GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 13 Dec 2019, 08:26 ### 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

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

Author Message
TAGS:

### Hide Tags

Current Student S
Joined: 30 Dec 2015
Posts: 187
Location: United States
Concentration: Strategy, Organizational Behavior
GPA: 3.88
WE: Business Development (Hospitality and Tourism)
For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75  [#permalink]

### Show Tags

6
65 00:00

Difficulty:   75% (hard)

Question Stats: 54% (01:54) correct 46% (02:05) wrong based on 514 sessions

### HideShow timer Statistics

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]
Math Expert V
Joined: 02 Aug 2009
Posts: 8310
Re: For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75  [#permalink]

### Show Tags

25
1
16
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]

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
_________________
Retired Moderator G
Joined: 18 Sep 2014
Posts: 1098
Location: India
For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75  [#permalink]

### Show Tags

4
4
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
= 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
##### General Discussion
Intern  B
Joined: 27 Jul 2011
Posts: 49
Re: For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75  [#permalink]

### Show Tags

2
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) Intern  Joined: 15 Oct 2015 Posts: 2 Re: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 [#permalink] ### Show Tags 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 Math Expert V Joined: 02 Sep 2009 Posts: 59721 Re: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 [#permalink] ### Show Tags 4 17 Intern  Joined: 15 Oct 2015 Posts: 2 Re: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 [#permalink] ### Show Tags Bunuel thank you so much! That was very helpful!! Intern  B Joined: 05 Jan 2015 Posts: 49 Location: United States WE: Consulting (Consulting) Re: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 [#permalink] ### Show Tags 1 1 chetan2u wrote: 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] 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.. Intern  B Joined: 25 May 2016 Posts: 2 GMAT 1: 570 Q44 V25 Re: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 [#permalink] ### Show Tags 1 riteshpatnaik wrote: chetan2u wrote: 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] 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! Intern  B Joined: 13 Sep 2016 Posts: 1 Re: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 [#permalink] ### Show Tags 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] Hi EMPOWERgmatRichC Can you please help me here with Test It ? Thank you! Manager  B Joined: 11 Jun 2017 Posts: 62 Re: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 [#permalink] ### Show Tags 2 1 Prashant420 wrote: 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] 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.
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15716
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75  [#permalink]

### Show Tags

3
1
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: GMAT assassins aren't born, they're made, Rich _________________ Intern  B Joined: 08 Dec 2017 Posts: 15 Re: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 [#permalink] ### Show Tags 1 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 ESADE School Moderator B Joined: 23 Jan 2018 Posts: 30 Location: India Concentration: General Management, Marketing GMAT 1: 710 Q49 V39 GPA: 3.45 WE: Analyst (Computer Software) Re: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 [#permalink] ### Show Tags 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 = 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 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. Intern  B Joined: 28 Jul 2016 Posts: 1 Re: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 [#permalink] ### Show Tags Can someone explain why not A? Because 0.75 is also a fraction and it needs to be formatted according to the given rule, no? Manager  B Joined: 16 Jul 2018 Posts: 69 Re: For each trip, a taxi company charges a fixed fee of$2.00 plus $0.75 [#permalink] ### Show Tags EMPOWERgmatRichC wrote: 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

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?
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15716
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75  [#permalink]

### Show Tags

1
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
_________________
Manager  B
Joined: 16 Jul 2018
Posts: 69
Re: For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75  [#permalink]

### Show Tags

EMPOWERgmatRichC wrote:
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

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 )
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15716
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75  [#permalink]

### Show Tags

1
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
_________________
Intern  S
Joined: 06 Mar 2018
Posts: 43
Re: For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75  [#permalink]

### Show Tags

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
= 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

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

[6.75]=7 and not 6 Re: For each trip, a taxi company charges a fixed fee of $2.00 plus$0.75   [#permalink] 03 Dec 2019, 03:55
Display posts from previous: Sort by

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