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

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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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New post 28 Mar 2016, 08:20
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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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New post 28 Mar 2016, 08:37
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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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New post 05 Apr 2016, 14:38
1
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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New post 30 Apr 2016, 11:28
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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New post 02 May 2016, 03:17
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paularagauskas wrote:
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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Some function [] rounds UP a number to the nearest integer. For example [1.5]=2, [2]=2, [-1.5]=-1, ...

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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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New post 02 May 2016, 07:15
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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New post 11 Jul 2016, 00:00
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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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New post 19 Oct 2016, 06:45
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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New post 28 Oct 2016, 23:33
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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 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
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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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New post 15 Oct 2017, 03:54
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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New post 24 Nov 2017, 05:05
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.
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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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New post 07 Dec 2017, 15:17
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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

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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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New post 08 Dec 2017, 23:43
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]

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New post 12 Sep 2018, 14:01
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[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




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.
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Re: For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 &nbs [#permalink] 12 Sep 2018, 14:01
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