NEW HERE? LEARN MORE
closeclose
Last visit was: 23 Apr 2024, 20:49 It is currently 23 Apr 2024, 20:49
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

Little Johnny wants to eat a candy (circular in shape) using chopstick

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618619 [0]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Little Johnny wants to eat a candy (circular in shape) using chopstick [#permalink] New post   02 Jun 2020, 05:19
Expert Reply
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

70% (01:28) correct 30% (02:19) wrong based on 23 sessions
Hide Show timer Statistics

Little Johnny wants to eat a candy (circular in shape) using chopsticks! For this he makes sure that one end of either chopstick is touching the other (held in his hand) and the other end is used to hold the candy, as shown in the figure below. If his mom wants him to maintain a distance of at least 10 cm between his hands and his mouth while eating, what is the minimum length (in cm) of chopsticks required by him to eat the candy using chopsticks? (Assume that both the chopsticks are of equal length and that the radius of the candy is 6 cm.)


A. 8
B. 9
C. 10
D. 11
E. 12

Show Spoiler
Attachment:
1.png
1.png [ 18.79 KiB | Viewed 826 times ]
ShowHide Answer
Official Answer
A
avatar
B
Shrinkhla21
Manager
Manager
Joined: 07 Dec 2019
Posts: 52
Own Kudos [?]: 30 [0]
Given Kudos: 16
Location: India
Concentration: Social Entrepreneurship, Technology
Schools: (A) Babson '22 (A$) Sauder '22 (II)
GMAT 1: 630 Q45 V32
Send PM
Reviews Badge
Re: Little Johnny wants to eat a candy (circular in shape) using chopstick [#permalink] New post   02 Jun 2020, 05:51
The answer is A.
The tangent subtends an angle of 90 degrees on the radius of the circle.
The next step is to use the pythagorus theorem.

Posted from my mobile device
User avatar
L
GMATWhizTeam
GMATWhiz Representative
Joined: 07 May 2019
Posts: 3409
Own Kudos [?]: 1800 [0]
Given Kudos: 68
Location: India
GMAT 1: 740 Q50 V41
GMAT 2: 760 Q51 V40
Send PM
Re: Little Johnny wants to eat a candy (circular in shape) using chopstick [#permalink] New post   02 Jun 2020, 06:53
Expert Reply
Bunuel wrote:

Little Johnny wants to eat a candy (circular in shape) using chopsticks! For this he makes sure that one end of either chopstick is touching the other (held in his hand) and the other end is used to hold the candy, as shown in the figure below. If his mom wants him to maintain a distance of at least 10 cm between his hands and his mouth while eating, what is the minimum length (in cm) of chopsticks required by him to eat the candy using chopsticks? (Assume that both the chopsticks are of equal length and that the radius of the candy is 6 cm.)


A. 8
B. 9
C. 10
D. 11
E. 12
Show Spoiler
Attachment:
1.png


Solution


    • We need to find the length of the chopstick i.e. PT.
    • To have minimum length of the PT, it should just be exactly equal to the length of the tangent to the circle.
    • As PT is tangent to the circle, triangle OTP is a right-angled triangle, right angled at T.
      o Thus, \(PT = \sqrt{10^2 – 6^2} = 8\)
Thus, the correct answer is Option A.
User avatar
G
NitishJain
IESE School Moderator
Joined: 11 Feb 2019
Posts: 271
Own Kudos [?]: 171 [0]
Given Kudos: 53
Send PM
Re: Little Johnny wants to eat a candy (circular in shape) using chopstick [#permalink] New post   02 Jun 2020, 08:45
IMO A

The angle between a tangent and a radius is 90°

So triangle POT is right angle triangle.

Using pythagoras theorem, OP^2 = OT^2 + PT^2
100 = 36 + PT^2

PT = 8
User avatar
L
Abhishek009
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6072
Own Kudos [?]: 4689 [0]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Send PM
GMAT ToolKit User
Re: Little Johnny wants to eat a candy (circular in shape) using chopstick [#permalink] New post   02 Jun 2020, 09:41
Bunuel wrote:

Little Johnny wants to eat a candy (circular in shape) using chopsticks! For this he makes sure that one end of either chopstick is touching the other (held in his hand) and the other end is used to hold the candy, as shown in the figure below. If his mom wants him to maintain a distance of at least 10 cm between his hands and his mouth while eating, what is the minimum length (in cm) of chopsticks required by him to eat the candy using chopsticks? (Assume that both the chopsticks are of equal length and that the radius of the candy is 6 cm.)


A. 8
B. 9
C. 10
D. 11
E. 12

Show Spoiler
Attachment:
1.png

Use Pythagorean Triple set concept, (3,4,5)

So, Length for the chopstick will be (6,8,10) Multiply 2 * (3,4,5)

Hence, Answer must be (A) 8
GMAT Club Bot
gmatclubot
Re: Little Johnny wants to eat a candy (circular in shape) using chopstick [#permalink]
02 Jun 2020, 09:41
Moderators:
Bunuel
Math Expert
92883 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