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

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Bunuel
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P persons have decided to rent a van to tour while on holidays. The pr [#permalink] New post   24 Nov 2014, 07:38
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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))

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BrentGMATPrepNow
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P persons have decided to rent a van to tour while on holidays. The pr [#permalink] New post   Updated on: 19 Jan 2020, 13:49
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Bunuel wrote:

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))


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: : [Px - (Px - Dx)]/(P)(P - D)
Simplify numerator to get: : (Dx)/(P)(P - D)

Answer: D

Originally posted by BrentGMATPrepNow on 24 Apr 2018, 06:53.
Last edited by BrentGMATPrepNow on 19 Jan 2020, 13:49, edited 1 time in total.
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Ankur9
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Re: P persons have decided to rent a van to tour while on holidays. The pr [#permalink] New post   24 Nov 2014, 08:11
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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.
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Re: P persons have decided to rent a van to tour while on holidays. The pr [#permalink] New post   24 Nov 2014, 09:45
The answer is D.
x/P-D - x/P = Dx/P(P-D)
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Re: P persons have decided to rent a van to tour while on holidays. The pr [#permalink] New post   24 Nov 2014, 10:46
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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
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Re: P persons have decided to rent a van to tour while on holidays. The pr [#permalink] New post   24 Nov 2014, 20:48
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 \(= \frac{x}{p-d} - \frac{x}{p} = x(\frac{1}{p-d} - \frac{1}{p}) = x * \frac{p-p+d}{p(p-d)} = \frac{xd}{p(p-d)}\)
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Re: P persons have decided to rent a van to tour while on holidays. The pr [#permalink] New post   25 Nov 2014, 06:35
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
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Re: P persons have decided to rent a van to tour while on holidays. The pr [#permalink] New post   25 Apr 2018, 16:42
Expert Reply
Bunuel wrote:

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))


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/[P(P-D)] - x(P-D)/[P(P-D)]

[xP - x(P-D)]/[P(P-D)] = xD/[P(P-D)]

Answer: D
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P persons have decided to rent a van to tour while on holidays. The pr [#permalink] New post   24 May 2021, 09:44
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 $.' Only 'D' results in 1$.
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Re: P persons have decided to rent a van to tour while on holidays. The pr [#permalink] New post   20 Apr 2024, 09:10
Hello from the GMAT Club BumpBot!

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Re: P persons have decided to rent a van to tour while on holidays. The pr [#permalink]
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