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03 Jan 2011, 18:22
3
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Difficulty:

85% (hard)

Question Stats:

54% (03:10) correct 46% (01:55) wrong based on 368 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 _________________ Verbal:new-to-the-verbal-forum-please-read-this-first-77546.html Math: new-to-the-math-forum-please-read-this-first-77764.html Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html ------------------------------------------------------------------------------------------------- Ajit Manager Joined: 21 Jul 2010 Posts: 56 Followers: 1 Kudos [?]: 26 [0], given: 3 Re: The toll for crossing a certain bridge [#permalink] ### Show Tags 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. Anyone? Math Expert Joined: 02 Sep 2009 Posts: 38908 Followers: 7739 Kudos [?]: 106258 [2] , given: 11618 Re: The toll for crossing a certain bridge [#permalink] ### Show Tags 04 Jan 2011, 03:50 2 This post received KUDOS Expert's post 7 This post was BOOKMARKED 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 $$13+2x*0.3<2x*0.75$$ --> $$x>14.4$$ --> $$x_{min}=15$$.

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Re: The toll for crossing a certain bridge [#permalink]

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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 Manager Joined: 18 Oct 2011 Posts: 90 Location: United States Concentration: Entrepreneurship, Marketing GMAT Date: 01-30-2013 GPA: 3.3 Followers: 2 Kudos [?]: 74 [0], given: 0 Re: Arithematic [#permalink] ### Show Tags 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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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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09 Nov 2014, 11:19
make equations!
For what value of x would the following be true:0.75*2*x> 0.3*2*x +13.
x>14.4, or 15 days.
B
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06 Mar 2017, 15:51
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