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For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 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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E
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For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 28 Mar 2016, 08:37
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lpetroski
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]
Show more

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 02 May 2016, 03:17
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paularagauskas
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
Show more

Some function [] rounds UP a number to the nearest integer. For example [1.5]=2, [2]=2, [-1.5]=-1, ...

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

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
https://gmatclub.com/forum/the-greatest-integer-function-223595.html#p1755424
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For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 05 Apr 2016, 14:38
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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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For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 30 Apr 2016, 11:28
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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
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For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 11 Jul 2016, 00:00
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chetan2u
lpetroski
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
Show more

Hi, Thanks for such a brilliant explanation. One doubt how no of 1/2 miles= 2r..
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For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 19 Oct 2016, 06:45
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chetan2u
lpetroski
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..
Show more


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 15 Oct 2017, 03:54
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lpetroski
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]
Show more

Hi EMPOWERgmatRichC Can you please help me here with Test It ? Thank you!
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For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 24 Nov 2017, 05:05
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Prashant420
lpetroski
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!
Show more

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

Final Answer:
Show Spoiler
E


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For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 08 Dec 2017, 23:43
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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.

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For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 12 Sep 2018, 14:01
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Nevernevergiveup
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
https://gmatclub.com/forum/the-greatest-integer-function-223595.html#p1755424
Show more



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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For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 22 Nov 2019, 09:04
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EMPOWERgmatRichC
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:
Show Spoiler
E


GMAT assassins aren't born, they're made,
Rich
Show more

Hi Rich,
Instead of using a decimal I picked 2 and 4 as the TEST it numbers (I tested 4 except for 2, because 2 was valid for both D and E) was my approach incorrect? Was I lucky to get the correct answer? Is it necessary to use decimals in this specific problem?
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For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 22 Nov 2019, 11:45
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Hi UNSTOPPABLE12,

If you chose R=4, then BOTH Answers D and E would have been a match for what you were looking for. Can you show me your work for those two calculations?

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For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 22 Nov 2019, 11:55
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Hi UNSTOPPABLE12,

If you chose R=4, then BOTH Answers D and E would have been a match for what you were looking for. Can you show me your work for those two calculations?

GMAT assassins aren't born, they're made,
Rich
Show more

Yes you are right Rich , it turns up I got extremely lucky on this one, making a calculation mistake on D and picking E. Could you please explain why in your example you decided to choose 2.1 and why did you afterwards multiplied it by 5? (I have read your explanation but still haven't understood the reason )
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Hi UNSTOPPABLE12,

If you start off by looking at the answer choices (before you read the prompt), you might recognize that, algebraically-speaking, Answers D and E appear to be the SAME ANSWER. That's 'weird' for a GMAT question - and without looking at the prompt, that pattern would either mean that neither of those answers is correct OR that that there's some 'twist' to the question that means the "format" of the answer will matter.

The prompt refers to 'fractions of a 1/2 mile' - and THAT means that the math involved is not the typical arithmetic/algebra that we'll see in most prompts. I want to reiterate that the prompt LITERALLY states "....FRACTIONS....", so that's a big clue to TEST a non-integer.

If we TEST R = 2.1

According to the prompt, for a 2.1-mile trip, we will be dealing with 4 "full 1/2 miles" and 1 "fraction of a 1/2 mile" (re: the extra 0.1 miles). Each of those 5 increments costs $0.75. Thus, the charge would be...

$2 + $0.75(5) = $5.75

Based on how we are supposed to use the [ x ] symbol, there's only one answer that matches...

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For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 03 Dec 2019, 03:55
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Nevernevergiveup
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
https://gmatclub.com/forum/the-greatest-integer-function-223595.html#p1755424
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The highlighted numbers in red are rounded down. According to question, it should be rounded up.

[6.75]=7 and not 6
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For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 13 Feb 2020, 06:33
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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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Let r = 1.1 = 1 + 0.1. Since the first 1 mile consists of two 1/2 miles and the last 0.1 mile consists of a fraction of 1/2 mile, we need to pay 3 times $0.75 plus the $2.00 fixed fee. That is, we need to pay 2 + (0.75)(3) = 2 + 2.25 = $4.25.

Now let’s see which answer choice also gives us $4.25 when we substitute 1.1 for r.

A. 2.00 + [0.75r/2] = 2 + [0.75(1.1)/2] = 2 + 1 = $3.00 (notice that 0.75(1.1)/2 is some value between 0 and 1, thus [0.75(1.1)/2] = 1)

B. 2.00 + 0.75[r/2] = 2 + 0.75[1.1/2] = 2 + 0.75 = $2.75 (again notice 1.1/2 is some value between 0 and 1)

C. 2.00 + 0.75[r] = 2 + 0.75[1.1] = 2 + 0.75(2) = $3.50

D. 2.00 + [1.5r] = 2 + [1.5(1.1)] = 2 + 2 = $4.00 (notice 1.5(1.1) is some value between 1 and 2)

We see that none of the first 4 answer choices are correct; therefore, by default, the correct answer must be E. However, let’s verify it anyway.

E. 2.00 + 0.75[2r] = 2 + 0.75[2(1.1)] = 2 + 0.75[2.2] = 2 + 0.75(3) = $4.25

Answer: E
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For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 06 Jul 2020, 07:36
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Nevernevergiveup
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
https://gmatclub.com/forum/the-greatest-integer-function-223595.html#p1755424
Show more

Correct me if i am horrendously wrong
Question stem says : [ x ] is defined to be the least integer greater than or equal to x

How is [1.6875]= 1 and [4.5]= 4
Shouldn't these be 2 and 5 respectively
Please help me out here
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