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P persons have decided to rent a van to tour while on

Expert replies
by AAPL » Tue Apr 24, 2018 4:57 am
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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 OA is D.

Initially, share per person = x/P

Total share of D person = (Dx)/P

When D person left then this share has to be divided equally among remaining P-D persons.

Thus additional share is (Dx)/(P(P-D)). Option D.

Has anyone another approach to solve this PS question? Regards!
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Source: — Problem Solving |

by GMATGuruNY » Tue Apr 24, 2018 5:17 am
AAPL wrote: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))
Let x = $10 and P = 10 people.
Since 10 people plan to split the $10 cost, the expected cost per person = (total cost)/(number of people) = 10/10 = $1.
Let D=9, implying that 9 of the 10 people cancel, with the result that the one remaining person must pay the entire $10.
Since the one remaining person must pay $10 instead of $1, the increase in the cost for this person = $9.
Now plug x=10, P=10 and D=9 into the answers to see which yields the additional amount paid by the one remaining person ($9).
Only D works:
Dx/[(P(P -D)] = (9*10)/[(10)(10-9)] = 9.

The correct answer is D.
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by Brent@GMATPrepNow » Tue Apr 24, 2018 5:48 am
AAPL wrote: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

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Scott@TargetTestPrep » Wed Apr 25, 2018 3:43 pm
AAPL wrote: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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