BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

points on PQ

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 431
Joined: Sat Jan 10, 2009 9:32 am
Thanked: 16 times
Followed by:1 members

points on PQ

by kanha81 » Wed May 27, 2009 10:35 am
In the attached figure, how many of the points on line segment PQ have coordinates that are both integers?

A) 5
B) 8
C) 10
D) 11
E) 20

Please explain.
Attachments
integers on PQ.pdf
(41.63 KiB) Downloaded 124 times
Want to Beat GMAT.
Always do what you're afraid to do. Whoooop GMAT
Top
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 139
Joined: Wed Oct 22, 2008 4:36 am
Thanked: 17 times

by sacx » Wed May 27, 2009 11:07 pm
I am getting 11 but I don't know if my method is correct

Slope of the line PQ = -3/5 or -0.6

so for every 0.6 increase in y-axis, x-axis decreases by 1

so the integer values for y-axis would be an interval of 3 (3,6,9,12,15,18,21,24,27,30)

So the points would be
(3,45)
(6,40)
(9,35)
(12,30)
(15,25)
(18,20)
(21,15)
(24,10)
(27,5)
(30,0)

and (50,0)

Whats the OA?
SACX
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 435
Joined: Sat Sep 27, 2008 2:02 pm
Location: San Jose, CA
Thanked: 43 times
Followed by:1 members
GMAT Score:720

by dumb.doofus » Wed May 27, 2009 11:12 pm
Just write the equation of the line..

y = -3/5x + 30..

Now for y to be an integer.. x needs to be a multiple of 5 or zero.

from 5 to 50 there are 10 multiples.. and when we include 0.. the total number of integers is 11..

so 11 points on the line are integers..

I have used the following formula to write the equation of a line..
When you have two points (x1,y1) and (x2,y2) .. then line joining these two points is

(x-x1)/(x2-x1) = (y-y1)/(y2-y1)
One love, one blood, one life. You got to do what you should.
https://dreambigdreamhigh.blocked/
https://gmattoughies.blocked/
Top
Master | Next Rank: 500 Posts
Posts: 122
Joined: Fri May 22, 2009 10:38 pm
Thanked: 8 times
GMAT Score:700

Find the equation of line

by rah_pandey » Thu May 28, 2009 1:19 am
The equation of the line is x=50-5/3*y

for x and Y to be integers it is necessary from the equation above that y is a factor of 3 with the condition that y<=30 otherwise infinite solns exist.

the factors are 0,3,6,9.....30. Now if 0 and 30 are included than 11 is correct answer and if both are excluded than 9 such points exist. if only one than 10 such points exist.
(50,0),(45,3),(40,6) and so on...
Top
Master | Next Rank: 500 Posts
Posts: 431
Joined: Sat Jan 10, 2009 9:32 am
Thanked: 16 times
Followed by:1 members

by kanha81 » Thu May 28, 2009 6:52 am
dumb.doofus wrote:Just write the equation of the line..

y = -3/5x + 30..

Now for y to be an integer.. x needs to be a multiple of 5 or zero.

from 5 to 50 there are 10 multiples.. and when we include 0.. the total number of integers is 11..

so 11 points on the line are integers..

I have used the following formula to write the equation of a line..
When you have two points (x1,y1) and (x2,y2) .. then line joining these two points is

(x-x1)/(x2-x1) = (y-y1)/(y2-y1)
Thank you all. The explanation makes sense. OA is [spoiler][D][/spoiler]
Want to Beat GMAT.
Always do what you're afraid to do. Whoooop GMAT
Top
Post new topic Post Reply
• Page 1 of 1