GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 28 Jan 2020, 01:43 ### 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 a particular model of moving truck, rental agency A charges a dail

Author Message
TAGS:

### Hide Tags

Manager  Joined: 17 Oct 2012
Posts: 60
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

9
32 00:00

Difficulty:   95% (hard)

Question Stats: 38% (02:18) correct 62% (02:32) wrong based on 346 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) $$\frac{m-p}{2(q-n)}$$

Originally posted by chetan86 on 22 Oct 2014, 04:48.
Last edited by Bunuel on 22 Oct 2014, 07:15, edited 1 time in total.
Edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 60688
Re: For a particular model of moving truck, rental agency A charges a dail  [#permalink]

### Show Tags

5
3
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.

_________________
##### General Discussion
Manager  Joined: 12 Sep 2014
Posts: 140
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

1
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.
Manager  Joined: 17 Oct 2012
Posts: 60
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

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.
Intern  Joined: 10 Jul 2014
Posts: 40
Concentration: Technology, Strategy
Re: For a particular model of moving truck, rental agency A charges a dail  [#permalink]

### Show Tags

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)
Math Expert V
Joined: 02 Sep 2009
Posts: 60688
Re: For a particular model of moving truck, rental agency A charges a dail  [#permalink]

### Show Tags

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.
_________________
Current Student B
Joined: 03 Jan 2014
Posts: 6
Concentration: Entrepreneurship, Technology
Re: For a particular model of moving truck, rental agency A charges a dail  [#permalink]

### Show Tags

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
Math Expert V
Joined: 02 Sep 2009
Posts: 60688
Re: For a particular model of moving truck, rental agency A charges a dail  [#permalink]

### Show Tags

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.
_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 60688
Re: For a particular model of moving truck, rental agency A charges a dail  [#permalink]

### Show Tags

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.
_________________
Current Student B
Joined: 03 Jan 2014
Posts: 6
Concentration: Entrepreneurship, Technology
Re: For a particular model of moving truck, rental agency A charges a dail  [#permalink]

### Show Tags

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.
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9144
Location: United States (CA)
Re: For a particular model of moving truck, rental agency A charges a dail  [#permalink]

### Show Tags

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

Scott@TargetTestPrep.com

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

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern  B
Joined: 04 Apr 2018
Posts: 28
For a particular model of moving truck, rental agency A charges a dail  [#permalink]

### Show Tags

Bunuel , chetan2u

Can you please explain why we need to divide the cents in 100?
I understand that n/100 gives dollars per mile, but why can't we leave it as cents? (i.e., why do we need to say p cents is 0.0n when its already mentioned that n is cents?)

Math Expert V
Joined: 02 Aug 2009
Posts: 8332
Re: For a particular model of moving truck, rental agency A charges a dail  [#permalink]

### Show Tags

1
Bunuel , chetan2u

Can you please explain why we need to divide the cents in 100?
I understand that n/100 gives dollars per mile, but why can't we leave it as cents? (i.e., why do we need to say p cents is 0.0n when its already mentioned that n is cents?)

Hi..

When we are finding the cost one way it is some dollars as a constant and some cents per mile..
So, if you have to add both, we have to get them into same units, either dollars or cents...

Say you take 1 hour for first few miles and then takes 30 minutes to complete the rest ..
Total cannot be 1+30, it will be 1+ (30/60) as we have to convert both into same units
_________________
Intern  B
Joined: 04 Apr 2018
Posts: 28
Re: For a particular model of moving truck, rental agency A charges a dail  [#permalink]

### Show Tags

chetan2u wrote:
Bunuel , chetan2u

Can you please explain why we need to divide the cents in 100?
I understand that n/100 gives dollars per mile, but why can't we leave it as cents? (i.e., why do we need to say p cents is 0.0n when its already mentioned that n is cents?)

Hi..

When we are finding the cost one way it is some dollars as a constant and some cents per mile..
So, if you have to add both, we have to get them into same units, either dollars or cents...

Say you take 1 hour for first few miles and then takes 30 minutes to complete the rest ..
Total cannot be 1+30, it will be 1+ (30/60) as we have to convert both into same units

Oh boy...
you're right, totally missed that.

Thank you very much chetan2u !
Non-Human User Joined: 09 Sep 2013
Posts: 14009
Re: For a particular model of moving truck, rental agency A charges a dail  [#permalink]

### Show Tags

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: For a particular model of moving truck, rental agency A charges a dail   [#permalink] 09 Dec 2019, 17:45
Display posts from previous: Sort by

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