Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
18 Mar 2019, 01:58
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
22% (02:05) correct
78%
(02:29)
wrong
based on 119
sessions
History
Date
Time
Result
Not Attempted Yet
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
Attachment:
Untitled.png [ 11.24 KiB | Viewed 5627 times ]
18 Mar 2019, 05:33
Kudos
Bookmarks
Bunuel
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 of any of the 8 colors 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 = \((\frac{8}{8})*(\frac{7}{3})*6!=1*7*6*5*4*2=1680\)
E
Edit: To further expand on bold portion above.
Look at the sketch.
We can pick any face and color with any of the available 8 colours. Hence \(\frac{8}{8}\), only one way
Now, we have 7 colours for the second face, but the face has to be adjoining to the blue, so that can fix the octahedron for the remaining 6 colors.
There are three adjoining faces, and 7 colors. The colour picked up can be placed in any of the three faces, but each of these will give us same arrangements of colours.
Here we have taken light brown, but it could be any of the 7 ways. Now the placement of this light brown colour can be at any of the adjoining triangle that is sharing a common side with the blue triangle.
Each of the three faces chosen will result in same arrangement and would depend on arrangements of colour for remaining 6 faces.
Example: We paint 1 next. Say light brown and next 2 as yellow and 3 as black and others in say A, B, C, D, E, F colors. Total ways (8/8)*7*6!
However this will include repetitions THREE times for each as shown in the sketch. Hence divided total by 3 = \((\frac{8}{8})*(\frac{7}{3})*6!=1*7*6*5*4*2=1680\)
Attachments
Untitled009.png [ 57.82 KiB | Viewed 4232 times ]
20 Mar 2019, 07:05
Kudos
Bookmarks
chetan2u
PLEASE EXPLAIN WHAT YOU MEAN BY FIX 2 FACES
