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Engineer1
Joined: 01 Jan 2014
Last visit: 15 Jun 2025
Posts: 207
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Given Kudos: 457
Location: United States (IN)
Concentration: Strategy, Finance
Schools: Booth (Chicago) (A$)
13 Jan 2024, 20:11
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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]
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]
chetan2u KarishmaB MartyMurray
Hi All, I did it correctly in my practice test 6. And I understand that in 5.5 miles, it would be 11 half miles, and in 5.7 it will be 12 half miles.
I also solved the kind of problems before similar to the sentence below, but just not together as it is in this problem. I got the answer of my calculation as E, so I checked it. But I could not figure out where the below sentence fit in. Is it because 5.7 means 6? Well, even without this sentence, the problem does not change, I guess. Any clarification is highly appreciated.
Thank you!
for every number x, [ x ] is defined to be the least integer greater than or equal to x,
13 Jan 2024, 20:46
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Engineer1
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]
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]
chetan2u KarishmaB MartyMurray
Hi All, I did it correctly in my practice test 6. And I understand that in 5.5 miles, it would be 11 half miles, and in 5.7 it will be 12 half miles.
I also solved the kind of problems before similar to the sentence below, but just not together as it is in this problem. I got the answer of my calculation as E, so I checked it. But I could not figure out where the below sentence fit in. Is it because 5.7 means 6? Well, even without this sentence, the problem does not change, I guess. Any clarification is highly appreciated.
Thank you!
for every number x, [ x ] is defined to be the least integer greater than or equal to x,
It is because r need not be an integer.
Say he traveled 0.6 miles. The cost he incurred is 2$ as fixed charge and 0.75$ for first 0.5 miles and another 0.75$ for remaining 0.1 miles.
Total becomes 2+2*0.75 = 3.5$
Now, if we did not have [x], the answer would be 2+0.75*(2*0.6) = 2.9$, which will be wrong.
The answer is 2+0.75[2*0.6] = 2+0.75*2 = 3.5$
So, [] is ensuring that you have miles in multiples of 1/2 mile.
11 Jun 2025, 11:28
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Instead of going the route of formula, take a random number, lets say 2.1 miles.
To get the number of half miles in 2.1, multiply it by 2, which gives 4.2, Now [4.2] is the integer GREATER than of EQUAL to 4.2 which will be 5, thus total charge is 2+ 0.75[2r]
Pitfall answer. If we take [r] first and then convert to half miles, then here 2.1 becomes 3 and half miles will be 6, which is not what the question stem is asking for.
Hope I am able to clarify.
To get the number of half miles in 2.1, multiply it by 2, which gives 4.2, Now [4.2] is the integer GREATER than of EQUAL to 4.2 which will be 5, thus total charge is 2+ 0.75[2r]
Pitfall answer. If we take [r] first and then convert to half miles, then here 2.1 becomes 3 and half miles will be 6, which is not what the question stem is asking for.
Hope I am able to clarify.
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]
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]
