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

 It is currently 21 Jun 2018, 09:03

### 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

# The figure above shows that 4 straight lines can have 6 points of

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 46251
The figure above shows that 4 straight lines can have 6 points of [#permalink]

### Show Tags

15 Aug 2017, 23:08
00:00

Difficulty:

(N/A)

Question Stats:

77% (00:38) correct 23% (00:05) wrong based on 31 sessions

### HideShow timer Statistics

The figure above shows that 4 straight lines can have 6 points of intersection. The greatest number of points of intersection of 5 straight lines is

(A) 9
(B) 10
(C) 12
(D) 15
(E) 20

Attachment:

2017-08-16_1006.png [ 5.31 KiB | Viewed 488 times ]

_________________
SC Moderator
Joined: 22 May 2016
Posts: 1757
The figure above shows that 4 straight lines can have 6 points of [#permalink]

### Show Tags

16 Aug 2017, 07:07
3
Bunuel wrote:

The figure above shows that 4 straight lines can have 6 points of intersection. The greatest number of points of intersection of 5 straight lines is

(A) 9
(B) 10
(C) 12
(D) 15
(E) 20

Attachment:
The attachment 2017-08-16_1006.png is no longer available

Attachment:

5lines.png [ 8.7 KiB | Viewed 354 times ]

(Count the black dots and the red ones I added to get the total # of intersections.)

Formula for maximum number of intersections made by n lines, which writing out the pattern helped me remember, is

$$\frac{n(n-1)}{2}$$

$$\frac{5(4)}{2}$$ = 10

Here's the pattern:

# of lines|(# of intersections) -->

1(0)
2(1)
3(3)
4(6)
5(10)

1 + 0 = 1 (for two lines)
2 + 1 = 3 (for three lines)
3 + 3 = 6 (for four lines)
4 + 6 = 10 (for five lines)

_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

The figure above shows that 4 straight lines can have 6 points of   [#permalink] 16 Aug 2017, 07:07
Display posts from previous: Sort by