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

 It is currently 16 Oct 2019, 22:26

### 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

# How many points (x, y) lie on the line segment between (22, 12 2/3) an

Author Message
TAGS:

### Hide Tags

Manager
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 244
How many points (x, y) lie on the line segment between (22, 12 2/3) an  [#permalink]

### Show Tags

Updated on: 14 Nov 2014, 09:20
2
11
00:00

Difficulty:

65% (hard)

Question Stats:

65% (02:38) correct 35% (02:56) wrong based on 242 sessions

### HideShow timer Statistics

How many points (x, y) lie on the line segment between (22, 12 2/3) and (7, 17 2/3) such that x and y are both integers?

A. 4
B. 5
C. 7
D. 8
E. 9

_________________
I'm the Dumbest of All !!

Originally posted by shrive555 on 28 Oct 2010, 17:17.
Last edited by Bunuel on 14 Nov 2014, 09:20, edited 1 time in total.
Renamed the topic and edited the question.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9705
Location: Pune, India
Re: How many points (x, y) lie on the line segment between (22, 12 2/3) an  [#permalink]

### Show Tags

28 Oct 2010, 19:03
3
3
The line joins the points (7, 17 2/3) and (22, 12 2/3).
The slope of the line will be (17 2/3 - 12 2/3)/(7 - 22) = -1/3

What does a slope of -1/3 imply? It implies that for every decrease of 1 unit in the value of y, x will increase by 3 units or in other words, for every decrease of 1/3 in value of y, x will increase by 1 unit.

Start from the left end point. When value of y becomes 17 i.e. a reduction of 2/3 , value of x will be increase by 2 and will become 9. When value of y reduces by another 1 unit, value of x will increase by 3 units and will become 12 and so on... You will have 5 integral values of y (17, 16, 15, 14 and 13). For each of these values, x will be integral.
Attachment:

Ques.jpg [ 8.16 KiB | Viewed 10975 times ]

The last point in the diagram above is 13, not 12.
_________________
Karishma
Veritas Prep GMAT Instructor

##### General Discussion
Intern
Joined: 26 Mar 2010
Posts: 26
Re: How many points (x, y) lie on the line segment between (22, 12 2/3) an  [#permalink]

### Show Tags

28 Oct 2010, 18:48
2
2
slope = (17 2/3 - 12 2/3) / (7 - 22) = -1/3
y = mx + b => 12 2/3 = -22/3 + b => b = 20
y = -x/3 + 20

Only integer values work, and the only multiples of 3 between 7 and 22 for x values are 9, 12, 15, 18 and 21, thus 5 points.
Manager
Joined: 20 Apr 2010
Posts: 169
Schools: ISB, HEC, Said
Re: How many points (x, y) lie on the line segment between (22, 12 2/3) an  [#permalink]

### Show Tags

30 Oct 2010, 03:58
VeritasPrepKarishma wrote:
The line joins the points (7, 17 2/3) and (22, 12 2/3).
The slope of the line will be (17 2/3 - 12 2/3)/(7 - 22) = -1/3

What does a slope of -1/3 imply? It implies that for every decrease of 1 unit in the value of y, x will increase by 3 units or in other words, for every decrease of 1/3 in value of y, x will increase by 1 unit.

Start from the left end point. When value of y becomes 17 i.e. a reduction of 2/3 , value of x will be increase by 2 and will become 9. When value of y reduces by another 1 unit, value of x will increase by 3 units and will become 12 and so on... You will have 5 integral values of y (17, 16, 15, 14 and 13). For each of these values, x will be integral.
Attachment:
Ques.jpg

The last point in the diagram above is 13, not 12.

I felt this as very time consuming. I got the answer the same way you have suggested. Is there any other way to solve this quickly?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9705
Location: Pune, India
Re: How many points (x, y) lie on the line segment between (22, 12 2/3) an  [#permalink]

### Show Tags

30 Oct 2010, 08:36
It takes under a minute to get to the solution since you know that x will be integral and you only have to count integral values from 12 2/3 to 17 2/3.

Nevertheless, let me think. If I come up with a solution that takes even less time, I will let you know...
_________________
Karishma
Veritas Prep GMAT Instructor

Math Expert
Joined: 02 Sep 2009
Posts: 58390
Re: How many points (x, y) lie on the line segment between (22, 12 2/3) an  [#permalink]

### Show Tags

14 Nov 2014, 09:21
shrive555 wrote:
How many points (x, y) lie on the line segment between (22, 12 2/3) and (7, 17 2/3) such that x and y are both integers?

A. 4
B. 5
C. 7
D. 8
E. 9

Similar questions to practice:
how-many-integer-points-lie-between-points-a-and-on-the-line-segment-109623.html
in-the-figure-above-how-many-of-the-points-on-line-segment-108673.html
_________________
Manager
Joined: 24 Jun 2017
Posts: 117
How many points (x, y) lie on the line segment between (22, 12 2/3) an  [#permalink]

### Show Tags

10 Sep 2017, 22:38
The fastest way I know:
you find the slope (17 2/3 - 12 2/3) / (7 - 22) = -1/3
you find the y intercept by taking x y for any point y = mx + b = 12 2/3 = -22/3 + b b = 20
then create a function for the line y = -1/3*x + 20

domain for the x (7 to 22)
Between 17 2/3 and 12 2/3 there are 5 integer values of y, 13, 14, 15, 16, 17
so y = -1/3*x + 20
13 = -1/3*x + 20 (-1/3*x = 7)
14 = -1/3*x + 20 (-1/3*x = 6)
when you resolve first 2 the rest is going much faster

however takes some time a bit more than >2mins
for such kind of questions main to pay attention of the points are on the line or between 2 suggested points
Non-Human User
Joined: 09 Sep 2013
Posts: 13204
Re: How many points (x, y) lie on the line segment between (22, 12 2/3) an  [#permalink]

### Show Tags

02 Feb 2019, 07:32
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.
_________________
Re: How many points (x, y) lie on the line segment between (22, 12 2/3) an   [#permalink] 02 Feb 2019, 07:32
Display posts from previous: Sort by