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

 It is currently 22 Oct 2019, 12:35 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  The vertex of a parallelogram are (1, 0), (3, 0), (1, 1) and (3, 1)

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

Hide Tags

Intern  Joined: 05 Nov 2013
Posts: 12
Schools: Cambridge, HEC '15
The vertex of a parallelogram are (1, 0), (3, 0), (1, 1) and (3, 1)  [#permalink]

Show Tags

3
32 00:00

Difficulty:   65% (hard)

Question Stats: 66% (02:29) correct 34% (02:20) wrong based on 106 sessions

HideShow timer Statistics

The vertex of a parallelogram are (1, 0), (3, 0), (1, 1) and (3, 1) respectively. If line L passes through the origin and divided the parallelogram into two identical quadrilaterals, what is the slope of line L?

A. 1/2
B. 2
C. 1/4
D. 3
E. 3/4

Hi, pls help with the solution of the above question. I find co-ordinate geometry very confusing. Are there some quick tips that you may recommend me to follow - when such questions appears in test?

Originally posted by amitasagar23 on 30 Dec 2013, 07:05.
Last edited by Bunuel on 07 Jun 2016, 21:59, edited 2 times in total.
Renamed the topic and edited the question.
Manager  S
Status: Don't Give Up!
Joined: 15 Aug 2014
Posts: 95
Location: India
Concentration: Operations, General Management
GMAT Date: 04-25-2015
WE: Engineering (Manufacturing)
Re: The vertex of a parallelogram are (1, 0), (3, 0), (1, 1) and (3, 1)  [#permalink]

Show Tags

10
2
amitasagar23 wrote:
The vertex of a parallelogram are (1, 0), (3, 0), (1, 1) and (3, 1) respectively. If line L passes through the origin and divided the parallelogram into two identical quadrilaterals, what is the slope of line L?

A. 1/2
B. 2
C. 1/4
D. 3
E. 3/4

Hi, pls help with the solution of the above question. I find co-ordinate geometry very confusing. Are there some quick tips that you may recommend me to follow - when such questions appears in test?

Hi,

Please check below attached approach
Attachments

File comment: Different approach IMG_1433.JPG [ 719.49 KiB | Viewed 6549 times ]

_________________
- Sachin

-If you like my explanation then please click "Kudos"
General Discussion
Senior Manager  Status: busyness school student
Joined: 09 Sep 2013
Posts: 415
Location: United States
Schools: Tepper '16 (M)
GMAT 1: 730 Q52 V37 Re: The vertex of a parallelogram are (1, 0), (3, 0), (1, 1) and (3, 1)  [#permalink]

Show Tags

7
First, quickly draw an xy graph and draw the rectangle. Look at the answer choices. You should see that B and D are immediately out. Slopes of 2 and 3 (or y = 2x and y = 3x) will miss the rectangle completely. Visually, this should take a second.

Now let's try answer choice A of slope 1/2 (y = .5x). It's the middle of 1/4 and 3/4. If the line has a slope of .5, then it must go through points (1, 0.5) and (2, 1) through the rectangle. Visualize that line and see where it goes through on the rectangle. Clearly, this doesn't divide the rectangle in half like we wanted, so answer choice A is out.

Answer choice E is out as well, since it's greater than 1/2. We need a smaller slope.

So at this point, I would put down answer choice C. But let's verify anyway. Slope 1/4 is the same as y = .25x, and it should be a line going through (2, 0.5). Since this is the center of the rectangle, it makes sense this would be the answer.

C it is!
_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 58427
Re: The vertex of a parallelogram are (1, 0), (3, 0), (1, 1) and (3, 1)  [#permalink]

Show Tags

1
3
amitasagar23 wrote:
The vertex of a parallelogram are (1, 0), (3, 0), (1, 1) and (3, 1) respectively. If line L passes through the origin and divided the parallelogram into two identical quadrilaterals, what is the slope of line L?

A. 1/2
B. 2
C. 1/4
D. 3
E. 3/4

Hi, pls help with the solution of the above question. I find co-ordinate geometry very confusing. Are there some quick tips that you may recommend me to follow - when such questions appears in test?

Theory on Coordinate Geometry: math-coordinate-geometry-87652.html

All DS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=41
All PS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=62

You also might find helpful the links in my signature.
_________________
Manager  Status: Oh GMAT ! I give you one more shot :)
Joined: 14 Feb 2013
Posts: 75
Location: United States (MI)
Concentration: General Management, Technology
GMAT 1: 580 Q44 V28 GMAT 2: 690 Q49 V34 GPA: 3.5
WE: Information Technology (Computer Software)
Re: The vertex of a parallelogram are (1, 0), (3, 0), (1, 1) and (3, 1)  [#permalink]

Show Tags

2
1
farful wrote:
First, quickly draw an xy graph and draw the rectangle. Look at the answer choices. You should see that B and D are immediately out. Slopes of 2 and 3 (or y = 2x and y = 3x) will miss the rectangle completely. Visually, this should take a second.

Now let's try answer choice A of slope 1/2 (y = .5x). It's the middle of 1/4 and 3/4. If the line has a slope of .5, then it must go through points (1, 0.5) and (2, 1) through the rectangle. Visualize that line and see where it goes through on the rectangle. Clearly, this doesn't divide the rectangle in half like we wanted, so answer choice A is out.

Answer choice E is out as well, since it's greater than 1/2. We need a smaller slope.

So at this point, I would put down answer choice C. But let's verify anyway. Slope 1/4 is the same as y = .25x, and it should be a line going through (2, 0.5). Since this is the center of the rectangle, it makes sense this would be the answer.

C it is!

Another way to solve this question is to imagine a line going through (0, 0) and (3, 1), let it be line L.
Now for a line to divide the parallelogram into equal quadrilaterals, it must have a slope less than that of line L but greater than 0.
The slope of line L is 1/3, hence the answer must be less than 1/3 and greater than 0. Only 1/4 fits the bill.

Hence C is is correct answer.
_________________
Life is a highway
I wanna ride it all night long
Intern  Joined: 20 Jul 2015
Posts: 2
Re: The vertex of a parallelogram are (1, 0), (3, 0), (1, 1) and (3, 1)  [#permalink]

Show Tags

1
Here's an alternative way to reach the answer using the equation for a line: $$y-y_1 = m(x-x_1)$$

By visualizing the line you can see that in order to divide the rectangle evenly it needs to intersect the rectangle's right side (i.e. it enters on the left and leaves on the right).

Let t be the y-value of the line at x = 1. Using this definition, the y-value at x=3 must be 1-t, since the height of the rectangle is 1. Note that if it weren't 1-t, the division of the rectangle would not be even.

This gives two points on the line: (1,t) and (3,1-t). So we have two equations for the same line:

(1) $$y-t = m(x-1)$$ [using the point (1,t) ]
(2) $$y-(1-t) = m(x-3)$$ [for the same line using the point (3, 1-t) ]

Since this is the same line, we can solve for m, the slope. Solving for t in (1) gives $$t = y-m(x-1)$$

Substituting this value of t in (2) gives:

$$y-(1-(y-m(x-1))) = m(x-3)$$
$$y-1+y-m(x-1)=m(x-3)$$
$$2y-1=m(x-3)+m(x-1)$$
$$2y-1=m((x-3)+(x-1))$$
$$\frac{(2y-1)}{((x-3)+(x-1))}=m$$

Since the origin is on the line, plug in x=0, y=0:

$$\frac{-1}{(-3-1)}=m =\frac{1}{4}$$

Note that plugging in x = y = 0 before the algebra would work as well, but I included the algebra because it's more illustrative.

Originally posted by doriangroove on 16 Aug 2015, 09:56.
Last edited by doriangroove on 16 Aug 2015, 18:32, edited 1 time in total.
CEO  S
Joined: 20 Mar 2014
Posts: 2595
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: The vertex of a parallelogram are (1, 0), (3, 0), (1, 1) and (3, 1)  [#permalink]

Show Tags

1
1
amitasagar23 wrote:
The vertex of a parallelogram are (1, 0), (3, 0), (1, 1) and (3, 1) respectively. If line L passes through the origin and divided the parallelogram into two identical quadrilaterals, what is the slope of line L?

A. 1/2
B. 2
C. 1/4
D. 3
E. 3/4

Hi, pls help with the solution of the above question. I find co-ordinate geometry very confusing. Are there some quick tips that you may recommend me to follow - when such questions appears in test?

Quickest method:

Attached image is borrowed from farful 's post above.

Added the line BE (the required line that divides the given parallelogram into 2 identical quadrilaterals).

Careful observation reveals that slope of the diagonal AD = (1-0)/(3-1) = 0.5. Thus the slope of line BE should be < slope of AD. Only option C is < 0.5 and is thus the correct answer.
Attachments 2015-08-16_20-38-38.jpg [ 11.03 KiB | Viewed 5786 times ]

Math Expert V
Joined: 02 Aug 2009
Posts: 8006
Re: The vertex of a parallelogram are (1, 0), (3, 0), (1, 1) and (3, 1)  [#permalink]

Show Tags

ruchi857 wrote:
The vertex of a parallelogram are (1,0); (3,0); (1,1); (3,1), respectively. If line L passes through the origin and divided the parallelogram into two identical quadrilaterals, what is the slope of line L?

A. 1/2
B. 2
C. 1/4
D. 3
E. 3/4

Hi,

Merging topics..
Please follow proper guidelines for post.. SEARCH beforr you post and give proper TOPIC name

your answer does not seem to be correct..
ans should be C. 1/4..
You can draw the quadrilateral and evevn the coord suggest that it is a rectangle...
the height of rectangle is 1 and length is 2...
1)this line passing through origin cuts the left side at say y... coord = (1,y)..
SLOPE with origin (0,0) = $$\frac{y-0}{1-0} = y$$
2)for the two quad to be similar, the line should cut the right side at y units below the upper vertex.. so coord = ( 3, 1-y)...
SLOPE = $$\frac{1-y-0}{3-0} = \frac{1-y}{3}..$$

but bothslopes should be SAME..
$$y = \frac{1-y}{3} .............3y = 1-y..........y = \frac{1}{4}....$$
so slope = y = 1/4
so sl
_________________
Manager  B
Status: One Last Shot !!!
Joined: 04 May 2014
Posts: 229
Location: India
Concentration: Marketing, Social Entrepreneurship
GMAT 1: 630 Q44 V32 GMAT 2: 680 Q47 V35 Re: The vertex of a parallelogram are (1, 0), (3, 0), (1, 1) and (3, 1)  [#permalink]

Show Tags

1
I tried and i am getting the answer as 1/4 (option C). Are you sure about the OA??

(Please refer the rough figure attached)
As we can see, the line L passes from below the point (3,1). Now, had the line passed through (3,1) the slope would have been 1/3. (line passing through (0,0) and (3,1)). Since our line L is passing from below (3,1) the slope has to be less than 1/3.

The only option less than 1/3 is option C 1/4.

Option C
Attachments Rectangle-slope.jpg [ 1.64 MiB | Viewed 5235 times ]

_________________
One Kudos for an everlasting piece of knowledge is not a bad deal at all... ------------------------------------------------------------------------------------------------------------------------
Twenty years from now you will be more disappointed by the things you didn't do than by the ones you did do. So throw off the bowlines. Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover.
-Mark Twain
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
Re: The vertex of a parallelogram are (1, 0), (3, 0), (1, 1) and (3, 1)  [#permalink]

Show Tags

1
amitasagar23 wrote:
The vertex of a parallelogram are (1, 0), (3, 0), (1, 1) and (3, 1) respectively. If line L passes through the origin and divided the parallelogram into two identical quadrilaterals, what is the slope of line L?

A. 1/2
B. 2
C. 1/4
D. 3
E. 3/4

Hi, pls help with the solution of the above question. I find co-ordinate geometry very confusing. Are there some quick tips that you may recommend me to follow - when such questions appears in test?

A good understanding of what slope means helps you solve this question in seconds. Draw out the parallelogram and you see that it is a rectangle with base at the x axis between 1 and 3. You want to split the rectangle into identical quads using line L passing through centre. So it will look like the diagram drawn by Engr2012 here: the-vertex-of-a-parallelogram-are-1-0-3-0-1-1-and-218118.html#p1561948

Now use the concept of slope, say the slope of line is n - the y co-ordinate increases by n every time the x co-ordinate increases by 1.
When the line moves from 0 to 1 x co-ordinate, its y co-ordinate increases by "n" (so AB is n). When it moves from x co-ordinate 1 to 3, y co-ordinate will increase by 2n. To make the quads identical, DE should be n too.
Hence the side of length 1 is split into n + 2n + n.
This means n = 0.25 = 1/4

A discussion on slope: http://www.veritasprep.com/blog/2016/04 ... line-gmat/
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Non-Human User Joined: 09 Sep 2013
Posts: 13411
Re: The vertex of a parallelogram are (1, 0), (3, 0), (1, 1) and (3, 1)  [#permalink]

Show Tags

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: The vertex of a parallelogram are (1, 0), (3, 0), (1, 1) and (3, 1)   [#permalink] 15 Mar 2019, 09:19
Display posts from previous: Sort by

The vertex of a parallelogram are (1, 0), (3, 0), (1, 1) and (3, 1)

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

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