GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 18 Oct 2019, 21:43

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.

Close

Request Expert Reply

Confirm Cancel

Eight congruent equilateral triangles, each of a different color, are

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58453
Eight congruent equilateral triangles, each of a different color, are  [#permalink]

Show Tags

New post 18 Mar 2019, 01:58
10
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

20% (01:47) correct 80% (02:23) wrong based on 40 sessions

HideShow timer Statistics

Image

Eight congruent equilateral triangles, each of a different color, are used to construct a regular octahedron. How many distinguishable ways are there to construct the octahedron? (Two colored octahedrons are distinguishable if neither can be rotated to look just like the other.)


(A) 210
(B) 560
(C) 840
(D) 1260
(E)}1680

_________________
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 7981
Re: Eight congruent equilateral triangles, each of a different color, are  [#permalink]

Show Tags

New post 18 Mar 2019, 05:33
Bunuel wrote:
Image

Eight congruent equilateral triangles, each of a different color, are used to construct a regular octahedron. How many distinguishable ways are there to construct the octahedron? (Two colored octahedrons are distinguishable if neither can be rotated to look just like the other.)


(A) 210
(B) 560
(C) 840
(D) 1260
(E)}1680


An octahedron has 8 triangles.
So, we have to fix 2 faces, before applying colours.
So, the first face that can be fixed can be any of the 8 faces but each face will be similar , so 8/8 ways.
Now, when you have fixed one face, the three adjoining faces are similar, so we have 7 colours for the second face, so 7/3.
Now, you can place any color anywhere, it will be a different arrangement, so 6!
Total = (8/8)*(7/3)*6!=1*7*6*5*4*2=1680

E
_________________
Intern
Intern
avatar
B
Joined: 21 Nov 2018
Posts: 8
Location: India
Re: Eight congruent equilateral triangles, each of a different color, are  [#permalink]

Show Tags

New post 20 Mar 2019, 07:05
chetan2u wrote:
Bunuel wrote:
Image

Eight congruent equilateral triangles, each of a different color, are used to construct a regular octahedron. How many distinguishable ways are there to construct the octahedron? (Two colored octahedrons are distinguishable if neither can be rotated to look just like the other.)


(A) 210
(B) 560
(C) 840
(D) 1260
(E)}1680


An octahedron has 8 triangles.
So, we have to fix 2 faces, before applying colours.
So, the first face that can be fixed can be any of the 8 faces but each face will be similar , so 8/8 ways.



Now, when you have fixed one face, the three adjoining faces are similar, so we have 7 colours for the second face, so 7/3.
Now, you can place any color anywhere, it will be a different arrangement, so 6!
Total = (8/8)*(7/3)*6!=1*7*6*5*4*2=1680

E










PLEASE EXPLAIN WHAT YOU MEAN BY FIX 2 FACES
Intern
Intern
avatar
B
Joined: 04 Feb 2019
Posts: 3
Re: Eight congruent equilateral triangles, each of a different color, are  [#permalink]

Show Tags

New post 20 Mar 2019, 07:14
chetan2u, Bunuel, VeritaKarishma please explain what do you mean by 7/3 ?
Intern
Intern
avatar
B
Joined: 12 Sep 2018
Posts: 27
Re: Eight congruent equilateral triangles, each of a different color, are  [#permalink]

Show Tags

New post 24 Mar 2019, 05:17
Divide the figure into 2 pyramids. Each will have a unique combination of 4 colours.
The number of these combinations is 8C4=70.
Then, considering the 4 faces of the pyramid, we need to find the number of different arrangements of the colour, hence the permutation 4!=24.

Finally 8C4x4!=70x24=1680 E
Manager
Manager
avatar
P
Joined: 01 Feb 2017
Posts: 242
Eight congruent equilateral triangles, each of a different color, are  [#permalink]

Show Tags

New post 28 Mar 2019, 04:07
1
Total number of faces= 8
Total number of colors= 8
Now, 8 colors can be placed in these 8 slots in 8! ways.

Among these 8! combinations, there are 24 sets of mirror images:
As octahedron has 6 vertices, there are 6 options for a vertices to be placed on.
And for each position of vertices, there are 4 rotations available.
Hence, there are 6*4 = 24 sets of mirror images.

Therefore, Distinguishable Octahedrons (i.e total combinations corrected for mirror images) = 8!/24= 1680.
Ans E
Intern
Intern
avatar
B
Joined: 24 Dec 2018
Posts: 33
GMAT 1: 740 Q50 V40
Re: Eight congruent equilateral triangles, each of a different color, are  [#permalink]

Show Tags

New post 10 May 2019, 11:31
Shobhit7 wrote:
Total number of faces= 8
Total number of colors= 8
Now, 8 colors can be placed in these 8 slots in 8! ways.

Among these 8! combinations, there are 24 sets of mirror images:
As octahedron has 6 vertices, there are 6 options for a vertices to be placed on.
And for each position of vertices, there are 4 rotations available.
Hence, there are 6*4 = 24 sets of mirror images.

Therefore, Distinguishable Octahedrons (i.e total combinations corrected for mirror images) = 8!/24= 1680.
Ans E


Can you please elaborate how did you came up with number of mirror images (may be by considering other 3-D figure).
_________________
+1 Kudos if you like the Question
GMAT Club Bot
Re: Eight congruent equilateral triangles, each of a different color, are   [#permalink] 10 May 2019, 11:31
Display posts from previous: Sort by

Eight congruent equilateral triangles, each of a different color, are

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne