It is currently 12 Sep 2026, 12:45

Toolkit

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

Request Expert Reply

Confirm Cancel

Sep 15
Live Online Class with Top GMAT Expert Rich Zwelling
07:00 PM EDT
-
09:00 PM EST
Elite scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Tues/Thurs Sept. 15, 2026 - Nov. 15, 2027, 7:00pm-9:00pm EST
Sep 21
Live Online Bootcamp Class with Top GMAT Expert Chris Peckover
07:00 PM EDT
-
10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included! Class starts Mon, Tues, Wed, Thur, Fri Sept. 21, 2026 - Oct. 9, 2027, 7:00pm-10:00pm EST

Back to Forum

Create Topic

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

1 2 3

lpetroski

Joined: 30 Dec 2015

Last visit: 07 Oct 2019

Posts: 179

Location: United States

Concentration: Strategy, Organizational Behavior

Schools: Judge"18 (WD) LBS '19 (A) INSEAD Jan'18 (M)

GPA: 3.88

WE:Business Development (Hospitality and Tourism)

Products:

Schools: Judge"18 (WD) LBS '19 (A) INSEAD Jan'18 (M)

Posts: 179

28 Mar 2016, 07:20

00:00

Start Timer

Pause Timer

Resume Timer

Show Answer

Hide

Show

History

Official Answer and Stats are available only to registered users. Register/Login.

Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

60% (02:03) correct

40% (02:05) wrong

based on 2925 sessions

History

Date

Time

Result

Not Attempted Yet

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 Answer

Official Answer

Official Answer and Stats are available only to registered users. Register/Login.

If this question felt shaky, try an adaptive mini quiz of similar problems in GMAT Club Forum Quiz →. Free plan gives 5 questions per day.

Kudos

289

Bookmarks

Most Helpful Reply

chetan2u

GMAT Expert

Joined: 02 Aug 2009

Last visit: 12 Sep 2026

Posts: 11,292

Status:Math and DI Expert

Location: India

Concentration: Human Resources, General Management

GMAT Focus 1: 735 Q90 V89 DI81 Verified score

Products:

Expert

Expert reply

GMAT Focus 1: 735 Q90 V89 DI81 Verified score

Posts: 11,292

28 Mar 2016, 07:37

lpetroski

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

_________________

Chetan Sharma,
1. Absolute modulus 2. Fractions 3. Percentage increase 4. Combinations

Signature Read More

Kudos

Bookmarks

Bunuel

Math Expert

Joined: 02 Sep 2009

Last visit: 12 Sep 2026

Posts: 113,479

Products:

Expert

Expert reply

Posts: 113,479

02 May 2016, 02:17

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

_________________

New to the GMAT Club?

Question Bank

Bunuel's Signature Collection

Reading Comprehension

Ultimate Quant Guide

All You Need for Quant

Quantitative

Verbal

Signature Read More

Kudos

Bookmarks

Nevernevergiveup

Retired Moderator

Joined: 18 Sep 2014

Last visit: 20 Aug 2023

Posts: 997

Location: India

Products:

Posts: 997

28 Oct 2016, 22:33

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:

as per the question charges= $2.00$ + $0.75*(4.5*2)$ = $$2.00$+ $$6.75$

Now let go to options

A. 2.00 + [ $\frac{0.75r}{2}$ ]

Since this value does not match with that of above one, this is incorrect.

B. 2.00 + 0.75[ $\frac{r}{2}$ ]

Since this value does not match with that of above one, this is incorrect.

C. 2.00 + 0.75[ r ]

Since this value does not match with that of above one, this is incorrect.

D. 2.00 + [1.5r ]

Since this value does not match with that of above one, this is incorrect.

E. 2.00 + 0.75 [ 2r]

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

Kudos

Bookmarks

General Discussion

smartyman

Joined: 27 Jul 2011

Last visit: 21 Jul 2017

Posts: 38

05 Apr 2016, 13:38

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)

Kudos

Bookmarks

paularagauskas

Joined: 15 Oct 2015

Last visit: 12 May 2016

Posts: 1

30 Apr 2016, 10:28

Kudos

Bookmarks

riteshpatnaik

Joined: 05 Jan 2015

Last visit: 19 Jun 2021

Posts: 48

Location: United States

WE:Consulting (Consulting)

Posts: 48

10 Jul 2016, 23:00

chetan2u

lpetroski

Hi, Thanks for such a brilliant explanation. One doubt how no of 1/2 miles= 2r..

Kudos

Bookmarks

heena.makhijani

Joined: 25 May 2016

Last visit: 20 Nov 2017

Posts: 2

GMAT 1: 570 Q44 V25 Verified score

Posts: 2

19 Oct 2016, 05:45

riteshpatnaik

chetan2u

lpetroski

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!

Kudos

Bookmarks

Prashant420

Joined: 13 Sep 2016

Last visit: 29 Nov 2017

Posts: 1

15 Oct 2017, 02:54

lpetroski

Hi EMPOWERgmatRichC Can you please help me here with Test It ? Thank you!

Kudos

Bookmarks

Poorvasha

Joined: 11 Jun 2017

Last visit: 16 Apr 2026

Posts: 56

24 Nov 2017, 04:05

Prashant420

lpetroski

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.

Kudos

Bookmarks

EMPOWERgmatRichC

Major Poster

Joined: 19 Dec 2014

Last visit: 31 Dec 2023

Posts: 21,775

Status:GMAT Assassin/Co-Founder

Affiliations: EMPOWERgmat

Location: United States (CA)

GMAT 1: 800 Q51 V49 Verified score

GRE 1: Q170 V170 Verified score

Expert

Expert reply

GMAT 1: 800 Q51 V49 Verified score

GRE 1: Q170 V170 Verified score

Posts: 21,775

07 Dec 2017, 14:17

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

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

Kudos

Bookmarks

Eulerelements

Joined: 08 Dec 2017

Last visit: 12 May 2024

Posts: 10

08 Dec 2017, 22:43

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.

Posted from my mobile device

Kudos

Bookmarks

gayathrikeerthanas

Joined: 23 Jan 2018

Last visit: 09 Oct 2019

Posts: 30

Location: India

Concentration: General Management, Marketing

Schools: HEC Sept19 intake (D) ESADE '21 (A)

GMAT 1: 710 Q49 V39 Verified score

GPA: 3.45

WE:Analyst (Computer Software)

Schools: HEC Sept19 intake (D) ESADE '21 (A)

GMAT 1: 710 Q49 V39 Verified score

Posts: 30

12 Sep 2018, 13:01

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.

Quote:

as per the question charges= $2.00$ + $0.75*(4.5*2)$ = $$2.00$+ $$6.75$

Now let go to options

A. 2.00 + [ $\frac{0.75r}{2}$ ]

Since this value does not match with that of above one, this is incorrect.

B. 2.00 + 0.75[ $\frac{r}{2}$ ]

Since this value does not match with that of above one, this is incorrect.

C. 2.00 + 0.75[ r ]

Since this value does not match with that of above one, this is incorrect.

D. 2.00 + [1.5r ]

Since this value does not match with that of above one, this is incorrect.

E. 2.00 + 0.75 [ 2r]

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

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.

Kudos

Bookmarks

gmexamtaker1

Joined: 16 Jul 2018

Last visit: 13 Feb 2023

Posts: 206

Products:

Posts: 206

22 Nov 2019, 08:04

EMPOWERgmatRichC

Show Spoiler

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

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?

Kudos

Bookmarks

EMPOWERgmatRichC

Major Poster

Joined: 19 Dec 2014

Last visit: 31 Dec 2023

Posts: 21,775

Status:GMAT Assassin/Co-Founder

Affiliations: EMPOWERgmat

Location: United States (CA)

GMAT 1: 800 Q51 V49 Verified score

GRE 1: Q170 V170 Verified score

Expert

Expert reply

GMAT 1: 800 Q51 V49 Verified score

GRE 1: Q170 V170 Verified score

Posts: 21,775

22 Nov 2019, 10:45

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

Kudos

Bookmarks

gmexamtaker1

Joined: 16 Jul 2018

Last visit: 13 Feb 2023

Posts: 206

Products:

Posts: 206

22 Nov 2019, 10:55

EMPOWERgmatRichC

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 )

Kudos

Bookmarks

EMPOWERgmatRichC

Major Poster

Joined: 19 Dec 2014

Last visit: 31 Dec 2023

Posts: 21,775

Status:GMAT Assassin/Co-Founder

Affiliations: EMPOWERgmat

Location: United States (CA)

GMAT 1: 800 Q51 V49 Verified score

GRE 1: Q170 V170 Verified score

Expert

Expert reply

GMAT 1: 800 Q51 V49 Verified score

GRE 1: Q170 V170 Verified score

Posts: 21,775

22 Nov 2019, 14:46

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...

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

Kudos

Bookmarks

jkbk1732

Joined: 06 Mar 2018

Last visit: 30 May 2020

Posts: 41

03 Dec 2019, 02:55

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.

Quote:

as per the question charges= $2.00$ + $0.75*(4.5*2)$ = $$2.00$+ $$6.75$

Now let go to options

A. 2.00 + [ $\frac{0.75r}{2}$ ]

1.00

Since this value does not match with that of above one, this is incorrect.

B. 2.00 + 0.75[ $\frac{r}{2}$ ]

Since this value does not match with that of above one, this is incorrect.

C. 2.00 + 0.75[ r ]

Since this value does not match with that of above one, this is incorrect.

D. 2.00 + [1.5r ]

Since this value does not match with that of above one, this is incorrect.

E. 2.00 + 0.75 [ 2r]

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

The highlighted numbers in red are rounded down. According to question, it should be rounded up.

[6.75]=7 and not 6

Kudos

Bookmarks

ScottTargetTestPrep

Target Test Prep Representative

Joined: 14 Oct 2015

Last visit: 11 Sep 2026

Posts: 22,738

Status:Founder & CEO

Affiliations: Target Test Prep

Location: United States (CA)

Expert

Expert reply

Posts: 22,738

13 Feb 2020, 05:33

lpetroski

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

_________________

Scott Woodbury-Stewart | Founder and CEO | [email protected]

OnDemand, the Most Comprehensive Video Course
Try 5 Days of Self-Study for FREE
Get 2 Extra Weeks for FREE
130-Score Improvement Guarantee

See why Target Test Prep is the top rated GMAT course on GMAT Club. Read Our Reviews

Signature Read More

Kudos

Bookmarks

Nityanshu1990

Joined: 11 Sep 2019

Last visit: 28 Mar 2022

Posts: 16

GMAT 1: 670 Q49 V33 Verified score

Posts: 16

06 Jul 2020, 06:36

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.

Quote:

as per the question charges= $2.00$ + $0.75*(4.5*2)$ = $$2.00$+ $$6.75$

Now let go to options

A. 2.00 + [ $\frac{0.75r}{2}$ ]

Since this value does not match with that of above one, this is incorrect.

B. 2.00 + 0.75[ $\frac{r}{2}$ ]

Since this value does not match with that of above one, this is incorrect.

C. 2.00 + 0.75[ r ]

Since this value does not match with that of above one, this is incorrect.

D. 2.00 + [1.5r ]

Since this value does not match with that of above one, this is incorrect.

E. 2.00 + 0.75 [ 2r]

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

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

Kudos

Bookmarks