It is currently 23 Jan 2018, 12:07

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the number of different pairs of parallel edges on a cubical

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43381
What is the number of different pairs of parallel edges on a cubical [#permalink]

Show Tags

New post 04 Dec 2017, 02:38
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

50% (00:53) correct 50% (00:53) wrong based on 17 sessions

HideShow timer Statistics

VP
VP
avatar
P
Joined: 22 May 2016
Posts: 1260
Premium Member CAT Tests
What is the number of different pairs of parallel edges on a cubical [#permalink]

Show Tags

New post 04 Dec 2017, 08:56
Bunuel wrote:
What is the number of different pairs of parallel edges on a cubical wooden block?

(A) 18
(B) 12
(C) 8
(D) 6
(E) 4

Attachment:
zzzzzzzz.png
zzzzzzzz.png [ 8.67 KiB | Viewed 228 times ]

There are a few ways to approach this problem.
I drew the first one. It seems the easiest to me.

Sets of parallel edges * 3
See diagram:
There are three sets of parallel edges (purple, green, pink)

Each edge is parallel to three other edges in three directions: top, bottom, diagonally across*

Without duplicates:
Purple edge A is parallel to B, to D, and to C
Purple edge B is parallel to C and D
Purple edge C is parallel to D

Pairs of parallel lines for purple edges?

(A-B), (A-C), (A-D), (B-C), (B-D), and (C-D) = 6 pairs of parallel lines

Pairs of parallel lines for pink edges and green edges will be the same:
So 3 sets * 6 pairs = 18 pairs

Answer A

Number of edges times number of pairs divided by 2

Each edge is parallel to three other edges (see above)
There are 12 edges with 3 pairs of parallel lines
12 * 3 = 36 pairs, but
That figure has double counting: 36/2 = 18 pairs of parallel lines

Answer A

Combinations
Someone else can explain; I can see it but I can't explain it well. :|
There are three edges: vertical, horizontal, and, in the diagram, "connecting" or "projecting" (backwards into 3-D perspective):
\(3 * (_4C_ 2) = 3 * 6 = 18\)

Answer A

*Regarding edges that are parallel on the diagonal plane: the top left edge is parallel to the bottom right edge, e.g.: you could insert a plane on the diagonal / slant. The lines will never meet and the distance between any two corresponding points on the two lines will always be the same. They are parallel edges on the same plane (the diagonal plane of symmetry).
_________________

At the still point, there the dance is. -- T.S. Eliot
Formerly genxer123

1 KUDOS received
Intern
Intern
avatar
B
Joined: 25 May 2017
Posts: 9
GMAT 1: 750 Q49 V44
Re: What is the number of different pairs of parallel edges on a cubical [#permalink]

Show Tags

New post 04 Dec 2017, 09:48
1
This post received
KUDOS
A cube has 12 edges. There are 3 *Groups* of parallel edges

Each Group therefore has 4 edges

Lets take Group 1:
We need pairs of parallel edges. Which means we need to pick 2 edges from 4 edges.
This is simply 4C2 = \(\frac{4 x 3}{2 x 1}\) = 6

Therefore Group 2 and Group 3 will also have the same = 6 and 6

6 + 6 + 6 = 18 total "pairs" of parallel edges.
_________________

GmatIvyPrep
Yale MBA Graduate and GMAT-Focused Tutor for 4+ years
Contact: gmativyprep@gmail.com for a consultation and private tutoring rates

Image

Material offered free of charge along with full end-to-end GMAT Quantitative Course:
- High-level (700+) practice question sets for Quantitative section by topic
- AWA writing template that helped students get a full score on the Essay
- Complete pack of Verbal Material for SC, RC and CR

Re: What is the number of different pairs of parallel edges on a cubical   [#permalink] 04 Dec 2017, 09:48
Display posts from previous: Sort by

What is the number of different pairs of parallel edges on a cubical

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.