Last visit was: 19 Nov 2025, 13:48 It is currently 19 Nov 2025, 13:48
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
   1   2   3 
avatar
Engineer1
avatar
Joined: 01 Jan 2014
Last visit: 15 Jun 2025
Posts: 201
Own Kudos:
656
Given Kudos: 457
Location: United States (IN)
Concentration: Strategy, Finance
Schools: Booth (Chicago) (A$)
Schools: Booth (Chicago) (A$)
Posts: 201
Kudos: 656
For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 13 Jan 2024, 20:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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


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,
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 15 Nov 2025
Posts: 11,238
Own Kudos:
43,706
 [1]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,238
Kudos: 43,706
 [1]
For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 13 Jan 2024, 20:46
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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]


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,
Show more


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.
User avatar
findingmyself
User avatar
Joined: 06 Apr 2025
Last visit: 19 Nov 2025
Posts: 230
Own Kudos:
157
Given Kudos: 57
Posts: 230
Kudos: 157
For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 11 Jun 2025, 11:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.

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
User avatar
GmatKnightTutor
User avatar
Major Poster
Joined: 31 Jan 2020
Last visit: 01 Nov 2025
Posts: 5,228
Own Kudos:
1,568
Given Kudos: 18
Posts: 5,228
Kudos: 1,568
For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 11 Jun 2025, 22:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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, people, let's get into this!

First, think of a random distance (e.g. 5.4 miles) and manually figure out the cost based on the prompt: $10.25

Then, see which of the options would spit out a similar value, keeping in mind the [x] condition. Remember, we’re looking for an equation that will give us more than $10 so (A), (B), and (C) are clearly out therefore.

When we look at (D) and (E),

(D) spits out 2 + [1.5 x 5.4] or 2 + [8.1]: $11

(E) is the answer therefore and we can also check it: $2 + $0.75 [2 (5.4)] = $2 + 0.75 (11) = $10.25

Note: Being a little extra careful and testing two distance values can be prudent.
User avatar
sujoykrdatta
User avatar
Joined: 26 Jun 2014
Last visit: 19 Nov 2025
Posts: 547
Own Kudos:
1,115
 [1]
Given Kudos: 13
Status:Mentor & Coach | GMAT Q51 | CAT 99.98
GMAT 1: 750 Q51 V39
Expert
Expert reply
GMAT 1: 750 Q51 V39
Posts: 547
Kudos: 1,115
 [1]
For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 29 Oct 2025, 16:49
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Fixed cost is $2
Extra variable pay:
If you cover 1/2 mile, you pay$0.75
If you cover n such 1/2 miles, you pay $0.75n
How many such 1/2 miles did you cover? That is r / (1/2) = 2r times
If 2r is a fractional value, we need the next higher integer, i.e. [2r]
ex. if r = 2.4, number of 1/2 miles = 2.4/(1/2) = 4.8 i.e. 5, which is [4.8]

Total = 2 + 0.75[2r] ... (E)

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
   1   2   3 
Moderators:
Bunuel
Math Expert
105390 posts
Krunaal
Tuck School Moderator
805 posts