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

 It is currently 14 Nov 2019, 13:00 ### 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.  # A total of n trucks and cars are parked in a lot. If the num

Author Message
TAGS:

### Hide Tags

Intern  Joined: 24 Oct 2009
Posts: 6
A total of n trucks and cars are parked in a lot. If the num  [#permalink]

### Show Tags

1
13 00:00

Difficulty:   35% (medium)

Question Stats: 75% (02:05) correct 25% (02:03) wrong based on 447 sessions

### HideShow timer Statistics

A total of n trucks and cars are parked in a lot. If the number of cars is 1/4 the number of trucks, and 2/3 of the trucks are pickups, how many pickups, in terms of n, are parked in the lot?

A. 1/6 n
B. 5/12 n
C. 1/2 n
D. 8/15 n
E. 11/12 n

I decided to use 100 for the total of trucks + cars. So n = 100.
Number of cars = 1/4 # of trucks, then there are 25 cars and 75 trucks
2/3 of the trucks are pickups, so 2/3 of 75 is 50.

Therefore, the number of pickups (50) in terms of n would be (1/2)n, which equals 100 * 1/2 = 50, the number of pickups. = C

However, this is not the correct answer- the correct answer is D, 8/15. Can someone explain???

Originally posted by cronkey7 on 24 Oct 2009, 17:11.
Last edited by Bunuel on 09 Oct 2013, 02:03, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9780
Location: Pune, India
Re: A total of n trucks and cars  [#permalink]

### Show Tags

8
1
2
ajit257 wrote:
A total of n trucks and cars are parked in a slot. If the number of cars is 1/4 the number
of trucks, and 2/3 of the trucks are pickups, how many pickups, in terms of n, are parked
in the slot?

A. 1/6 n
B. 5/12 n
C. 1/2 n
D. 8/15 n
E. 11/12 n

Try and use ratios where possible. They make your life very easy.

No of cars : No of trucks = 1:4 (Since for every 4 trucks, there is 1 car)
So total cars and trucks (n) in ratio terms = 1+4 = 5
Now out of 4 trucks, 2/3 are pickup (p) i.e. 4*2/3 = 8/3 are pick up.
So p/n = (8/3)/5 or p = 8/15 n
_________________
Karishma
Veritas Prep GMAT Instructor

##### General Discussion
Director  Joined: 01 Apr 2008
Posts: 619
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Re: Picking numbers on algebra question- Something is wrong!  [#permalink]

### Show Tags

2
2
n = t+c.
c=1/4 *t
so the total number of vehicles in terms of t is n=5/4 *t
Now, 2/3 * t are pickups

Q asks: 2/3 * t = n * F ( F is the required fraction )
2/3 * t = 5/4 * F => F = 8/15.
Manager  Joined: 28 Aug 2010
Posts: 149
A total of n trucks and cars  [#permalink]

### Show Tags

2
A total of n trucks and cars are parked in a slot. If the number of cars is 1/4 the number
of trucks, and 2/3 of the trucks are pickups, how many pickups, in terms of n, are parked
in the slot?

A. 1/6 n
B. 5/12 n
C. 1/2 n
D. 8/15 n
E. 11/12 n

Current Student B
Joined: 23 May 2013
Posts: 183
Location: United States
Concentration: Technology, Healthcare
GMAT 1: 760 Q49 V45 GPA: 3.5
Re: A total of n trucks and cars are parked in a lot. If the num  [#permalink]

### Show Tags

2
cronkey7 wrote:
A total of n trucks and cars are parked in a lot. If the number of cars is 1/4 the number of trucks, and 2/3 of the trucks are pickups, how many pickups, in terms of n, are parked in the lot?

A. 1/6 n
B. 5/12 n
C. 1/2 n
D. 8/15 n
E. 11/12 n

I decided to use 100 for the total of trucks + cars. So n = 100.
Number of cars = 1/4 # of trucks, then there are 25 cars and 75 trucks
2/3 of the trucks are pickups, so 2/3 of 75 is 50.

Therefore, the number of pickups (50) in terms of n would be (1/2)n, which equals 100 * 1/2 = 50, the number of pickups. = C

However, this is not the correct answer- the correct answer is D, 8/15. Can someone explain???

C = Cars, T = Trucks, and P = Pickups.

$$C + T = n$$

$$C = \frac{1}{4} T$$
$$\frac{2}{3}T = P$$

We'd like to write everything in terms of Pickups, since that's what the question is asking us about. Thus,

$$T = \frac{3}{2}P$$,
$$C = \frac{1}{4}T = \frac{1}{4} * \frac{3}{2} P = \frac{3}{8}P$$

Therefore,

$$n = C + T = \frac{3}{8} P + \frac{3}{2} P = \frac{30}{16}P = \frac{15}{8}P.$$

Solving for P, we see that $$P = \frac{8}{15} n.$$

Retired Moderator Joined: 02 Sep 2010
Posts: 722
Location: London
Re: A total of n trucks and cars  [#permalink]

### Show Tags

1
2
ajit257 wrote:
A total of n trucks and cars are parked in a slot. If the number of cars is 1/4 the number
of trucks, and 2/3 of the trucks are pickups, how many pickups, in terms of n, are parked
in the slot?

A. 1/6 n
B. 5/12 n
C. 1/2 n
D. 8/15 n
E. 11/12 n

Let there be c cars and t trucks and p pickup trucks
n = t+c
t=4c
So n = 5c
(2/3)t = p
p = (2/3)t = (2/3)(4c) = (8/3)c = (8/3)(n/5) = (8/15)n

_________________
Senior Manager  B
Joined: 11 May 2011
Posts: 290
Re: Quants - FDP - Plz help on this  [#permalink]

### Show Tags

1
SreeViji wrote:
Hi,

Can anyone help me in resolving this problem? I know it is simple. But I'm missing a small step somewhere.....

A total of n trucks and cars are parked in a lot. If the number of cars is 1/4 the number of trucks, and 2/3 of the trucks are pickups, how many pickups, in terms of n, are parked in the lot?
(A) 1n/6
(B) 5n/12
(C) 1n/2
(D) 8n/15
(E) 11n/12

Lets consider the number of trucks = x
Hence, total number of cars is = x/4
from the question we know, x+x/4 = n = > x = 4n/5
Number of trucks that are pickups = (2/3)4n/5 = 8n/15.

Cheers!
_________________
-----------------------------------------------------------------------------------------
What you do TODAY is important because you're exchanging a day of your life for it!
-----------------------------------------------------------------------------------------
Retired Moderator Joined: 29 Oct 2013
Posts: 248
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Re: A total of n trucks and cars are parked in a lot. If the num  [#permalink]

### Show Tags

1
This is all variables in answer choices question. So lets pick smart numbers. Let n=15 {why 15? Since cars=1/4*trucks, total trucks+cars should be divisible by 5 (1+4). Additionally since we have another fraction 2/3 to work with, the total should be divisible by 3}
n=15
cars+trucks= 15
cars+4*cars = 15 -> cars=3 so trucks=12
pick-up trucks = 12*2/3 = 8
Now plug 15 in answer choices. Only D gives 8. Ans D
_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8375
Location: United States (CA)
Re: A total of n trucks and cars are parked in a lot. If the num  [#permalink]

### Show Tags

1
cronkey7 wrote:
A total of n trucks and cars are parked in a lot. If the number of cars is 1/4 the number of trucks, and 2/3 of the trucks are pickups, how many pickups, in terms of n, are parked in the lot?

A. 1/6 n
B. 5/12 n
C. 1/2 n
D. 8/15 n
E. 11/12 n

We can let the number of cars = c and number of trucks = t; thus:

c + t = n

and

c = (1/4)t

Thus:

(1/4)t + t = n

t + 4t = 4n

5t = 4n

t = 4n/5

Since 2/3 of the trucks are pickups, there are (2/3)(4n/5) = 8n/15 pickups in the parking lot.

_________________

# 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  Status: Sophomore
Affiliations: President of Student Associoation
Joined: 09 Dec 2010
Posts: 32
Schools: HBS 2+2, IESE YTP
Re: A total of n trucks and cars  [#permalink]

### Show Tags

D.
x+x/4=n => x=4n/5 => 2x/3=8n/15
Manager  Joined: 26 Feb 2012
Posts: 88
Location: India
Concentration: General Management, Finance
WE: Engineering (Telecommunications)
Re: A total of n trucks and cars are parked in a lot. If the num  [#permalink]

### Show Tags

1
Lets say Total truck is 12. So car is 3.
Now pickups are =2/3rd of 12= 8
so total fraction is 8/15 ..ans
VP  P
Joined: 07 Dec 2014
Posts: 1222
A total of n trucks and cars are parked in a lot. If the num  [#permalink]

### Show Tags

let t=number of trucks
n=t+(t/4)=5t/4
let p=number of pickups
t=3p/2
substituting, n=5(3p/2)/4
p=8/15 n
Manager  B
Joined: 30 Apr 2013
Posts: 75
Re: A total of n trucks and cars are parked in a lot. If the num  [#permalink]

### Show Tags

Number of trucks = x
Number of cars = 1/4x

Therefore, x +1/4x = n ( Total number of vehicles parked)
X= 4n/5

We are given 2/3 of x are pick up trucks.
So 2/3 *4n/5 = 8/15n
Director  D
Joined: 13 Mar 2017
Posts: 733
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: A total of n trucks and cars are parked in a lot. If the num  [#permalink]

### Show Tags

cronkey7 wrote:
A total of n trucks and cars are parked in a lot. If the number of cars is 1/4 the number of trucks, and 2/3 of the trucks are pickups, how many pickups, in terms of n, are parked in the lot?

A. 1/6 n
B. 5/12 n
C. 1/2 n
D. 8/15 n
E. 11/12 n

I decided to use 100 for the total of trucks + cars. So n = 100.
Number of cars = 1/4 # of trucks, then there are 25 cars and 75 trucks
2/3 of the trucks are pickups, so 2/3 of 75 is 50.

Therefore, the number of pickups (50) in terms of n would be (1/2)n, which equals 100 * 1/2 = 50, the number of pickups. = C

However, this is not the correct answer- the correct answer is D, 8/15. Can someone explain???

t+c = n
c = t/4

t+t/4 = n
t = 4/5 n

c = 2/3 t = 2/3 * 4/5 = 8/15 n

_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Intern  Joined: 20 Aug 2018
Posts: 1
Re: A total of n trucks and cars are parked in a lot. If the num  [#permalink]

### Show Tags

Thanks for sharing
Non-Human User Joined: 09 Sep 2013
Posts: 13585
Re: A total of n trucks and cars are parked in a lot. If the num  [#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: A total of n trucks and cars are parked in a lot. If the num   [#permalink] 25 Aug 2019, 07:13
Display posts from previous: Sort by

# A total of n trucks and cars are parked in a lot. If the num  