It is currently 20 Jan 2018, 08:30

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

For a particular model of moving truck, rental agency A charges a dail

Author Message
TAGS:

Hide Tags

Manager
Joined: 17 Oct 2012
Posts: 70

Kudos [?]: 132 [3], given: 52

Location: India
Concentration: Strategy, Finance
WE: Information Technology (Computer Software)
For a particular model of moving truck, rental agency A charges a dail [#permalink]

Show Tags

22 Oct 2014, 03:48
3
KUDOS
13
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

39% (01:08) correct 61% (01:13) wrong based on 360 sessions

HideShow timer Statistics

For a particular model of moving truck, rental agency A charges a daily fee of m dollars, plus n cents per mile. For the same model of truck, rental agency B charges a daily fee of p dollars, plus q cents per mile. If a driver plans to rent this model of truck for two days, which of the following expressions gives the number of miles this driver must drive for the two rental agencies’ total charges to be equal?

(A) $$\frac{100(m-p)}{q-n}$$

(B) $$\frac{200(p-m)}{n-q}$$

(C) $$\frac{50(m-p)}{q-n}$$

(D) $$\frac{2(p-m)}{n-q}$$

(E) $$\frac{m-p}{2(q-n)}$$
[Reveal] Spoiler: OA

Last edited by Bunuel on 22 Oct 2014, 06:15, edited 1 time in total.
Edited the question.

Kudos [?]: 132 [3], given: 52

Math Expert
Joined: 02 Sep 2009
Posts: 43334

Kudos [?]: 139565 [3], given: 12794

Re: For a particular model of moving truck, rental agency A charges a dail [#permalink]

Show Tags

22 Oct 2014, 06:24
3
KUDOS
Expert's post
4
This post was
BOOKMARKED
chetan86 wrote:
For a particular model of moving truck, rental agency A charges a daily fee of m dollars, plus n cents per mile. For the same model of truck, rental agency B charges a daily fee of p dollars, plus q cents per mile. If a driver plans to rent this model of truck for two days, which of the following expressions gives the number of miles this driver must drive for the two rental agencies’ total charges to be equal?

(A) $$\frac{100(m-p)}{q-n}$$

(B) $$\frac{200(p-m)}{n-q}$$

(C) $$\frac{50(m-p)}{q-n}$$

(D) $$\frac{2(p-m)}{n-q}$$

(E) $$\frac{m-p}{2(q-n)}$$

Let x be the number of miles this driver must drive for the two rental agencies’ total charges to be equal.

Agency A's charges for two days = 2m + n/100*x (n/100 gives dollars per mile).
Agency B's charges for two days = 2p + q/100*x (q/100 gives dollars per mile).

Equate and solve for x:

$$2m + \frac{n}{100}*x=2p + \frac{q}{100}*x$$;

$$200m+nx=200p+qx$$;

$$x=\frac{200p-200m}{n-q}$$.

Hope it's clear.

_________________

Kudos [?]: 139565 [3], given: 12794

Manager
Joined: 12 Sep 2014
Posts: 167

Kudos [?]: 88 [1], given: 103

GMAT 1: 740 Q49 V41
GPA: 3.94
Re: For a particular model of moving truck, rental agency A charges a dail [#permalink]

Show Tags

22 Oct 2014, 09:41
1
KUDOS
This is mostly like a plug and chug. Let the # of days =2 and the # of miles be equal for both drivers. Just remember to divide n and q by 100 to convert from cents to dollars.

You should get 2m+n*miles/100 = 2p + q*miles/100

Solving for miles gets you B.

Kudos [?]: 88 [1], given: 103

Manager
Joined: 17 Oct 2012
Posts: 70

Kudos [?]: 132 [0], given: 52

Location: India
Concentration: Strategy, Finance
WE: Information Technology (Computer Software)
Re: For a particular model of moving truck, rental agency A charges a dail [#permalink]

Show Tags

23 Oct 2014, 23:08
Bunuel wrote:
chetan86 wrote:
For a particular model of moving truck, rental agency A charges a daily fee of m dollars, plus n cents per mile. For the same model of truck, rental agency B charges a daily fee of p dollars, plus q cents per mile. If a driver plans to rent this model of truck for two days, which of the following expressions gives the number of miles this driver must drive for the two rental agencies’ total charges to be equal?

(A) $$\frac{100(m-p)}{q-n}$$

(B) $$\frac{200(p-m)}{n-q}$$

(C) $$\frac{50(m-p)}{q-n}$$

(D) $$\frac{2(p-m)}{n-q}$$

(E) $$\frac{m-p}{2(q-n)}$$

Let x be the number of miles this driver must drive for the two rental agencies’ total charges to be equal.

Agency A's charges for two days = 2m + n/100*x (n/100 gives dollars per mile).
Agency B's charges for two days = 2p + q/100*x (q/100 gives dollars per mile).

Equate and solve for x:

$$2m + \frac{n}{100}*x=2p + \frac{q}{100}*x$$;

$$200m+nx=200p+qx$$;

$$x=\frac{200p-200m}{n-q}$$.

Hope it's clear.

Hi Bunuel,
Thanks a lot for your explanation.
Next time I will take care to formulate mathematical expression correctly. Thanks for the link.

Kudos [?]: 132 [0], given: 52

Intern
Joined: 10 Jul 2014
Posts: 41

Kudos [?]: 20 [0], given: 35

Concentration: Technology, Strategy
Re: For a particular model of moving truck, rental agency A charges a dail [#permalink]

Show Tags

24 Oct 2014, 12:40
Bunuel wrote:
chetan86 wrote:
For a particular model of moving truck, rental agency A charges a daily fee of m dollars, plus n cents per mile. For the same model of truck, rental agency B charges a daily fee of p dollars, plus q cents per mile. If a driver plans to rent this model of truck for two days, which of the following expressions gives the number of miles this driver must drive for the two rental agencies’ total charges to be equal?

(A) $$\frac{100(m-p)}{q-n}$$

(B) $$\frac{200(p-m)}{n-q}$$

(C) $$\frac{50(m-p)}{q-n}$$

(D) $$\frac{2(p-m)}{n-q}$$

(E) $$\frac{m-p}{2(q-n)}$$

Let x be the number of miles this driver must drive for the two rental agencies’ total charges to be equal.

Agency A's charges for two days = 2m + n/100*x (n/100 gives dollars per mile).
Agency B's charges for two days = 2p + q/100*x (q/100 gives dollars per mile).

Equate and solve for x:

$$2m + \frac{n}{100}*x=2p + \frac{q}{100}*x$$;

$$200m+nx=200p+qx$$;

$$x=\frac{200p-200m}{n-q}$$.

Hope it's clear.

Agency A's charges for two days = 2m + n/100*x (n/100 gives dollars per mile).

Hi Bunuel,
Can you please clarify why we are not multiplying 2 days to cents? I was stuck on this question because I calculated as 2(m + n/100)

Kudos [?]: 20 [0], given: 35

Math Expert
Joined: 02 Sep 2009
Posts: 43334

Kudos [?]: 139565 [0], given: 12794

Re: For a particular model of moving truck, rental agency A charges a dail [#permalink]

Show Tags

25 Oct 2014, 05:11
Expert's post
1
This post was
BOOKMARKED
pairakesh10 wrote:
Bunuel wrote:
chetan86 wrote:
For a particular model of moving truck, rental agency A charges a daily fee of m dollars, plus n cents per mile. For the same model of truck, rental agency B charges a daily fee of p dollars, plus q cents per mile. If a driver plans to rent this model of truck for two days, which of the following expressions gives the number of miles this driver must drive for the two rental agencies’ total charges to be equal?

(A) $$\frac{100(m-p)}{q-n}$$

(B) $$\frac{200(p-m)}{n-q}$$

(C) $$\frac{50(m-p)}{q-n}$$

(D) $$\frac{2(p-m)}{n-q}$$

(E) $$\frac{m-p}{2(q-n)}$$

Let x be the number of miles this driver must drive for the two rental agencies’ total charges to be equal.

Agency A's charges for two days = 2m + n/100*x (n/100 gives dollars per mile).
Agency B's charges for two days = 2p + q/100*x (q/100 gives dollars per mile).

Equate and solve for x:

$$2m + \frac{n}{100}*x=2p + \frac{q}{100}*x$$;

$$200m+nx=200p+qx$$;

$$x=\frac{200p-200m}{n-q}$$.

Hope it's clear.

Agency A's charges for two days = 2m + n/100*x (n/100 gives dollars per mile).

Hi Bunuel,
Can you please clarify why we are not multiplying 2 days to cents? I was stuck on this question because I calculated as 2(m + n/100)

Because x is already the total number of miles driven in two days.
_________________

Kudos [?]: 139565 [0], given: 12794

Non-Human User
Joined: 09 Sep 2013
Posts: 14219

Kudos [?]: 291 [0], given: 0

Re: For a particular model of moving truck, rental agency A charges a dail [#permalink]

Show Tags

09 Jan 2016, 13:19
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.
_________________

Kudos [?]: 291 [0], given: 0

Intern
Joined: 03 Jan 2014
Posts: 6

Kudos [?]: 5 [0], given: 1

Concentration: Entrepreneurship, Technology
Re: For a particular model of moving truck, rental agency A charges a dail [#permalink]

Show Tags

18 Jul 2016, 01:00
Bunuel wrote:
chetan86 wrote:
For a particular model of moving truck, rental agency A charges a daily fee of m dollars, plus n cents per mile. For the same model of truck, rental agency B charges a daily fee of p dollars, plus q cents per mile. If a driver plans to rent this model of truck for two days, which of the following expressions gives the number of miles this driver must drive for the two rental agencies’ total charges to be equal?

(A) $$\frac{100(m-p)}{q-n}$$

(B) $$\frac{200(p-m)}{n-q}$$

(C) $$\frac{50(m-p)}{q-n}$$

(D) $$\frac{2(p-m)}{n-q}$$

(E) $$\frac{m-p}{2(q-n)}$$

Let x be the number of miles this driver must drive for the two rental agencies’ total charges to be equal.

Agency A's charges for two days = 2m + n/100*x (n/100 gives dollars per mile).
Agency B's charges for two days = 2p + q/100*x (q/100 gives dollars per mile).

Equate and solve for x:

$$2m + \frac{n}{100}*x=2p + \frac{q}{100}*x$$;

$$200m+nx=200p+qx$$;

$$x=\frac{200p-200m}{n-q}$$.

Hope it's clear.

Hi Bunuel,
Could you please explain why you are taking the number of miles for both the agencies as equal. Couldn't it be possible that -
Agency A's charges for two days = 2m + n/100*x (n/100 gives dollars per mile).
Agency B's charges for two days = 2p + q/100*y (q/100 gives dollars per mile).

And the total miles would be x+y.

Thanks

Kudos [?]: 5 [0], given: 1

Math Expert
Joined: 02 Sep 2009
Posts: 43334

Kudos [?]: 139565 [0], given: 12794

Re: For a particular model of moving truck, rental agency A charges a dail [#permalink]

Show Tags

18 Jul 2016, 02:23
gmat730 wrote:
Bunuel wrote:
chetan86 wrote:
For a particular model of moving truck, rental agency A charges a daily fee of m dollars, plus n cents per mile. For the same model of truck, rental agency B charges a daily fee of p dollars, plus q cents per mile. If a driver plans to rent this model of truck for two days, which of the following expressions gives the number of miles this driver must drive for the two rental agencies’ total charges to be equal?

(A) $$\frac{100(m-p)}{q-n}$$

(B) $$\frac{200(p-m)}{n-q}$$

(C) $$\frac{50(m-p)}{q-n}$$

(D) $$\frac{2(p-m)}{n-q}$$

(E) $$\frac{m-p}{2(q-n)}$$

Let x be the number of miles this driver must drive for the two rental agencies’ total charges to be equal.

Agency A's charges for two days = 2m + n/100*x (n/100 gives dollars per mile).
Agency B's charges for two days = 2p + q/100*x (q/100 gives dollars per mile).

Equate and solve for x:

$$2m + \frac{n}{100}*x=2p + \frac{q}{100}*x$$;

$$200m+nx=200p+qx$$;

$$x=\frac{200p-200m}{n-q}$$.

Hope it's clear.

Hi Bunuel,
Could you please explain why you are taking the number of miles for both the agencies as equal. Couldn't it be possible that -
Agency A's charges for two days = 2m + n/100*x (n/100 gives dollars per mile).
Agency B's charges for two days = 2p + q/100*y (q/100 gives dollars per mile).

And the total miles would be x+y.

Thanks

The question asks: which of the following expressions gives the number of miles (x in our case) this driver must drive for the two rental agencies’ total charges to be equal? So, for what x, are the charges of two agencies equal.
_________________

Kudos [?]: 139565 [0], given: 12794

Math Expert
Joined: 02 Sep 2009
Posts: 43334

Kudos [?]: 139565 [0], given: 12794

Re: For a particular model of moving truck, rental agency A charges a dail [#permalink]

Show Tags

18 Jul 2016, 02:25
gmat730 wrote:
Bunuel wrote:
chetan86 wrote:
For a particular model of moving truck, rental agency A charges a daily fee of m dollars, plus n cents per mile. For the same model of truck, rental agency B charges a daily fee of p dollars, plus q cents per mile. If a driver plans to rent this model of truck for two days, which of the following expressions gives the number of miles this driver must drive for the two rental agencies’ total charges to be equal?

(A) $$\frac{100(m-p)}{q-n}$$

(B) $$\frac{200(p-m)}{n-q}$$

(C) $$\frac{50(m-p)}{q-n}$$

(D) $$\frac{2(p-m)}{n-q}$$

(E) $$\frac{m-p}{2(q-n)}$$

Let x be the number of miles this driver must drive for the two rental agencies’ total charges to be equal.

Agency A's charges for two days = 2m + n/100*x (n/100 gives dollars per mile).
Agency B's charges for two days = 2p + q/100*x (q/100 gives dollars per mile).

Equate and solve for x:

$$2m + \frac{n}{100}*x=2p + \frac{q}{100}*x$$;

$$200m+nx=200p+qx$$;

$$x=\frac{200p-200m}{n-q}$$.

Hope it's clear.

Hi Bunuel,
Could you please explain why you are taking the number of miles for both the agencies as equal. Couldn't it be possible that -
Agency A's charges for two days = 2m + n/100*x (n/100 gives dollars per mile).
Agency B's charges for two days = 2p + q/100*y (q/100 gives dollars per mile).

And the total miles would be x+y.

Thanks

To understand better check similar questions:
salesperson-a-s-compensation-for-any-week-is-360-plus-30977.html
health-insurance-plan-a-requires-the-insured-to-pay-1000-or-106447.html

Hope it helps.
_________________

Kudos [?]: 139565 [0], given: 12794

Intern
Joined: 03 Jan 2014
Posts: 6

Kudos [?]: 5 [0], given: 1

Concentration: Entrepreneurship, Technology
Re: For a particular model of moving truck, rental agency A charges a dail [#permalink]

Show Tags

18 Jul 2016, 02:46
Hi Bunuel,
Could you please explain why you are taking the number of miles for both the agencies as equal. Couldn't it be possible that -
Agency A's charges for two days = 2m + n/100*x (n/100 gives dollars per mile).
Agency B's charges for two days = 2p + q/100*y (q/100 gives dollars per mile).

And the total miles would be x+y.

Thanks[/quote]

To understand better check similar questions:
salesperson-a-s-compensation-for-any-week-is-360-plus-30977.html
health-insurance-plan-a-requires-the-insured-to-pay-1000-or-106447.html

Hope it helps.[/quote]

Got it. Thank you. I was thinking about another possibility in which the driver could travel x miles for agency A and y miles for agency B and still get the total charges as equal.

Kudos [?]: 5 [0], given: 1

Non-Human User
Joined: 09 Sep 2013
Posts: 14219

Kudos [?]: 291 [0], given: 0

Re: For a particular model of moving truck, rental agency A charges a dail [#permalink]

Show Tags

15 Sep 2017, 02:51
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.
_________________

Kudos [?]: 291 [0], given: 0

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2056

Kudos [?]: 1087 [0], given: 4

Location: United States (CA)
Re: For a particular model of moving truck, rental agency A charges a dail [#permalink]

Show Tags

21 Sep 2017, 13:48
chetan86 wrote:
For a particular model of moving truck, rental agency A charges a daily fee of m dollars, plus n cents per mile. For the same model of truck, rental agency B charges a daily fee of p dollars, plus q cents per mile. If a driver plans to rent this model of truck for two days, which of the following expressions gives the number of miles this driver must drive for the two rental agencies’ total charges to be equal?

(A) $$\frac{100(m-p)}{q-n}$$

(B) $$\frac{200(p-m)}{n-q}$$

(C) $$\frac{50(m-p)}{q-n}$$

(D) $$\frac{2(p-m)}{n-q}$$

(E) $$\frac{m-p}{2(q-n)}$$

We can create the following equation in which z = the number of miles driven. Since the daily fee is in dollars and the mileage fee is in cents, we convert the daily fee to cents. We should remember that m dollars = 100m cents and p dollars = 100p cents.

2(100m) + nz = 2(100p) + qz

200m + nz = 200p + qz

nz - qz = 200p - 200m

z(n - q) = 200(p - m)

z = 200(p - m)/(n - q)

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 1087 [0], given: 4

Re: For a particular model of moving truck, rental agency A charges a dail   [#permalink] 21 Sep 2017, 13:48
Display posts from previous: Sort by