At a certain instant in time, the number of cars, N : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 18 Jan 2017, 09:22

# STARTING SOON:

Open Admission Chat with MBA Experts of Personal MBA Coach - Join Chat Room to Participate.

### 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

# At a certain instant in time, the number of cars, N

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 178
Followers: 5

Kudos [?]: 2321 [0], given: 0

At a certain instant in time, the number of cars, N [#permalink]

### Show Tags

02 Dec 2012, 07:02
8
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

82% (03:22) correct 18% (02:54) wrong based on 858 sessions

### HideShow timer Statistics

At a certain instant in time, the number of cars, N, traveling on a portion of a certain highway can be estimated by the formula

$$N=\frac{20Ld}{600+s^2}$$

where L is the number of lanes in the same direction, d is the length of the portion of the highway, in feet, and s is the average speed of the cars, in miles per hour. Based on the formula, what is the estimated number of cars traveling on a 1/2-mile portion of the highway if the highway has 2 lanes in the same direction and the average speed of the cars is 40 miles per hour? (5,280 feet = 1 mile)

(A) 155
(B) 96
(C) 80
(D) 48
(E) 2
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 36545
Followers: 7076

Kudos [?]: 93087 [0], given: 10542

Re: At a certain instant in time, the number of cars, N [#permalink]

### Show Tags

02 Dec 2012, 07:02
Expert's post
1
This post was
BOOKMARKED
At a certain instant in time, the number of cars, N, traveling on a portion of a certain highway can be estimated by the formula

$$N=\frac{20Ld}{600+s^2}$$

where L is the number of lanes in the same direction, d is the length of the portion of the highway, in feet, and s is the average speed of the cars, in miles per hour. Based on the formula, what is the estimated number of cars traveling on a 1/2-mile portion of the highway if the highway has 2 lanes in the same direction and the average speed of the cars is 40 miles per hour? (5,280 feet = 1 mile)

(A) 155
(B) 96
(C) 80
(D) 48
(E) 2

Given:
L = 2 lanes;
d = 1/2*5,280 feet;
s = 40 miles per hour.

Thus, $$N=\frac{20*2*\frac{1}{2}*5,280}{600+40^2}=48$$.

_________________
Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 25

Kudos [?]: 433 [0], given: 11

Re: At a certain instant in time, the number of cars, N [#permalink]

### Show Tags

19 Dec 2012, 05:29
$$N=\frac{20*2*(1}{2)*5280/600+40^{2}}$$
$$N=\frac{20 * 5280}{2200}=\frac{528}{11}=48$$

_________________

Impossible is nothing to God.

Current Student
Joined: 10 Feb 2013
Posts: 15
Concentration: Finance, Economics
GMAT 1: Q V0
GPA: 3.35
WE: Asset Management (Investment Banking)
Followers: 0

Kudos [?]: 7 [0], given: 16

Re: At a certain instant in time, the number of cars, N [#permalink]

### Show Tags

24 Jun 2013, 18:25
1
This post was
BOOKMARKED
How come you wouldn't adjust the speed to 1/2 of 40?
Math Expert
Joined: 02 Sep 2009
Posts: 36545
Followers: 7076

Kudos [?]: 93087 [0], given: 10542

Re: At a certain instant in time, the number of cars, N [#permalink]

### Show Tags

25 Jun 2013, 01:41
AlphaMan21 wrote:
How come you wouldn't adjust the speed to 1/2 of 40?

Why should we do that? The average speed of the cars is 40 miles per hour means that the speed is 40 miles per hour for any portion of the highway (1/2-mile, 1-mile, ...).
_________________
Senior Manager
Joined: 07 Apr 2012
Posts: 464
Followers: 2

Kudos [?]: 53 [0], given: 58

Re: At a certain instant in time, the number of cars, N [#permalink]

### Show Tags

12 Oct 2013, 08:42
Bunuel wrote:
At a certain instant in time, the number of cars, N, traveling on a portion of a certain highway can be estimated by the formula

$$N=\frac{20Ld}{600+s^2}$$

where L is the number of lanes in the same direction, d is the length of the portion of the highway, in feet, and s is the average speed of the cars, in miles per hour. Based on the formula, what is the estimated number of cars traveling on a 1/2-mile portion of the highway if the highway has 2 lanes in the same direction and the average speed of the cars is 40 miles per hour? (5,280 feet = 1 mile)

(A) 155
(B) 96
(C) 80
(D) 48
(E) 2

Given:
L = 2 lanes;
d = 1/2*5,280 feet;
s = 40 miles per hour.

Thus, $$N=\frac{20*2*\frac{1}{2}*5,280}{600+40^2}=48$$.

Hi

Is there any shortcut to the calculation?
It took me about 40 seconds to calculate and that's precious time wasted....
Intern
Joined: 25 Jul 2014
Posts: 20
Concentration: Finance, General Management
GPA: 3.54
WE: Asset Management (Venture Capital)
Followers: 0

Kudos [?]: 23 [0], given: 52

At a certain instant in time, the number of cars, N [#permalink]

### Show Tags

28 Aug 2014, 15:19
ronr34 wrote:

Hi

Is there any shortcut to the calculation?
It took me about 40 seconds to calculate and that's precious time wasted....

(20*(5280/2)*2)/(600+1600)

eliminate 2 = 20*5280/2200
eliminate 2 zero = 2*528/22 = approximately 2*500/20 = 1000/20 = 50 ---> D is closet

Last edited by MulanQ on 12 Sep 2014, 12:51, edited 1 time in total.
Manager
Joined: 07 Apr 2014
Posts: 147
Followers: 1

Kudos [?]: 23 [0], given: 81

Re: At a certain instant in time, the number of cars, N [#permalink]

### Show Tags

11 Sep 2014, 02:12
At a certain instant in time, the number of cars, N, traveling on a portion of a certain highway can be estimated by the formula

$$N=\frac{20Ld}{600+s^2}$$

where L is the number of lanes in the same direction, d is the length of the portion of the highway, in feet, and s is the average speed of the cars, in miles per hour. Based on the formula, what is the estimated number of cars traveling on a 1/2-mile portion of the highway if the highway has 2 lanes in the same direction and the average speed of the cars is 40 miles per hour? (5,280 feet = 1 mile)

(A) 155
(B) 96
(C) 80
(D) 48
(E) 2

its very simple & straight stuff but took lot for time for me to understand it.

(40*5280) / 2 (600+40^2) = 48
Intern
Joined: 06 Nov 2014
Posts: 13
Followers: 0

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

Re: At a certain instant in time, the number of cars, N [#permalink]

### Show Tags

24 Nov 2014, 10:19
At a certain instant in time, the number of cars, N, traveling on a portion of a certain highway can be estimated by the formula

N=\frac{20Ld}{600+s^2}

where L is the number of lanes in the same direction, d is the length of the portion of the highway, in feet, and s is the average speed of the cars, in miles per hour. Based on the formula, what is the estimated number of cars traveling on a 1/2-mile portion of the highway if the highway has 2 lanes in the same direction and the average speed of the cars is 40 miles per hour? (5,280 feet = 1 mile)

(A) 155
(B) 96
(C) 80
(D) 48
(E) 24

I just ballparked to save time= (20*2*2650)=(600+1600), so (20*2*2650)/(2200), just divided by roughly 2200 to leave something like 20*2 left (but a little more). The only answer option close to 40 is 48. So answer D
Intern
Joined: 30 Apr 2015
Posts: 3
Followers: 0

Kudos [?]: 2 [0], given: 45

Re: At a certain instant in time, the number of cars, N [#permalink]

### Show Tags

01 Aug 2015, 12:34

If speed is in miles/hour and distance is in feet . Then why can't we convert feet into miles or vice versa and then perform the calculation ?
Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2654
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Followers: 116

Kudos [?]: 1337 [0], given: 789

Re: At a certain instant in time, the number of cars, N [#permalink]

### Show Tags

01 Aug 2015, 12:50
Atul11 wrote:

If speed is in miles/hour and distance is in feet . Then why can't we convert feet into miles or vice versa and then perform the calculation ?

You need to be economical with your choices in terms of both effort and time spent. Ideally, your best bet is to find a way that gives you the best ROI with least amount of time or energy spent.

Try to change minimum number of variables that will give you the correct answer. There is no 1 way for this question. You can approach it from either direction.

I did it by converting distance from miles to feet (thats it!). It was simple to do this conversion as d was 0.5, much simpler than having a d of 0.23 or 0.37 etc.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Current Student
Joined: 23 Mar 2016
Posts: 38
Schools: Tulane '18 (M)
Followers: 0

Kudos [?]: 2 [0], given: 0

Re: At a certain instant in time, the number of cars, N [#permalink]

### Show Tags

02 May 2016, 14:52
This is an easy one to miss if you don't keep your math straight and don't read the instructions correctly

Let's give it a go

N = (20Ld) / (600+s^2)

L = 2
d = .5(5280) = 2640
s = 40
Plug and Play

N = 20(2)(2640)
Current Student
Joined: 23 Mar 2016
Posts: 38
Schools: Tulane '18 (M)
Followers: 0

Kudos [?]: 2 [0], given: 0

Re: At a certain instant in time, the number of cars, N [#permalink]

### Show Tags

02 May 2016, 14:54
This is an easy one to miss if you don't keep your math straight and don't read the instructions correctly

Let's give it a go

N = (20Ld) / (600+s^2)

L = 2
d = .5(5280) = 2640
s = 40
Plug and Play

N = 20(2)(2640)
....... 600+1600

N = 20(2)(2640)
..........2200

N = 2(2)(264) / 22
N = 2(2)(12)
N = 48
Director
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 511
Location: United States (CA)
Followers: 19

Kudos [?]: 182 [2] , given: 2

Re: At a certain instant in time, the number of cars, N [#permalink]

### Show Tags

03 May 2016, 04:31
2
KUDOS
At a certain instant in time, the number of cars, N, traveling on a portion of a certain highway can be estimated by the formula

$$N=\frac{20Ld}{600+s^2}$$

where L is the number of lanes in the same direction, d is the length of the portion of the highway, in feet, and s is the average speed of the cars, in miles per hour. Based on the formula, what is the estimated number of cars traveling on a 1/2-mile portion of the highway if the highway has 2 lanes in the same direction and the average speed of the cars is 40 miles per hour? (5,280 feet = 1 mile)

(A) 155
(B) 96
(C) 80
(D) 48
(E) 2

Although this problem may seem wordy and confusing, it has much more bark than bite. In the given equation, we have variables L, d, and S, and the entire equation is set equal to N.

We also are told the following:

N = the number of cars in a certain instant in time

L = number of lanes in the same direction

d = length of the portion of the highway, in feet

s = average speed of the cars, in miles per hour

We are given the following values for the variables:

d = ½ mile

L = 2 lanes

s = 40 mph

Before plugging these values into the equation, we must convert ½ mile to feet. Since we know that (5,280 feet = 1 mile), we know that:

½ mile = ½ x 5,280 = 2,640 feet

So now we can plug all this info into the equation to determine the estimated number of cars N.

N = (20Ld)/(600 + s^2)

N = (20 x 2 x 2,640)/(600 + 40^2)

N = (40 x 2,640)/2,200

N = (4 x 264)/22

N = (2 x 264)/11

N = 528/11 = 48

Note: Notice that at the end we kept reducing our equation so that we did not have to work with numbers that were too large; keep things as simple as possible.
_________________

Jeffrey Miller
Scott Woodbury-Stewart
Founder and CEO

Senior Manager
Affiliations: Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 308
GMAT 1: 770 Q47 V48
WE: Education (Education)
Followers: 45

Kudos [?]: 263 [0], given: 42

Re: At a certain instant in time, the number of cars, N [#permalink]

### Show Tags

17 May 2016, 18:08
Attached is a visual that should help.
Attachments

Screen Shot 2016-05-17 at 7.06.46 PM.png [ 114.46 KiB | Viewed 3084 times ]

_________________

Harvard grad and 770 GMAT scorer, offering high-quality private GMAT tutoring, both in-person and via Skype, since 2002.

McElroy Tutoring

Intern
Joined: 16 Jun 2015
Posts: 8
Followers: 0

Kudos [?]: 1 [0], given: 62

Re: At a certain instant in time, the number of cars, N [#permalink]

### Show Tags

13 Jul 2016, 13:25
What i do not understand is: on the highways, cars go in two different directions, that is a common knowledge, so having to estimate number of cars on the highway, not on the part of the highway that goes only in one direction, implies that number of lanes has to be multiplied by 2.
I think this is a clear miss in the problem wording, there is no leap of additional knowledge required, it is pretty much as taking for granted that sun rises on the east, yet for some reason problem gives it that highway has only one direction, which completely inconsistent with reality.
Senior Manager
Affiliations: Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 308
GMAT 1: 770 Q47 V48
WE: Education (Education)
Followers: 45

Kudos [?]: 263 [1] , given: 42

At a certain instant in time, the number of cars, N [#permalink]

### Show Tags

13 Jul 2016, 15:42
1
KUDOS
v1801philip wrote:
What i do not understand is: on the highways, cars go in two different directions, that is a common knowledge, so having to estimate number of cars on the highway, not on the part of the highway that goes only in one direction, implies that number of lanes has to be multiplied by 2.
I think this is a clear miss in the problem wording, there is no leap of additional knowledge required, it is pretty much as taking for granted that sun rises on the east, yet for some reason problem gives it that highway has only one direction, which completely inconsistent with reality.

If you read carefully, it says in the question that L represents the number of lanes going in the same direction. You don't need to multiply the answer by 2, because the formula is for the number of cars traveling on a portion of a certain highway, which is exactly what you are solving for and thus the formula provided should have already accounted for that fact.

If for some reason the formula provided by GMAC were flawed or open-ended, then you still wouldn't be responsible for realizing that fact, so I suggest that you just trust the formula as it is.

"At a certain instant in time, the number of cars, N, traveling on a portion of a certain highway can be estimated by the formula (...) where L is the number of lanes in the same direction, d is the length of the portion of the highway, in feet, and s is the average speed of the cars, in miles per hour. Based on the formula, what is the estimated number of cars traveling on a 1/2-mile portion of the highway if the highway has 2 lanes in the same direction and the average speed of the cars is 40 miles per hour? (5,280 feet = 1 mile)"
_________________

Harvard grad and 770 GMAT scorer, offering high-quality private GMAT tutoring, both in-person and via Skype, since 2002.

McElroy Tutoring

Intern
Joined: 17 Feb 2014
Posts: 24
Location: United States (CA)
GMAT 1: 700 Q49 V35
WE: Programming (Computer Software)
Followers: 0

Kudos [?]: 6 [1] , given: 27

At a certain instant in time, the number of cars, N [#permalink]

### Show Tags

18 Sep 2016, 18:38
1
KUDOS
Since the values in answer choices are reasonably far apart, approximation can get you answer pretty quickly.

=> $$\frac{20 * 2 * 0.5 * 5280}{600 + 40^2}$$ => $$\frac{20 * 5280}{2200}$$ (on simplification)

$$\approx{\frac{20 * 5}{2}}$$ => $$10 * 5$$
$$( 5280/2200\approx{5000/2000})$$

$$\approx{50}$$

At a certain instant in time, the number of cars, N   [#permalink] 18 Sep 2016, 18:38
Similar topics Replies Last post
Similar
Topics:
The number of cars present at a particular time was measured at 3,999 3 03 Jun 2015, 09:45
38 The numbers of cars sold at a certain dealership on six of 11 06 Aug 2012, 01:43
6 The ratio of the number of red cars in a certain parking lot 12 26 Sep 2010, 10:34
11 A parking garage has places for a certain number of cars. If 10 17 Sep 2010, 00:05
3 A certain list consists of 21 different numbers. If n is in 8 30 Aug 2010, 09:29
Display posts from previous: Sort by