NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 05:28 It is currently 26 Apr 2024, 05:28
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Which of the following is closest to the distance traveled by the tip

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92931
Own Kudos [?]: 619155 [0]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Which of the following is closest to the distance traveled by the tip [#permalink] New post   18 Sep 2018, 22:05
Expert Reply
00:00
A
B
C
D
E

Difficulty:

75% (hard)

Question Stats:

33% (01:53) correct 67% (01:54) wrong based on 47 sessions
Hide Show timer Statistics
Which of the following is closest to the distance traveled by the tip of a 9-inch hour hand of a clock in 18 minutes?


A. 17 inches
B. 10.8 inches
C. 5.4 inches
D. 3 inches
E. 1.4 inches
ShowHide Answer
Official Answer
E
User avatar
L
pushpitkc
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 2873
Own Kudos [?]: 5206 [1]
Given Kudos: 47
Location: India
GPA: 3.12
Send PM
Re: Which of the following is closest to the distance traveled by the tip [#permalink] New post   19 Sep 2018, 02:58
1
Kudos
Hey karthikpoluri

Welcome to GMATClub!

If you read the question stem carefully - it is asking us to find the distance
travelled by the 9-inch hour hand in 18 minutes.

That's the reason that why you have made the incorrect calculations.

Hope it's clear :)
User avatar
L
pushpitkc
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 2873
Own Kudos [?]: 5206 [0]
Given Kudos: 47
Location: India
GPA: 3.12
Send PM
Which of the following is closest to the distance traveled by the tip [#permalink] New post   19 Sep 2018, 00:55
Bunuel wrote:
Which of the following is closest to the distance traveled by the tip of a 9-inch hour hand of a clock in 18 minutes?


A. 17 inches
B. 10.8 inches
C. 5.4 inches
D. 3 inches
E. 1.4 inches


In 12 minutes, the hour hand moves by \(\frac{30}{5} = 6\) degree. The hour hand moves 9 degree in 18 minutes.

We can now represent this as a sector with an angle of 9 degrees and the radius of the circle is 9 inch.

Diagrammatic representation
Attachment:
Distance_Clock.png
Distance_Clock.png [ 4.63 KiB | Viewed 1005 times ]


Formula used: Length of the sector = \(\frac{A}{360} * 2 * \pi * R\) where A = angle of sector

Length = \(\frac{A}{360} * 2 * \pi * R = \frac{9}{360} * 2 * \pi * 9 = \frac{1}{20} * \frac{22}{7} * 9 = \frac{11*9}{10*7} = \frac{99}{70} = 1.4\) inches

Therefore, the distance travelled by the hour hand is the length of the sector, which is 1.4 inches(Option E)
avatar
B
karthikpoluri
Intern
Intern
Joined: 18 Sep 2018
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 9
Send PM
Re: Which of the following is closest to the distance traveled by the tip [#permalink] New post   19 Sep 2018, 02:13
according to the given info
we have to find the distance travelled by the minute needle

assume that clock is in the circular shaope and radial measurement is 360
for each minute the radial measurement is 360/60=6
for given 18 minutes = 6* 18= 108
so that 18 minutes part can be taken out of the circle arc part and now the leanth of the minutes needle can be taken as RADIOUS

important formulae is

L = (108/360)*2 PI R

WHERE r= 9,

after solving this we ll get L = 5.4pi
User avatar
L
EgmatQuantExpert
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3726
Own Kudos [?]: 16844 [1]
Given Kudos: 165
Send PM
Re: Which of the following is closest to the distance traveled by the tip [#permalink] New post   19 Sep 2018, 03:14
1
Bookmarks
Expert Reply

Solution


Given:
    • The length of the hour-hand of a clock = 9 inches

To find:
    • The distance covered by the tip of the hour hand in 18 minutes

Approach and Working:
    • The length of hour-hand of a clock = the radius of the circle = 9 inches
    • Hour-hand covers 360 degrees in 12 hours = 12 * 60 minutes
      o So, in 18 minutes it covers, \(360 * \frac{18}{720} = 9\) degrees
    • Thus, the distance covered in 18 minutes = perimeter of the arc, which subtended an angle of 9 degrees at the center = \(2 * ᴨ * r * \frac{9}{360} = 2 * \frac{22}{7} * 9 * \frac{9}{360} = 1.41\)inches

Hence, the correct answer is option E.

Answer: E

avatar
B
iamzyw
Intern
Intern
Joined: 26 Aug 2018
Posts: 4
Own Kudos [?]: 6 [0]
Given Kudos: 57
Location: Mexico
Schools: INSEAD Jan'21 Intake Yale '22 LBS '23 Kellogg 1Year '22
Send PM
GMAT ToolKit User
Re: Which of the following is closest to the distance traveled by the tip [#permalink] New post   19 Sep 2018, 08:15
Clock perimeter = 2*π*R = 2*3.14*9 = 56.52

Distance = 56.52*18/60 = 56.52*0.3 = 16.95, which is closest to 17.

Answer A
GMAT Club Bot
gmatclubot
Re: Which of the following is closest to the distance traveled by the tip [#permalink]
19 Sep 2018, 08:15
Moderators:
Bunuel
Math Expert
92931 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions