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

 It is currently 20 Oct 2019, 17:00

### 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

# In a rectangular coordinate system, which of the following

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

### Hide Tags

Manager
Joined: 22 Sep 2010
Posts: 71
In a rectangular coordinate system, which of the following  [#permalink]

### Show Tags

Updated on: 22 Sep 2012, 10:03
2
21
00:00

Difficulty:

55% (hard)

Question Stats:

66% (02:06) correct 34% (02:27) wrong based on 412 sessions

### HideShow timer Statistics

In a rectangular coordinate system, which of the following points is intersected by the line connected by the coordinates (5,6) and (21,18)?

A. (9,9)
B. (12,12)
C. (13,13)
D. (12,13)
E. (16,15)

Originally posted by pzazz12 on 20 Oct 2010, 02:55.
Last edited by Bunuel on 22 Sep 2012, 10:03, edited 1 time in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 58434
Re: In a rectangular coordinate system ............  [#permalink]

### Show Tags

20 Oct 2010, 03:05
8
6
pzazz12 wrote:
In a rectangular coordinate system ,which of the following points is intersected by the line connected by the coordinates (5,6) and(21,18)?
A.(9,9)
B.(12,12)
C.(13,13)
D.(12,13)
E.(16,15)

The slope of a line passing through the points (5,6) and (21,18) is "rise over run": $$\frac{18-6}{21-5}=\frac{3}{4}$$.

The slope of a line passing through the point (5,6) and one of the points from the answer choice must also be $$\frac{3}{4}$$ (as it's the same lin), so $$\frac{y-6}{x-5}=\frac{3}{4}$$.

Answer choice A works: $$\frac{9-6}{9-5}=\frac{3}{4}$$.

For more on these issues check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html

Hope it helps.
_________________
##### General Discussion
Manager
Joined: 08 Sep 2010
Posts: 150
Location: India
WE 1: 6 Year, Telecom(GSM)
Re: In a rectangular coordinate system ............  [#permalink]

### Show Tags

20 Oct 2010, 03:15
pzazz12 wrote:
In a rectangular coordinate system ,which of the following points is intersected by the line connected by the coordinates (5,6) and(21,18)?
A.(9,9)
B.(12,12)
C.(13,13)
D.(12,13)
E.(16,15)

Equation of the line connecting the two points,(5,6) and (21,18);

y-6= {(6-18)/(5-21)}(x-5) or , 4y-3x=9

Only ( 9,9) is satisfying the equation.Hence answer is A.

Consider KUDOS if its helpful to u .Thanks.
Current Student
Joined: 23 May 2013
Posts: 183
Location: United States
Concentration: Technology, Healthcare
GMAT 1: 760 Q49 V45
GPA: 3.5
In a rectangular coordinate system, which of the following  [#permalink]

### Show Tags

31 Dec 2014, 10:24
1
I found the equation of the line to be $$y = \frac{3x}{4} + \frac{9}{4}.$$. Then, noticing that 3 of the options had the same value for x and y, I wanted to check at which point on the line the x and y values were equal. So I solved for x:

$$x = \frac{3x}{4} + \frac{9}{4}$$
$$\frac{x}{4} = \frac{9}{4}.$$
$$x = 9.$$

Therefore, (9,9) is a point on the line and our answer is A.

Further: If we would have found some other value (one that wasn't listed on the answer choices) then we at least could have eliminated 3 of the answer choices and then manually checked the other two.
Director
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 531
Location: India
Re: In a rectangular coordinate system, which of the following  [#permalink]

### Show Tags

08 Mar 2017, 02:19
equation of line: y-6 = {(18-6)/(21-5)} (x-5)
rearranging we get 4y-3x = 9. Put the co ordinates, given in the option, in the equation.

we will get (9,9) as answer

Option A
_________________
GMAT Mentors
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8117
Location: United States (CA)
Re: In a rectangular coordinate system, which of the following  [#permalink]

### Show Tags

10 Mar 2017, 10:35
1
pzazz12 wrote:
In a rectangular coordinate system, which of the following points is intersected by the line connected by the coordinates (5,6) and (21,18)?

A. (9,9)
B. (12,12)
C. (13,13)
D. (12,13)
E. (16,15)

Let’s first create the equation of a line for coordinates (5,6) and (21,18).

Slope = Δy/Δx = 12/16 = 3/4.

We can substitute in either ordered pair to calculate the y-intercept. Let’s use (5,6):

y = (3/4)x + b

6 = (3/4)(5) + b

6 = 15/4 + b

24/4 = 15/4 + b

9/4 = b

Thus, y = (3/4)x + 9/4

Let’s now substitute each set of coordinates to see which holds true in our equation.

A) (9,9)

9 = (3/4)(9) + 9/4 ?

9 = 27/4 + 9/4 ?

9 = 36/4 ?

9 = 9 ? → Yes!

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager
Joined: 30 Apr 2013
Posts: 76
Re: In a rectangular coordinate system, which of the following  [#permalink]

### Show Tags

01 Sep 2017, 00:56
Can someone solve this using graph?
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4015
Re: In a rectangular coordinate system, which of the following  [#permalink]

### Show Tags

29 Mar 2018, 16:37
2
Top Contributor
1
pzazz12 wrote:
In a rectangular coordinate system, which of the following points is intersected by the line connected by the coordinates (5,6) and (21,18)?

A. (9,9)
B. (12,12)
C. (13,13)
D. (12,13)
E. (16,15)

One approach is to first find the slope
Slope = (18 - 6)/(21 - 5) = 12/16 = 3/4

IMPORTANT: if the slope is 3/4, then we can start at (5,6) and move up 3 spaces and then move right 4 spaces to find other points on the line (with INTEGER values)

Start at: (5,6)
Move 3 units up and 4 units to the right to get to the point (9,9) (check answer choices - it's there!)

Cheers ,
Brent
_________________
Test confidently with gmatprepnow.com
Non-Human User
Joined: 09 Sep 2013
Posts: 13317
Re: In a rectangular coordinate system, which of the following  [#permalink]

### Show Tags

20 May 2019, 07:43
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: In a rectangular coordinate system, which of the following   [#permalink] 20 May 2019, 07:43
Display posts from previous: Sort by

# In a rectangular coordinate system, which of the following

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne