Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 06 Jul 2015, 13:18

### 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

# An absent minded scientist walks on an escalator at a rate

Author Message
TAGS:
Manager
Joined: 07 Feb 2010
Posts: 160
Followers: 2

Kudos [?]: 208 [3] , given: 101

An absent minded scientist walks on an escalator at a rate [#permalink]  08 Nov 2010, 02:19
3
KUDOS
6
This post was
BOOKMARKED
00:00

Difficulty:

85% (hard)

Question Stats:

50% (02:44) correct 50% (01:42) wrong based on 230 sessions
An absent minded scientist walks on an escalator at a rate of 4 steps per second and reaches the other end in 15 seconds. While coming back, walking at the same speed he reaches the starting point in 45 seconds. What is the number of steps on the escalator?

A. 60
B. 90
C. 105
D. 120
E. 140
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Jul 2013, 08:02, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 28331
Followers: 4483

Kudos [?]: 45373 [3] , given: 6759

Re: an absent minded scientist [#permalink]  08 Nov 2010, 02:40
3
KUDOS
Expert's post
3
This post was
BOOKMARKED
anilnandyala wrote:
an absent minded scientist walks on an escalator at a rate of 4 steps per second and reaches the other end in 15 seconds . while coming back , walking at the same speed he reaches the starting point in 45 seconds . what is the number of steps on the escalator?
a 60
b 90
c 105
d 120
e 140

Let the rate of the escalator be $$x$$ steps per second and the length of the escalator $$y$$ steps.

Then $$\frac{y}{x+4}=15$$ and $$\frac{y}{4-x}=45$$ --> solving for $$y$$ --> $$y=90$$.

_________________
Manager
Joined: 01 Nov 2010
Posts: 182
Location: Zürich, Switzerland
Followers: 2

Kudos [?]: 21 [0], given: 20

Re: an absent minded scientist [#permalink]  08 Nov 2010, 02:54
Scientist is absent minded. He uses same escalator while walking in both directions

Let S be speed of escalator

Case1-->same direction as that of escalator, so D/(4+S)= 15
Case2-->against direction of escalator, so D/(4-S) = 45
Combining above 2 equations- 15(4+S)= 45(4-S), S=2

Therefore number of stairs= 90. Answer: B.
Intern
Joined: 20 Oct 2010
Posts: 16
Followers: 0

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

Re: an absent minded scientist [#permalink]  08 Nov 2010, 07:09
Bunuel wrote:
anilnandyala wrote:
an absent minded scientist walks on an escalator at a rate of 4 steps per second and reaches the other end in 15 seconds . while coming back , walking at the same speed he reaches the starting point in 45 seconds . what is the number of steps on the escalator?
a 60
b 90
c 105
d 120
e 140

Let the rate of the escalator be $$x$$ steps per second and the length of the escalator $$y$$ steps.

Then $$\frac{y}{x+4}=15$$ and $$\frac{y}{4-x}=45$$ --> solving for $$y$$ --> $$y=90$$.

Is this a GMAT question.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5682
Location: Pune, India
Followers: 1415

Kudos [?]: 7352 [6] , given: 186

Re: an absent minded scientist [#permalink]  08 Nov 2010, 08:38
6
KUDOS
Expert's post
2
This post was
BOOKMARKED
anilnandyala wrote:
an absent minded scientist walks on an escalator at a rate of 4 steps per second and reaches the other end in 15 seconds . while coming back , walking at the same speed he reaches the starting point in 45 seconds . what is the number of steps on the escalator?
a 60
b 90
c 105
d 120
e 140

Escalator questions tend to confuse people but the point to note here is that they are just like Boats and Streams questions. If you are going in the direction of the escalator, it is like going downstream and your effective speed will be your speed + escalator speed. When you are going against the escalator, it is like going upstream and your effective speed will be your speed - escalator speed. The total distance to be traveled is the total number of steps on the escalator.
Then, you can very easily make the equations made by Bunuel and Sarang above:
$$\frac{y}{x+4}=15 and \frac{y}{4-x}=45$$

You can take a couple of quick guesses to solve this and in most cases you will get your answer in a couple of guesses.
e.g. lets say if x = 1, y = 75 from 1st equation
but x = 1 gives y = 135 in 2nd equation. So x is not 1
If x = 2, y = 90, from 1st equation
x = 2 gives y = 90 in 2nd equation. So x = 2 and y = 90.
Fun fact about GMAT: They give you numbers that make your life easy but twist concepts to make you think.

Also, if I am not wrong, these are CAT questions. I have not seen such questions in OG/Test prep material that I have come across. Nevertheless, every question is good for practice if you have the time. If time is less, you would do better to focus on 'GMAT type' questions available in OG.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Math Expert
Joined: 02 Sep 2009
Posts: 28331
Followers: 4483

Kudos [?]: 45373 [0], given: 6759

Re: An absent minded scientist walks on an escalator at a rate [#permalink]  09 Jul 2013, 08:05
Expert's post
Bumping for review and further discussion.
_________________
Senior Manager
Joined: 13 May 2013
Posts: 475
Followers: 1

Kudos [?]: 84 [0], given: 134

Re: An absent minded scientist walks on an escalator at a rate [#permalink]  05 Aug 2013, 11:16
An absent minded scientist walks on an escalator at a rate of 4 steps per second and reaches the other end in 15 seconds. While coming back, walking at the same speed he reaches the starting point in 45 seconds. What is the number of steps on the escalator?

It took me a while to figure out why the fact that the scientist was "absent minded" was relevant. He walked on the escalator the right way then went in the opposite direction against the direction it was moving in!

We are given time and rate for both directions. We have to realize that because the escalator is moving, that adds (or subtracts) from his forward momentum.

time = distance/speed
t1: 15 = d/(r+4)
15r+60 = d

t2: 45 = d/(4-r) The scientist moves at the same speed but because he is going against the motion of the escalator his forward movement is slowed down. Therefore, we subtract the escalators rate from his rate of 4 steps/second.
180-45r = d

15r+60 = 180-45r
60r - 120
r=2

15 = d/(r+4)
15 = d(2+4)
15 = d(6)
90 = d

Manager
Joined: 14 Nov 2008
Posts: 70
Followers: 2

Kudos [?]: 17 [0], given: 1

Re: An absent minded scientist walks on an escalator at a rate [#permalink]  01 Sep 2013, 02:34
T = total no. of steps in escalator
n = speed of escalator in steps per second
4 = steps per sec of the scientist

(n+4)=T/15 and (4-n) = T/45
=> n = 2
=> T = 90
Intern
Joined: 26 Aug 2013
Posts: 1
Followers: 0

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

Re: An absent minded scientist walks on an escalator at a rate [#permalink]  02 Sep 2013, 06:24
As we can see, ratio of time take when going with the escalator to time taken against the escalator is 3

Also it is understandable that, speed of the escalator must be less then the speed of the scientist ( as the scientist is able to come down while moving against the escalator )

Futher is we assume X (steps/sec) be the avg. speed of the escalator then

(4+X)/(4-X) = 3
i.e. X=2

Hence no of steps = (4+X)*15 = (4-X)*45 = 90
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 5389
Followers: 311

Kudos [?]: 60 [0], given: 0

Re: An absent minded scientist walks on an escalator at a rate [#permalink]  31 Oct 2014, 03:07
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.
_________________
Director
Joined: 07 Aug 2011
Posts: 588
GMAT 1: 630 Q49 V27
Followers: 2

Kudos [?]: 223 [0], given: 75

Re: An absent minded scientist walks on an escalator at a rate [#permalink]  02 Mar 2015, 07:11
anilnandyala wrote:
An absent minded scientist walks on an escalator at a rate of 4 steps per second and reaches the other end in 15 seconds. While coming back, walking at the same speed he reaches the starting point in 45 seconds. What is the number of steps on the escalator?

A. 60
B. 90
C. 105
D. 120
E. 140

time taken going up 45sec
time taken going down 15sec
it tells going down speed is 3times the speed going up.
4+E=3(4-E)
E=2
in 15secs scientist will move 60 steps
in 15secs escalator will move 2×15=30 steps
_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the to appreciate my post !!

Re: An absent minded scientist walks on an escalator at a rate   [#permalink] 02 Mar 2015, 07:11
Similar topics Replies Last post
Similar
Topics:
Three friends-whose walking rates are ..... 3 05 Oct 2010, 04:41
Walk 2 24 Aug 2009, 00:57
A hiker walking at a constatnt rate of 4 miles/hr is passed 4 14 Aug 2007, 10:12
A hiker walking at a constant rate of 4 miles per hour is 4 03 Feb 2006, 23:01
A hiker walking at a constant rate of 4 miles per hour is 11 16 Oct 2005, 15:09
Display posts from previous: Sort by