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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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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]
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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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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)



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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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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
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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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Re: For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 [#permalink]
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02 May 2016, 06:15
Bunuel thank you so much! That was very helpful!!



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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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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..



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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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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!



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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 Oct 2016, 22:33
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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 backsolving 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 preanalysis.Refer below link for info on greatest integer function http://gmatclub.com/forum/thegreatestintegerfunction223595.html#p1755424
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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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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!



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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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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
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 nonintegers... Let's TEST R = 2.1 According to the prompt, for a 2.1mile 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: GMAT assassins aren't born, they're made, Rich
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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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