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

It is currently 20 Oct 2018, 14:22

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

What is the maximum number of points common to the intersection of a s

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

Hide Tags

SVP
SVP
User avatar
V
Status: Preparing GMAT
Joined: 02 Nov 2016
Posts: 1737
Location: Pakistan
GPA: 3.39
Premium Member CAT Tests
What is the maximum number of points common to the intersection of a s  [#permalink]

Show Tags

New post 14 Aug 2017, 04:40
1
6
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

70% (01:02) correct 30% (01:02) wrong based on 93 sessions

HideShow timer Statistics

What is the maximum number of points common to the intersection of a square and a triangle if no two sides coincide?

(A) 4
(B) 5
(C) 6
(D) 8
(E) 9

_________________

Official PS Practice Questions
Press +1 Kudos if this post is helpful

Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 2036
Premium Member CAT Tests
Re: What is the maximum number of points common to the intersection of a s  [#permalink]

Show Tags

New post 14 Aug 2017, 07:21
1
SajjadAhmad wrote:
What is the maximum number of points common to the intersection of a square and a triangle if no two sides coincide?

(A) 4
(B) 5
(C) 6
(D) 8
(E) 9

Attachment:
zzz.jpg
zzz.jpg [ 17.43 KiB | Viewed 4223 times ]

Without using trigonometry, as far as I know, you can do no more than to draw the shapes.

If anyone knows a method that does not involve trigonometry, please post it. (I thought about line equation intersections . . . )

Maximum number is 6.

Answer C
_________________

___________________________________________________________________
For what are we born if not to aid one another?
-- Ernest Hemingway

CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 3021
Location: Canada
Re: What is the maximum number of points common to the intersection of a s  [#permalink]

Show Tags

New post 14 Aug 2017, 07:48
2
Top Contributor
SajjadAhmad wrote:
What is the maximum number of points common to the intersection of a square and a triangle if no two sides coincide?

(A) 4
(B) 5
(C) 6
(D) 8
(E) 9


We might start by examining the number of ways that ONE SIDE of a triangle can intersect a square.
In other words, in how many ways can a LINE intersect a square?
After a bit of mental imagery, we might conclude that a SINGLE LINE can intersect a square in at MOST 2 ways

A triangle is composed of THREE LINE SEGMENTS.
If each SINGLE LINE can intersect a square in at MOST 2 ways, then the 3-sided triangle can intersect a square in AT MOST 6 ways (with 2 intersections per line)
So, the correct answer must be 6 or less

At that point, if we're able to sketch a scenario in which there are 6 intersections, we can be certain that this is, indeed, the GREATEST number of intersections.

Answer:

Cheers,
Brent
_________________

Brent Hanneson – GMATPrepNow.com
Image
Sign up for our free Question of the Day emails

Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 2036
Premium Member CAT Tests
What is the maximum number of points common to the intersection of a s  [#permalink]

Show Tags

New post 14 Aug 2017, 09:17
GMATPrepNow wrote:
SajjadAhmad wrote:
What is the maximum number of points common to the intersection of a square and a triangle if no two sides coincide?

(A) 4
(B) 5
(C) 6
(D) 8
(E) 9


We might start by examining the number of ways that ONE SIDE of a triangle can intersect a square.
In other words, in how many ways can a LINE intersect a square?
After a bit of mental imagery, we might conclude that a SINGLE LINE can intersect a square in at MOST 2 ways

A triangle is composed of THREE LINE SEGMENTS.
If each SINGLE LINE can intersect a square in at MOST 2 ways, then the 3-sided triangle can intersect a square in AT MOST 6 ways (with 2 intersections per line)
So, the correct answer must be 6 or less

At that point, if we're able to sketch a scenario in which there are 6 intersections, we can be certain that this is, indeed, the GREATEST number of intersections.

Answer:

Cheers,
Brent

GMATPrepNow
Brent, I did exactly that which you describe. I concluded similarly that
Quote:
If each SINGLE LINE can intersect a square in at MOST 2 ways, then the 3-sided triangle can intersect a square in AT MOST 6 ways (with 2 intersections per line).

Then, however, you write, "if we're able to sketch a scenario in which there are 6 intersections," our calculation is correct.

It sounds as if the outcome depends on whether or not the maximum number intersection points we have calculated can be drawn. Is that impression accurate?

If not, may we assume that, for two co-planar shapes without concave sides, the maximum number of intersection points can be calculated by taking the figure with fewer sides "S," and multiplying S by two? (If same S, use S.)
_________________

___________________________________________________________________
For what are we born if not to aid one another?
-- Ernest Hemingway

CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 3021
Location: Canada
Re: What is the maximum number of points common to the intersection of a s  [#permalink]

Show Tags

New post 14 Aug 2017, 10:35
1
Top Contributor
genxer123 wrote:
Brent, I did exactly that which you describe. I concluded similarly that
Quote:
If each SINGLE LINE can intersect a square in at MOST 2 ways, then the 3-sided triangle can intersect a square in AT MOST 6 ways (with 2 intersections per line).

Then, however, you write, "if we're able to sketch a scenario in which there are 6 intersections," our calculation is correct.

It sounds as if the outcome depends on whether or not the maximum number intersection points we have calculated can be drawn. Is that impression accurate?

If not, may we assume that, for two co-planar shapes without concave sides, the maximum number of intersection points can be calculated by taking the figure with fewer sides "S," and multiplying S by two? (If same S, use S.)


You're correct on the first part.
Once we've determined that the answer cannot be greater than 6, then we need to first check whether we can get 6 intersections. If we can, then we're done.
If we can't we need to figure out whether it's actually impossible to get 6 intersections OR whether we just didn't do a good enough job finding a case with 6 intersections.

If the given shapes all have interior angles LESS THAN 180 degrees, then the maximum number of intersections will be 2S (where S = the number of sides of the polygon with the fewest sides)

HOWEVER, if any of the interior angles GREATER THAN 180 degrees, then all bets are off!

Cheers,
Brent
_________________

Brent Hanneson – GMATPrepNow.com
Image
Sign up for our free Question of the Day emails

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8484
Premium Member
Re: What is the maximum number of points common to the intersection of a s  [#permalink]

Show Tags

New post 20 Sep 2018, 03:13
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: What is the maximum number of points common to the intersection of a s &nbs [#permalink] 20 Sep 2018, 03:13
Display posts from previous: Sort by

What is the maximum number of points common to the intersection of a s

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.