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

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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 13 Feb 2020, 05:33
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]


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

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New post 06 Jul 2020, 06:36
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[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


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

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New post 06 Jul 2020, 16:43
Hi Nityanshu1990,

Yes - you are correct. The original post that you're referring to is several years old - and a number of posters (including yourself) have caught the error in those calculations.

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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 06 Jul 2020, 17:23
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]

Lets take a value, say r= 3.25
The company charges 2 + 3/(1/2) *0.75 + 0.75= 2+ 0.75*(7)

The answer should be 2 + 0.75*(7)

We can easily see that Choice E is exactly that since 2+ 0.75[2r]= 2+0.75[6.5] = 2+0.75*7
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For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75   [#permalink] 06 Jul 2020, 17:23

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