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The toll for crossing a certain bridge is $0.75 each crossin

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The toll for crossing a certain bridge is $0.75 each crossin [#permalink] New post 03 Jan 2011, 18:22
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38% (02:05) correct 61% (01:27) wrong based on 4 sessions
The toll for crossing a certain bridge is $0.75 each crossing. Drivers who frequently use the bridge may instead purchase a sticker each month for $13.00 and then pay only $0.30 each crossing during that month. If a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day, what is the least value of x for which this driver can save money by using the sticker?

A. 14
B. 15
C. 16
D. 28
E. 29
[Reveal] Spoiler: OA

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Re: The toll for crossing a certain bridge [#permalink] New post 04 Jan 2011, 01:03
I don't get this one. I would do for D. I plugged the number of the OA in my equation but it does not work for me.

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Re: The toll for crossing a certain bridge [#permalink] New post 04 Jan 2011, 03:50
ajit257 wrote:
The toll for crossing a certain bridge is $0.75 each crossing. Drivers who frequently use the bridge may instead purchase a sticker each month for $13.00 and then pay only $0.30 each crossing during that month. If a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day, what is the least value of x for which this driver can save money by using the sticker?
A. 14
B. 15
C. 16
D. 28
E. 29


Cost for the driver for 2x (twice on each of x days) crosses without the sticker will be: 2x*0.75;
Cost for the driver for 2x (twice on each of x days) crosses with the sticker will be: 13+2x*0.3;

Question: what is the least value of x for which 13+2x*0.3<2x*0.75 --> x>14.4 --> x_{min}=15.

Answer: B.
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Re: The toll for crossing a certain bridge [#permalink] New post 04 Jan 2011, 09:16
Savings per crossings = 0.45 (.75-.30)

Saving per crossing x 2 times (crossing bothways) x Number of days >= $13

(.45)2x>=13
.9x>=13
x>14.44

Xmin =15 days
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Arithematic [#permalink] New post 11 Feb 2013, 18:16
The toll for crossing a certain bridge is $0.75 each crossing. Drivers who frequently use
the bridge may instead purchase a sticker each month for $13.00 and then pay only $0.30
each crossing during that month. If a particular driver will cross the bridge twice on each
of x days next month and will not cross the bridge on any other day, what is the least
value of x for which this driver can save money by using the sticker?
A. 14
B. 15
C. 16
D. 28
E. 29
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Re: Arithematic [#permalink] New post 11 Feb 2013, 19:19
Option #1: $0.75/crossing....Cross twice a day = $1.5/day
Option #2: $0.30/crossing....Cross twice a day = $0.6/day + $13 one time charge.

If we go down the list of possible answers, you can quickly see that 14 days will not be worth purchasing the sticker. 1.5x14 (21) is cheaper than 0.6x14 +13 (21.4)...it's pretty close so let's see if one more day will make it worth it... If we raise the number of days to 15, the sticker option looks like a better deal...1.5x15 (22.5) vs 0.6x15 + 13 (22). Answer: B
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Re: Arithematic [#permalink] New post 11 Feb 2013, 22:59
For the given condition,

0.3*2*x+13<0.75*x*2

or

0.6*x+13<1.5*x

or 0.9*x>13

x>130*0.11 = 14.3

Thus x = 15.

B.
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Re: Arithematic [#permalink] New post 12 Feb 2013, 00:47
4112019 wrote:
The toll for crossing a certain bridge is $0.75 each crossing. Drivers who frequently use
the bridge may instead purchase a sticker each month for $13.00 and then pay only $0.30
each crossing during that month. If a particular driver will cross the bridge twice on each
of x days next month and will not cross the bridge on any other day, what is the least
value of x for which this driver can save money by using the sticker?
A. 14
B. 15
C. 16
D. 28
E. 29


Merging similar topics.
_________________

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!


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Re: Arithematic   [#permalink] 12 Feb 2013, 00:47
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