P persons have decided to rent a van to tour while on holidays. The pr

Question

Tough and Tricky questions: Word Problems.

P persons have decided to rent a van to tour while on holidays. The price of the van is x dollars and each person is to pay an equal share. If D persons cancel their trip thus failing to pay their share, which of the following represents the  additional  number of dollars per person that each remaining person must pay in order to still rent the van?

A) Dx
B) x/(P −D)
C) Dx/(P −D)
D) Dx/(P(P −D))
E) x/(P(P −D))

Kudos for a correct  solution .

Source: Chili Hot GMAT

BrentGMATPrepNow · Accepted Answer

P persons have decided to rent a van to tour while on holidays. The price of the van is x dollars and each person is to pay an equal share.   
ORIGINAL cost per person = (total cost)/(number of people paying) =  x/P

D persons cancel their trip thus failing to pay their share   
So, now the number of people paying =  P - D 
REVISED cost per person = TOTAL cost/(number of people paying)
= x/( P - D )

Which of the following represents the  additional number of dollars per person  that each remaining person must pay in order to still rent the van?   
Answer = (REVISED cost per person) - (ORIGINAL cost per person)
= x/( P - D ) -  x/P

Check the answer choices....not there. It looks like we need to rewrite x/( P - D ) -  x/P  as a single term
Take: x/( P - D ) -  x/P 
Get common denominator: (x)(P)/(P)(P - D) - (x)(P - D)/(P)(P - D) 
Expand numerators to get: : (Px)/(P)(P - D) - (Px - Dx)/(P)(P - D) 
Combine numerators to get: :  /(P)(P - D) 
Simplify numerator to get: : (Dx)/(P)(P - D)

Answer: D

Ankur9 · Answer

Initially share per person =  x/P 
total share of D persons =  Dx/P 
when D persons left then this share has to be divided equally among remaining P-D persons.
thus additional share is  Dx/P(P-D) 
Answer D.

vietnammba · Answer

The answer is D. 
x/P-D - x/P = Dx/P(P-D)

AliciaSierra · Answer

Initial number of person:  P

Total Rent:  X  dollars

Initial rent per person: \frac{X}{P}   dollars/person

Number of Person left:  D

So count of remaining people:  P-D

Now rent per person will be : \frac{X}{(P-D)}   dollars/person

Additional number of dollars that each person pay is:  \frac{X}{(P-D)}   -   \frac{X}{P}  =  \frac{XD}{P(P-D)}

Answer: D

PareshGmat · Answer

Answer = D)  \frac{Dx}{P(P −D)}

Persons ....................... Total ......................... Per Head

P ................................. X .....................................  \frac{x}{p}

p-d ............................... x ......................................  \frac{x}{p-d}  (D people cancelled; less the denominator, more would be value)

Difference per head  = \frac{x}{p-d} - \frac{x}{p} = x(\frac{1}{p-d} - \frac{1}{p}) = x * \frac{p-p+d}{p(p-d)} = \frac{xd}{p(p-d)}

akumar5 · Answer

Share per person =x/p
When D person left, share per person = x/(p-D)

So the additional share per person is =x/(D-p) - x/p = (px-Dx+px)/p(D-p)=Dx/p(D-p)

Answer D

ScottTargetTestPrep · Answer

The original number of dollars each person was to pay is x/P dollars.

After D people cancel, there are (P - D) people remaining to pay the full cost x. Thus, the new number of dollars per person is x/(P - D) dollars. So, the additional amount of dollars per person is the difference between the new dollars per person and the original dollars per person:

x/(P-D) - x/P

x/(P-D) * (P/P) - (x/P) * (P-D)/(P-D)

xP/  - x(P-D)/

/  = xD/

Answer: D

thisso · Answer

there is a much easier way if you are not good at algebra like me. Just pick some numbers. for ex: p= 10, D=5, and x=10. That means each person would pay 1$

When 5 people back out, then each person would have to pay for 2$. The question asks for how many ADDITIONAL dollars, which in this case would be 1$. Plug in numbers into the answers and see which one results in '1 $.' Only 'D' results in 1$.

bumpbot · Answer

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P persons have decided to rent a van to tour while on holidays. The pr

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