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

 It is currently 22 Oct 2019, 04:22

### 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

# Let S be the set of points (a, b) in the coordinate plane, where each

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58428
Let S be the set of points (a, b) in the coordinate plane, where each  [#permalink]

### Show Tags

21 Mar 2019, 04:52
1
7
00:00

Difficulty:

95% (hard)

Question Stats:

25% (02:13) correct 75% (02:00) wrong based on 48 sessions

### HideShow timer Statistics

Let S be the set of points (a, b) in the coordinate plane, where each of a and b may be -1, 0, or 1. How many distinct lines pass through at least two members of S?

(A) 8
(B) 20
(C) 24
(D) 27
(E) 36

_________________
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5031
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Let S be the set of points (a, b) in the coordinate plane, where each  [#permalink]

### Show Tags

21 Mar 2019, 09:33
1
Bunuel wrote:
Let S be the set of points (a, b) in the coordinate plane, where each of a and b may be -1, 0, or 1. How many distinct lines pass through at least two members of S?

(A) 8
(B) 20
(C) 24
(D) 27
(E) 36

total pairs of points which can be formed is 9
and line passing through 2 such points 9c2 = 36

we have overcounted all of the lines which pass through three points. In fact, each line which passes through three points will have been counted 3c2 = 3 times
3 horizontal, 3 vertical, and 2 diagonal lines, so the answer is 36 - 2(3+3+2) = 20
IMO B
Intern
Joined: 09 Apr 2018
Posts: 13
Re: Let S be the set of points (a, b) in the coordinate plane, where each  [#permalink]

### Show Tags

24 Mar 2019, 13:49
Archit3110 wrote:
Bunuel wrote:
Let S be the set of points (a, b) in the coordinate plane, where each of a and b may be -1, 0, or 1. How many distinct lines pass through at least two members of S?

(A) 8
(B) 20
(C) 24
(D) 27
(E) 36

total pairs of points which can be formed is 9
and line passing through 2 such points 9c2 = 36

we have overcounted all of the lines which pass through three points. In fact, each line which passes through three points will have been counted 3c2 = 3 times
3 horizontal, 3 vertical, and 2 diagonal lines, so the answer is 36 - 2(3+3+2) = 20
IMO B

Can you please elaborate the process for counting lines passing through 3 points?

Posted from my mobile device
Manager
Joined: 11 Aug 2017
Posts: 59
Re: Let S be the set of points (a, b) in the coordinate plane, where each  [#permalink]

### Show Tags

25 Mar 2019, 02:56
Archit3110 wrote:
Bunuel wrote:
Let S be the set of points (a, b) in the coordinate plane, where each of a and b may be -1, 0, or 1. How many distinct lines pass through at least two members of S?

(A) 8
(B) 20
(C) 24
(D) 27
(E) 36

total pairs of points which can be formed is 9
and line passing through 2 such points 9c2 = 36

we have overcounted all of the lines which pass through three points. In fact, each line which passes through three points will have been counted 3c2 = 3 times
3 horizontal, 3 vertical, and 2 diagonal lines, so the answer is 36 - 2(3+3+2) = 20
IMO B

Could you please elaborate 2nd part of the explanation.. It's a bouncer for me.
Manager
Joined: 17 Jun 2018
Posts: 52
Schools: IMD '20
GPA: 2.84
WE: Engineering (Real Estate)
Re: Let S be the set of points (a, b) in the coordinate plane, where each  [#permalink]

### Show Tags

25 Mar 2019, 10:21
chetan2u please can you explain how to crack this one ?
Math Expert
Joined: 02 Aug 2009
Posts: 8006
Re: Let S be the set of points (a, b) in the coordinate plane, where each  [#permalink]

### Show Tags

25 Mar 2019, 21:07
Bunuel wrote:
Let S be the set of points (a, b) in the coordinate plane, where each of a and b may be -1, 0, or 1. How many distinct lines pass through at least two members of S?

(A) 8
(B) 20
(C) 24
(D) 27
(E) 36

The points should tell you that you are looking at a square with coordinates (-1,-1), (-1,1), (1,1) and (1,-1). The centre of the square and midpoint of each side are other points..
So, in total we have 9 points. But, the centre will always be part of 3 points.

So we are left with 8 points, and we have to choose 2 out of it, so 8C2=8*7/2=28.
Now, the sides of the square consists of 3 points. We have counted each side thrice, so 4*2 are repeated. Thus, 28-8=20.
For example.. side containing points A(-1,-1), B(-1,0) and C(-1,1).. The line is only one but we have calculated it thrice in our calculations. AB, BC and AC, whereas it is just on eline AC.

B
Attachments

coordi.png [ 55.58 KiB | Viewed 391 times ]

_________________
Re: Let S be the set of points (a, b) in the coordinate plane, where each   [#permalink] 25 Mar 2019, 21:07
Display posts from previous: Sort by