during the test I would not probably have opted to spend another 1 min on this with another set of variables. Additionally this realization would take additional time if i checked all 5 choices.
So should I shunt VICS and stick to the algebra (i am pretty close to test day-about 3 weeks- and i have been getting 99% vic problems right with plug approach).


{EDIT : read the vic chapter again- will picking multiples of distinct prime numbers "decrease the likelihood of such crashes" ?- if i picked t =40(multiple of 2),s=30(multiple of 3) and x=240; the solution is perfect }

Thanks
bblast

Definitely do not leave number picking for VICs! That is one of the greatest strategies you have on the GMAT. It sounds as if you have figured out how to minimize the chances of having this problem again.

I would encourage you to take that extra minute, run another set of numbers, and check the two possibilities. I doubt it would even take you a minute to do that.

_________________
Jamie Nelson
ManhattanGMAT Instructor

Yup, thanks Jamie, the VICS technique which I learnt via MGMAT guides is a powerful technique, which involves much less hassle than algebra.

And ya, the big takeaway from my mistake is always try to pick multiples of distinct prime numbers, such as pick 20 and 30 if we need two variables ; instead of picking 50 and 100 which have 5 and 2 in common.

guys, don't stress (and don't waste time) thinking excessively much about “the best numbers to pick” -- just pick some numbers, run them through the problem, and check all the choices. if you happen to get any repeats, no problem -- just pick another set of numbers and go at it again.

considering how little time it takes to plug in any one particular set of numbers, it's really not worth it to deliberate excessively over what numbers to pick.

Thank you Ron/Jamie. Just a few hours away from the test.
:)

hope it went well for you.

[/quote]
hope it went well for you.[/quote]


Thanks for the good wishes, I will preserve them for the retry. I fell short of my mark. :( Working hard again.

make sure you take enough time off, too. if you study too much (e.g., studying 7 days per week), your brain actually won't be able to develop the proper neuronal connections for the kind of thinking required on this test.

I take all ur advises very seriously. I retook in a month. Studied less and rested more - improved from 680-710.

Thank you Ron Purewal for making GMATland a lot better place through MGMAT forums.

Thanks
bblast