Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 29 May 2017, 19:41

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If a taxicab charges x cents for the first 1/9 mile and x/5

Author Message
TAGS:

### Hide Tags

Intern
Joined: 06 Aug 2007
Posts: 31
Location: Montreal
Followers: 0

Kudos [?]: 39 [1] , given: 19

If a taxicab charges x cents for the first 1/9 mile and x/5 [#permalink]

### Show Tags

19 Jul 2010, 16:17
1
KUDOS
14
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

62% (03:24) correct 38% (02:05) wrong based on 308 sessions

### HideShow timer Statistics

If a taxicab charges x cents for the first 1/9 mile and x/5 cents for each additional 1/9 mile or fraction thereof, what is the charge, in cents, for a ride of y miles, where y is a whole number?

(A) x + (xy-x)/45
(B) x - (xy-x)/45
(C) 2x+9y/5
(D) x + (9x-y)/5
(E) x + (9xy-x)/5

Last edited by Safiya on 20 Jul 2010, 15:16, edited 2 times in total.
Manager
Joined: 20 Mar 2010
Posts: 84
Followers: 2

Kudos [?]: 96 [1] , given: 1

### Show Tags

19 Jul 2010, 19:07
1
KUDOS
Safiya wrote:
Hi All,

I hope someone can explain me the solution of the below problem;

If a taxicab charges x cents for the first 1/9 mile and x/9 cents for each additional 1/9 mile or fraction thereof, what is the charge, in cents, for a ride of y miles, where y is a whole number?

(A) x+ xy-x /45
(B) x- xy-x /45
(C) 2x+9y / 5
(D) x+ 9x-y / 5
(E) x+ 9xy-x / 5

Total cost for y miles = cost for first 1/9 mile + cost for the additional (y-1/9) miles
= x + (y-1/9)* x (Since each additional 1/9 th mile costs x/9 cents , each additional mile costs x cents and (y-1/9) additional miles cost (y-1/9)*x cents)
= x + xy -x/9 which i don't see in the answers
Are you sure the answer choices are accurate?

Thanks
Harsha
_________________

___________________________________
Please give me kudos if you like my post

Intern
Joined: 06 Aug 2007
Posts: 31
Location: Montreal
Followers: 0

Kudos [?]: 39 [0], given: 19

### Show Tags

19 Jul 2010, 19:57
Total cost for y miles = cost for first 1/9 mile + cost for the additional (y-1/9) miles
= x + (y-1/9)* x (Since each additional 1/9 th mile costs x/9 cents , each additional mile costs x cents and (y-1/9) additional miles cost (y-1/9)*x cents)
= x + xy -x/9 which i don't see in the answers
Are you sure the answer choices are accurate?

Thanks
Harsha[/quote]

Hi Harsha,

I double checked - the answer choices are correct
Math Expert
Joined: 02 Sep 2009
Posts: 39062
Followers: 7756

Kudos [?]: 106578 [2] , given: 11628

### Show Tags

20 Jul 2010, 02:13
2
KUDOS
Expert's post
3
This post was
BOOKMARKED
Safiya wrote:
Hi All,

I hope someone can explain me the solution of the below problem;

If a taxicab charges x cents for the first 1/9 mile and x/9 cents for each additional 1/9 mile or fraction thereof, what is the charge, in cents, for a ride of y miles, where y is a whole number?

(A) x+ xy-x /45
(B) x- xy-x /45
(C) 2x+9y / 5
(D) x+ 9x-y / 5
(E) x+ 9xy-x / 5

Charge will be the sum of the following:
$$x$$ cents for for the first $$\frac{1}{9}$$ mile;

In 1 mile there are 9 parts of $$\frac{1}{9}$$, hence in $$y$$ miles (where $$y$$ is a whole number) there are $$9y$$ parts of $$\frac{1}{9}$$ miles minus one part (first $$\frac{1}{9}$$ mile) = $$9y-1$$ parts of $$\frac{1}{9}$$ miles to be charged additionally. $$\frac{x}{9}$$ cents per part = $$(9y-1)*\frac{x}{9}$$ cents;

$$x+(9y-1)*\frac{x}{9}=x+\frac{9xy-x}{9}$$.

If you say that OA is E, then charge for each additional 1/9 mile should be x/5 cents instead of x/9.

Hope it helps.
_________________
Intern
Joined: 06 Aug 2007
Posts: 31
Location: Montreal
Followers: 0

Kudos [?]: 39 [0], given: 19

### Show Tags

20 Jul 2010, 15:18
Crack 700 and Bunuel ;

I am so sorry it was written x/9 instead of x/5 , I've just edited the question. Many thanks for the answer!
Math Expert
Joined: 02 Sep 2009
Posts: 39062
Followers: 7756

Kudos [?]: 106578 [0], given: 11628

Re: If a taxicab charges x cents for the first 1/9 mile and x/5 [#permalink]

### Show Tags

24 Jun 2013, 04:03
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

All DS Fractions/Ratios/Decimals questions: search.php?search_id=tag&tag_id=36
All PS Fractions/Ratios/Decimals questions: search.php?search_id=tag&tag_id=57

_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7380
Location: Pune, India
Followers: 2292

Kudos [?]: 15168 [4] , given: 224

Re: If a taxicab charges x cents for the first 1/9 mile and x/5 [#permalink]

### Show Tags

18 Jul 2013, 22:28
4
KUDOS
Expert's post
3
This post was
BOOKMARKED
Safiya wrote:
If a taxicab charges x cents for the first 1/9 mile and x/5 cents for each additional 1/9 mile or fraction thereof, what is the charge, in cents, for a ride of y miles, where y is a whole number?

(A) x+ (xy-x) /45
(B) x- (xy-x) /45
(C) 2x+9y / 5
(D) x+ (9x-y) / 5
(E) x+ (9xy-x) / 5

Responding to a pm:

You can assume values for x and y to get the answer.

Charges for first 1/9 mile = x = 5 cents (assume)
Charges for each subsequent 1/9 mile = x/5 = 1 cent (if x = 5 cents)

So say, we need to cover a total distance of y = 1 mile. How much would be the charge?
5 cents for the first 1/9 mile. Now we are left with 8/9 mile distance. 1 cent for every subsequent 1/9 mile i.e. 8 cents.
So total charge = 5 + 8 = 13 cents

Now put x = 5 and y = 1 in the options. The moment you put y = 1, you see that options (A), (B) and (C) are out of the picture since they give very small values. In option (D), 9x - y will be 1 less than a multiple of 5 so it will not be divisible by 5. Only (E) gives you 13.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 22 Nov 2013 Posts: 40 Followers: 1 Kudos [?]: 95 [0], given: 3 Re: If a taxicab charges x cents for the first 1/9 mile and x/5 [#permalink] ### Show Tags 30 Nov 2013, 03:18 VeritasPrepKarishma wrote: Safiya wrote: If a taxicab charges x cents for the first 1/9 mile and x/5 cents for each additional 1/9 mile or fraction thereof, what is the charge, in cents, for a ride of y miles, where y is a whole number? (A) x+ (xy-x) /45 (B) x- (xy-x) /45 (C) 2x+9y / 5 (D) x+ (9x-y) / 5 (E) x+ (9xy-x) / 5 Responding to a pm: You can assume values for x and y to get the answer. Charges for first 1/9 mile = x = 5 cents (assume) Charges for each subsequent 1/9 mile = x/5 = 1 cent (if x = 5 cents) So say, we need to cover a total distance of y = 1 mile. How much would be the charge? 5 cents for the first 1/9 mile. Now we are left with 8/9 mile distance. 1 cent for every subsequent 1/9 mile i.e. 8 cents. So total charge = 5 + 8 = 13 cents Now put x = 5 and y = 1 in the options. The moment you put y = 1, you see that options (A), (B) and (C) are out of the picture since they give very small values. In option (D), 9x - y will be 1 less than a multiple of 5 so it will not be divisible by 5. Only (E) gives you 13. Answer (E) I tried solving it this way, however failed. What am I doing wrong? Many thanks. I did the following: x=5 y=9 Charges for the first 1/9 mile: 1/9 * 9 * 5 = 5 Charges for the remaining 1/9 miles: 8/9 * 9 * 5/5 = 8 The sum of both is indeed: 5+8 = 13 Putting this into answer E: x+(9xy-x) / 5 yields the following: 5 + (9*5*9 - 5)/5 = 5 + (405 - 5)/5 = 5 + 80 = 85 ...thus, not 13. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7380 Location: Pune, India Followers: 2292 Kudos [?]: 15168 [1] , given: 224 Re: If a taxicab charges x cents for the first 1/9 mile and x/5 [#permalink] ### Show Tags 01 Dec 2013, 23:37 1 This post received KUDOS Expert's post BabySmurf wrote: VeritasPrepKarishma wrote: Safiya wrote: If a taxicab charges x cents for the first 1/9 mile and x/5 cents for each additional 1/9 mile or fraction thereof, what is the charge, in cents, for a ride of y miles, where y is a whole number? (A) x+ (xy-x) /45 (B) x- (xy-x) /45 (C) 2x+9y / 5 (D) x+ (9x-y) / 5 (E) x+ (9xy-x) / 5 Responding to a pm: You can assume values for x and y to get the answer. Charges for first 1/9 mile = x = 5 cents (assume) Charges for each subsequent 1/9 mile = x/5 = 1 cent (if x = 5 cents) So say, we need to cover a total distance of y = 1 mile. How much would be the charge? 5 cents for the first 1/9 mile. Now we are left with 8/9 mile distance. 1 cent for every subsequent 1/9 mile i.e. 8 cents. So total charge = 5 + 8 = 13 cents Now put x = 5 and y = 1 in the options. The moment you put y = 1, you see that options (A), (B) and (C) are out of the picture since they give very small values. In option (D), 9x - y will be 1 less than a multiple of 5 so it will not be divisible by 5. Only (E) gives you 13. Answer (E) I tried solving it this way, however failed. What am I doing wrong? Many thanks. I did the following: x=5 y=9 Charges for the first 1/9 mile: 1/9 * 9 * 5 = 5 Charges for the remaining 1/9 miles: 8/9 * 9 * 5/5 = 8 The sum of both is indeed: 5+8 = 13 Putting this into answer E: x+(9xy-x) / 5 yields the following: 5 + (9*5*9 - 5)/5 = 5 + (405 - 5)/5 = 5 + 80 = 85 ...thus, not 13. The first 1/9 mile is charged at 5 cents (as per the numbers assumed) Now every remaining 1/9th of a mile will be charged at 1 cent. If you have to cover a distance of total 9 miles, the first 1/9th of a mile will be charged ta 5 cents. Now remaining distance is 8 miles and 8/9th of a mile. For every 1 mile now the fare will be 9 cents (1 cent per 1/9th of a mile) and for the 8/9th of a mile, the fare will be 8 cents. So total fare of the remaining distance will be 9*8 + 8 = 80 Total fare of first 1/9th of a mile + additional 8/9th of a mile and 8 more miles = 5 + 80 = 85 Note that I had assumed y = 1. You assumed y = 9. Hence total fare for both cannot be 13 cents. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15524
Followers: 651

Kudos [?]: 211 [0], given: 0

Re: If a taxicab charges x cents for the first 1/9 mile and x/5 [#permalink]

### Show Tags

07 Apr 2015, 20:36
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Intern
Joined: 17 Jul 2015
Posts: 5
Followers: 1

Kudos [?]: 1 [0], given: 1

Re: If a taxicab charges x cents for the first 1/9 mile and x/5 [#permalink]

### Show Tags

03 Aug 2015, 16:29

First 1/9 mile:
x * 1/9

additional miles past the first 1/9:
x/5 * (y - 1/9)

x/9 + x/5(y - 1/9) = x/9 + xy/5 - x/45

Now remember that E is:
x + (9xy-x)/5

so if we multiple our equation by 9, we get:
x + 9/5 * xy - x/5

factor out the 1/5 in second part of the equation:
x + 1/5 ( 9xy - x)
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15524
Followers: 651

Kudos [?]: 211 [0], given: 0

Re: If a taxicab charges x cents for the first 1/9 mile and x/5 [#permalink]

### Show Tags

21 Dec 2016, 09:52
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If a taxicab charges x cents for the first 1/9 mile and x/5   [#permalink] 21 Dec 2016, 09:52
Similar topics Replies Last post
Similar
Topics:
1 The mall charges 50 cents for the first hour of parking and \$3 for eac 2 27 Jun 2016, 12:24
1 A taxicab fare costs x dollars for the first quarter of a mile and 1/4 3 09 Jun 2016, 03:38
7 A taxi charges d dollars for the first two miles and c cents per quart 7 20 Apr 2015, 04:57
1 If a taxi driver charges x cents for the first quarter-mile of a trip 7 11 Jun 2016, 02:32
8 The rental charge for a car is 34 cents for the first 1/4 mi 10 18 Oct 2016, 10:14
Display posts from previous: Sort by