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VIC question -- picking numbers

This topic has 2 expert replies and 4 member replies

VIC question -- picking numbers

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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


I know this problem can be solved with algebra, but I wanted to try and do it picking smart numbers. Unfortunately, the first few sets of numbers I picked gave me both A & D as possible answers. What am I doing wrong when picking smart numbers? Here's an example:

T=10
X=20
S=5

So, originally each person had to pay $2. Since five people didn't pay, the remaining people must pay an extra $2 each. If I plug into A, I get:

T/S = 2

And if I plug into D, I get:

Sx/T(T-S)
100/10(5)
= 2

-------

Here's another set I tried:

T=10
X=20
S=5

So, originally each person was to pay $2 each. Since 5 people failed to pay, the remaining people have to pay $ 4 each, or an extra $2/pp.

Putting the aforementioned numbers in answer A:

T/S = 10/5 = 2

And putting it into D:

Sx/T(T-S)
100/50
= 2


I picked several sets of numbers and it kept coming out the same before I finally found a set that only worked for D. On the real test, I wouldn't have time to fool around with several sets of numbers, so I'm wondering what I can do differently to pick smart numbers?

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Legendary Member Default Avatar
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Very valid question!

I picked T=10 X=100 S=10

a) AND d) bothe worked.

Anytime u pick S to be half of T I think a and d will both work so

I picked T=4 X=24 S=1 (made sure that x is divisible(picking x to be the LCM of t and t-s or the lcm's mutliple) not only by t but also t-s since they both appear in the denominator for choice d)

Eliminated a and ended up with d


By the way is this not a gmat prep q?

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Master | Next Rank: 500 Posts Default Avatar
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cramya wrote:
Very valid question!

I picked T=10 X=100 S=10

a) AND d) bothe worked.

Anytime u pick S to be half of T I think a and d will both work so

I picked T=4 X=24 S=1 (made sure that x is divisible(picking x to be the LCM of t and t-s or the lcm's mutliple) not only by t but also t-s since they both appear in the denominator for choice d)

Eliminated a and ended up with d


By the way is this not a gmat prep q?
Yes, it's a GMAT prep question. I scored a 740 on the exam, but missed this one because I couldn't figure out why the numbers wouldn't work.

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u can use variables...as the answers are in variables..

total coworkers= T

Total cost of lunch = x

Cost per person will be = X/T...(1)

Coworkers that failed to pay = S

Coworkers that will bear the remaining cost = T-S

Cost per person after S coworkers refused to pay = X/T-S...(2)

Additional cost per coworker will be (2) - (1)

i.e = X/T-S - X/T

= SX/ T(T-S)

thus D

thanks.

imo
picking up numbers will be time consuming in this question.

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Junior | Next Rank: 30 Posts Default Avatar
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Ans = Cost to be paid by S members / T-S

Cost to be paid by 1 member = x/T
Cost to be paid be S members = Sx/T

Therefore, ans = Sx/T (T-S)

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GMAT/MBA Expert

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Stockmoose16 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

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

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Stockmoose16 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


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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scott@targettestprep.com



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