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# For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75

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Joined: 30 Dec 2015
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For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75 [#permalink]

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28 Mar 2016, 07:20
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53% (01:03) correct 47% (01:09) wrong based on 450 sessions

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For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75 for each 1/2 mile or fraction of 1/2 miles. If, for every number x, [ x ] is defined to be the least integer greater than or equal to x, then which of the following represents the company's charge, in dollars, for a trip that is r miles long?

A. 2.00 + [ $$\frac{0.75r}{2}$$ ]
B. 2.00 + 0.75[ $$\frac{r}{2}$$ ]
C. 2.00 + 0.75[ r ]
D. 2.00 + [1.5r ]
E. 2.00 + 0.75 [ 2r]
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Aug 2009
Posts: 5662
Re: For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75 [#permalink]

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28 Mar 2016, 07:37
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lpetroski wrote:
For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75 for each 1/2 mile or fraction of 1/2 miles. If, for every number x, [ x ] is defined to be the least integer greater than or equal to x, then which of the following represents the company's charge, in dollars, for a trip that is r miles long?

A. 2.00 + [ $$\frac{0.75r}{2}$$ ]
B. 2.00 + 0.75[ $$\frac{r}{2}$$ ]
C. 2.00 + 0.75[ r ]
D. 2.00 + [1.5r ]
E. 2.00 + 0.75 [ 2r]

Hi,
Fixed fee= 2.00
fee dependent on miles = 0.75 per 1/2 mile or fraction there off
no of miles = r
no of 1/2 miles= 2r..
and to convert 2r into integer mile [2r]..
total cost on miles= 0.75[2r]..
total = 2.00 + 0.75 [ 2r]

E
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Re: For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75 [#permalink]

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05 Apr 2016, 13:38
Use substitution,
If
r=3.7; [r]=4
r=3.2; [r]=4

Therefore
Charges $0.75 = 0.5 mile$ y = 4 miles

y = (4 * $0.75 ) / 0.5 = r * 0.75 *2 Therefore Total = 2 + 0.75(2r) Intern Joined: 15 Oct 2015 Posts: 2 Re: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 [#permalink] ### Show Tags 30 Apr 2016, 10:28 Hello, Can someone please try to explain to me and an easy way? I didn't understand the explanations. I appreciate any help !! The part that says "for every number x, [x] is defined to be the least integer greater than or equal to x" confuses me. Thank you ! Paula Posted from my mobile device Math Expert Joined: 02 Sep 2009 Posts: 43896 Re: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 [#permalink] ### Show Tags 02 May 2016, 02:17 Expert's post 8 This post was BOOKMARKED Intern Joined: 15 Oct 2015 Posts: 2 Re: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 [#permalink] ### Show Tags 02 May 2016, 06:15 Bunuel thank you so much! That was very helpful!! Intern Joined: 05 Jan 2015 Posts: 45 Location: United States WE: Consulting (Consulting) Re: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 [#permalink] ### Show Tags 10 Jul 2016, 23:00 1 This post received KUDOS chetan2u wrote: lpetroski wrote: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 for each 1/2 mile or fraction of 1/2 miles. If, for every number x, [ x ] is defined to be the least integer greater than or equal to x, then which of the following represents the company's charge, in dollars, for a trip that is r miles long? A. 2.00 + [ $$\frac{0.75r}{2}$$ ] B. 2.00 + 0.75[ $$\frac{r}{2}$$ ] C. 2.00 + 0.75[ r ] D. 2.00 + [1.5r ] E. 2.00 + 0.75 [ 2r] Hi, Fixed fee= 2.00 fee dependent on miles = 0.75 per 1/2 mile or fraction there off no of miles = r no of 1/2 miles= 2r.. and to convert 2r into integer mile [2r].. total cost on miles= 0.75[2r].. total = 2.00 + 0.75 [ 2r] E Hi, Thanks for such a brilliant explanation. One doubt how no of 1/2 miles= 2r.. Intern Joined: 25 May 2016 Posts: 2 GMAT 1: 570 Q44 V25 Re: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 [#permalink] ### Show Tags 19 Oct 2016, 05:45 riteshpatnaik wrote: chetan2u wrote: lpetroski wrote: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 for each 1/2 mile or fraction of 1/2 miles. If, for every number x, [ x ] is defined to be the least integer greater than or equal to x, then which of the following represents the company's charge, in dollars, for a trip that is r miles long? A. 2.00 + [ $$\frac{0.75r}{2}$$ ] B. 2.00 + 0.75[ $$\frac{r}{2}$$ ] C. 2.00 + 0.75[ r ] D. 2.00 + [1.5r ] E. 2.00 + 0.75 [ 2r] Hi, Fixed fee= 2.00 fee dependent on miles = 0.75 per 1/2 mile or fraction there off no of miles = r no of 1/2 miles= 2r.. and to convert 2r into integer mile [2r].. total cost on miles= 0.75[2r].. total = 2.00 + 0.75 [ 2r] E Hi, Thanks for such a brilliant explanation. One doubt how no of 1/2 miles= 2r.. If 1/2 a mile is r then a full mile will be 2r. Hope this helps! Retired Moderator Joined: 18 Sep 2014 Posts: 1199 Location: India For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 [#permalink] ### Show Tags 28 Oct 2016, 22:33 1 This post received KUDOS 1 This post was BOOKMARKED I got it wrong after spending a lot of time for a mere calculation mistake. That too this was the first question in my practice test. I hope my solution helps others. Its easy to solve if we pick the numbers. Since it is nowhere mentioned that r is an integer, we can take r=4.5 miles for our convenience and apply back-solving approach. Quote: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 for each 1/2 mile or fraction of 1/2 miles. If, for every number x, [ x ] is defined to be the least integer greater than or equal to x, then which of the following represents the company's charge, in dollars, for a trip that is r miles long? as per the question charges= $$2.00$$ + $$0.75*(4.5*2)$$ = $$2.00$$+ $$6.75$$ Now let go to options A. 2.00 + [ $$\frac{0.75r}{2}$$ ] = 2.00 + [ $$\frac{(0.75*4.5)}{2}$$ ] = 2.00 + [1.6875] = 2.00 + 1.00 Since this value does not match with that of above one, this is incorrect. B. 2.00 + 0.75[ $$\frac{r}{2}$$ ] = 2.00 + 0.75[ $$\frac{4.5}{2}$$ ] = 2.00 + 0.75[2.25] = 2.00 + $$0.75*2$$ = 2.00 + 1.5 Since this value does not match with that of above one, this is incorrect. C. 2.00 + 0.75[ r ] = 2.00 + 0.75[4.5] = 2.00 + 0.75*4 = 2.00 + 3.00 Since this value does not match with that of above one, this is incorrect. D. 2.00 + [1.5r ] = 2.00 + [1.5 * 4.5 ] = 2.00 + [6.75] = 2.00 + 6 Since this value does not match with that of above one, this is incorrect. E. 2.00 + 0.75 [ 2r] = 2.00 + 0.75[2*4.5] = 2.00 + 0.75[9] = 2.00 + 0.75*9 = 2.00 + 6.75 This is the value we got above in pre-analysis. Refer below link for info on greatest integer function http://gmatclub.com/forum/the-greatest-integer-function-223595.html#p1755424 _________________ The only time you can lose is when you give up. Try hard and you will suceed. Thanks = Kudos. Kudos are appreciated http://gmatclub.com/forum/rules-for-posting-in-verbal-gmat-forum-134642.html When you post a question Pls. Provide its source & TAG your questions Avoid posting from unreliable sources. My posts http://gmatclub.com/forum/beauty-of-coordinate-geometry-213760.html#p1649924 http://gmatclub.com/forum/calling-all-march-april-gmat-takers-who-want-to-cross-213154.html http://gmatclub.com/forum/possessive-pronouns-200496.html http://gmatclub.com/forum/double-negatives-206717.html http://gmatclub.com/forum/the-greatest-integer-function-223595.html#p1721773 https://gmatclub.com/forum/improve-reading-habit-233410.html#p1802265 Intern Joined: 13 Sep 2016 Posts: 2 Re: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 [#permalink] ### Show Tags 15 Oct 2017, 02:54 lpetroski wrote: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 for each 1/2 mile or fraction of 1/2 miles. If, for every number x, [ x ] is defined to be the least integer greater than or equal to x, then which of the following represents the company's charge, in dollars, for a trip that is r miles long? A. 2.00 + [ $$\frac{0.75r}{2}$$ ] B. 2.00 + 0.75[ $$\frac{r}{2}$$ ] C. 2.00 + 0.75[ r ] D. 2.00 + [1.5r ] E. 2.00 + 0.75 [ 2r] Hi EMPOWERgmatRichC Can you please help me here with Test It ? Thank you! Manager Joined: 11 Jun 2017 Posts: 84 Re: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 [#permalink] ### Show Tags 24 Nov 2017, 04:05 Prashant420 wrote: lpetroski wrote: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 for each 1/2 mile or fraction of 1/2 miles. If, for every number x, [ x ] is defined to be the least integer greater than or equal to x, then which of the following represents the company's charge, in dollars, for a trip that is r miles long? A. 2.00 + [ $$\frac{0.75r}{2}$$ ] B. 2.00 + 0.75[ $$\frac{r}{2}$$ ] C. 2.00 + 0.75[ r ] D. 2.00 + [1.5r ] E. 2.00 + 0.75 [ 2r] Hi EMPOWERgmatRichC Can you please help me here with Test It ? Thank you! Hi Prashant420, Suppose if the number of miles covered are 5.2. Each 1/2 mile or fraction of half costs 0.75$. 5 miles consist of 10 half miles and 0.2 would account for another half. Total 11 halves*0.75$=$8.25 (for miles covered). Total cost = 10.25$. This can be obtained through option E: 2+0.75[2*5.2] = 2+0.75*[10.4] = 2+0.75*11 =$10.25.

Hope this helps.
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Re: For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75 [#permalink]

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07 Dec 2017, 14:17
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Expert's post
Hi All,

This question can be solved by TESTing Values (although since the prompt discusses 'fractions of a 1/2 mile' iit's 'hinting' that we should be thinking about non-integers...

Let's TEST R = 2.1

According to the prompt, for a 2.1-mile trip, the taxi company will charge $2 +$0.75(5) = $5.75 When we plug R = 2.1 into the answers, and we follow the definition of [x], we get.... Answer A: 2 + 1 = 3 NOT a match Answer B: 2 + 1.5 = 3.5 NOT a match Answer C: 2 + 2.25 = 4.25 NOT a match Answer D: 2 + 4 = 6 NOT a match Answer E: 2 + 3.75 = 5.75 This IS a match Final Answer: [Reveal] Spoiler: E GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75 [#permalink]

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08 Dec 2017, 22:43
Ignoring the least integer part the equation is clearly 2+.75(2r). This can be 2+1.5r as well so it's between d and e. Going 1 mile should cost 1.50. With choice d, it costs 2 so e has to be the answer. One problem with choice d is that whenever one goes an odd number of miles the round up results in an overcharge.

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Re: For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75   [#permalink] 08 Dec 2017, 22:43
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