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Current Student S
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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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56 00:00

Difficulty:   75% (hard)

Question Stats: 53% (01:54) correct 47% (02:06) wrong based on 442 sessions

### HideShow timer Statistics 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]
Math Expert V
Joined: 02 Aug 2009
Posts: 7763
Re: For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75  [#permalink]

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

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3
2
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
= 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
##### General Discussion
Manager  B
Joined: 27 Jul 2011
Posts: 52
Re: For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75  [#permalink]

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2
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 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 V Joined: 02 Sep 2009 Posts: 56306 Re: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 [#permalink] ### Show Tags 3 13 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 Bunuel thank you so much! That was very helpful!! Intern  B Joined: 05 Jan 2015 Posts: 49 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 1 1 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  B 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 1 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! Intern  B 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 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  B Joined: 11 Jun 2017 Posts: 68 Re: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 [#permalink] ### Show Tags 2 1 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.
EMPOWERgmat Instructor V
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Affiliations: EMPOWERgmat
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Posts: 14603
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75  [#permalink]

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3
1
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: 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 *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** # Rich Cohen Co-Founder & GMAT Assassin Follow Special Offer: Save$75 + GMAT Club Tests Free
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Intern  B
Joined: 08 Dec 2017
Posts: 17
Re: For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75  [#permalink]

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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.

Posted from my mobile device B
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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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1
Nevernevergiveup wrote:
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
= 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

Your approach really helped but just one correction: while eliminating option D you have missed out that it is the least integer greater than or equal to x which in this case is [6.75]=7.

But in any case, the final answer by D is still wrong; E still holds true.

Thank you for the approach! Found it the most helpful.
Intern  B
Joined: 28 Jul 2016
Posts: 1
Re: For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75  [#permalink]

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Can someone explain why not A? Because 0.75 is also a fraction and it needs to be formatted according to the given rule, no? Re: For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75   [#permalink] 17 Mar 2019, 07:33
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