It is currently 18 Oct 2017, 06:29

### 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

# What is the probability of randomly selecting one of the shortest diag

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 41884

Kudos [?]: 128710 [2], given: 12182

What is the probability of randomly selecting one of the shortest diag [#permalink]

### Show Tags

07 Sep 2016, 04:41
2
KUDOS
Expert's post
5
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

59% (00:58) correct 41% (01:17) wrong based on 99 sessions

### HideShow timer Statistics

What is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular hexagon?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 7/9
[Reveal] Spoiler: OA

_________________

Kudos [?]: 128710 [2], given: 12182

Math Forum Moderator
Joined: 02 Aug 2009
Posts: 4969

Kudos [?]: 5459 [0], given: 112

Re: What is the probability of randomly selecting one of the shortest diag [#permalink]

### Show Tags

07 Sep 2016, 05:16
Bunuel wrote:
What is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular hexagon?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 7/9

Hi,
Two ways...
1) just imagine any any vertex or a corner....
It has two vertices on sides, which do not make a diagonal but a side..
So remaining 3 vertices make diagonals... only the opposite vertex will make largest diagonal and other TWO smaller ones..
So prob =2/(2+1)=2/3

2) each vertex will make the largest diagonal, so 6/2=3..
Total diagonals=6C2-number of sides= 5*6/2 - 6=15-6=9..
Ans (9-3)/9=2/3

D
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5459 [0], given: 112

Senior Manager
Joined: 23 Apr 2015
Posts: 332

Kudos [?]: 112 [0], given: 36

Location: United States
WE: Engineering (Consulting)
Re: What is the probability of randomly selecting one of the shortest diag [#permalink]

### Show Tags

11 Sep 2016, 00:15
Bunuel wrote:
What is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular hexagon?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 7/9

A regular hexagon has 3 diagonals in which 2 are of same length and shorter than the other.
so probability = $$\frac{2}{3}$$ Answer is D

Kudos [?]: 112 [0], given: 36

Manager
Joined: 21 Jul 2017
Posts: 80

Kudos [?]: 8 [0], given: 59

Location: India
GMAT 1: 750 Q51 V41
GPA: 4
Re: What is the probability of randomly selecting one of the shortest diag [#permalink]

### Show Tags

14 Aug 2017, 10:07
The number of diagonals of a polygon is given in the formula: n(n-3)/2 , where n is the number of sides. In the case of the hexagon, the n=6.

A regular hexagon has diagonals: 6(6-3)/2=9 diagonals

Of these 9, 6 are smaller diagonals and three are longer diagonals.

That's a 6/9 = 2/3 chance of randomly picking a shorter diagonal.

Kudos [?]: 8 [0], given: 59

Re: What is the probability of randomly selecting one of the shortest diag   [#permalink] 14 Aug 2017, 10:07
Display posts from previous: Sort by