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A roller coaster park offers two types of passes. Pass A costs $100 an

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A roller coaster park offers two types of passes. Pass A costs $100 an  [#permalink]

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New post 02 Jan 2018, 23:43
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A
B
C
D
E

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  65% (hard)

Question Stats:

56% (02:26) correct 44% (02:21) wrong based on 84 sessions

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A roller coaster park offers two types of passes. Pass A costs $100 and entitles its holder up to 10 rides at no extra cost, and every ride in excess of 10 at a cost of $5 per ride. Pass B costs $10 and entitles its holder to one ride at no cost and each extra ride for $9. What is the least number of rides taken that would make Pass A a better deal than Pass B?

A. 13
B. 12
C. 11
D. 10
E. 9

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A roller coaster park offers two types of passes. Pass A costs $100 an  [#permalink]

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New post 04 Jan 2018, 11:19
Bunuel wrote:
A roller coaster park offers two types of passes. Pass A costs $100 and entitles its holder up to 10 rides at no extra cost, and every ride in excess of 10 at a cost of $5 per ride. Pass B costs $10 and entitles its holder to one ride at no cost and each extra ride for $9. What is the least number of rides taken that would make Pass A a better deal than Pass B?

A. 13
B. 12
C. 11
D. 10
E. 9


Let after \(n\) rides Cost of Pass A \(<\) Cost of Pass B

\(=>100+(n-10)*5<10+(n-1)*9\)

\(=>4n>49 => n>12.25\)

Therefore at \(n=13\), Pass A is better deal

Option A

—————————————-
Another method would be to work through the options
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Re: A roller coaster park offers two types of passes. Pass A costs $100 an  [#permalink]

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New post 04 Jan 2018, 12:04
A .. for Ride A — after 13 rides 115 is total cost
For ride b — after 13 rides 118


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A roller coaster park offers two types of passes. Pass A costs $100 an  [#permalink]

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New post 04 Jan 2018, 15:32
Bunuel wrote:
A roller coaster park offers two types of passes. Pass A costs $100 and entitles its holder up to 10 rides at no extra cost, and every ride in excess of 10 at a cost of $5 per ride. Pass B costs $10 and entitles its holder to one ride at no cost and each extra ride for $9. What is the least number of rides taken that would make Pass A a better deal than Pass B?

A. 13
B. 12
C. 11
D. 10
E. 9

Answer choices can be used if setting up the inequality is difficult.

Pass A: $100 for 10 rides; $5 each after 10 rides

Pass B: $10 for 1 ride; $9 each after 1 ride

Start with C to get a benchmark.

Answer C) 11 rides
Pass A: 10 rides = $100. +1 ride = $5
Pass A Total: $105
Pass B: 1 ride= $10. Plus 10 rides * $9 = $90
Pass B total: $100

11 rides is too few. Even at $9 per extra ride, for 11 rides, Pass B equals the cost of Pass A.

We need more rides so that the $9 per ride vs. $5 per ride will have an effect (will make B more costly than A). Eliminate answers D and E

Answer B) 12 rides
Use Answer C cost for each (11 rides) + cost of one more ride (=12 rides)

For A, cost of 11=$105, + $5*(1 more ride): $110
For B, cost of 11=$100, + $9*(1 more ride): $109

Pass B is still a better deal than Pass A. By POE, the answer is A. Check:

Answer A) 13 rides
For A, add $5 to cost in answer B (+1 ride): $115
For B, add $9 to cost in answer B: $118
Pass B cost > Pass A cost at 13 rides

ANSWER A
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Re: A roller coaster park offers two types of passes. Pass A costs $100 an  [#permalink]

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New post 09 Feb 2019, 11:31
Bunuel wrote:
A roller coaster park offers two types of passes. Pass A costs $100 and entitles its holder up to 10 rides at no extra cost, and every ride in excess of 10 at a cost of $5 per ride. Pass B costs $10 and entitles its holder to one ride at no cost and each extra ride for $9. What is the least number of rides taken that would make Pass A a better deal than Pass B?

A. 13
B. 12
C. 11
D. 10
E. 9


Better deal would mean that the difference between Pass A and Pass B is the maximum for number of rides

Pass A, 10 free rides , after that $5 per ride
Pass B, 1 free ride, after that $9 per ride

From C 105 to 109, difference is not that much

From A 100+15, Pass B = 10 + 14*9 = 136

So one will be able to enjoy more rides with Pass A
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Re: A roller coaster park offers two types of passes. Pass A costs $100 an   [#permalink] 09 Feb 2019, 11:31
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