GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 28 Mar 2020, 08:00

### 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

# A quadrilateral P has (1, 1), (3, 1), (3, 5) and (1, 5) as 4 vertices

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8722
GMAT 1: 760 Q51 V42
GPA: 3.82
A quadrilateral P has (1, 1), (3, 1), (3, 5) and (1, 5) as 4 vertices  [#permalink]

### Show Tags

08 Jan 2020, 23:42
00:00

Difficulty:

65% (hard)

Question Stats:

54% (02:46) correct 46% (02:41) wrong based on 26 sessions

### HideShow timer Statistics

[GMAT math practice question]

A quadrilateral $$P$$ has $$(1, 1), (3, 1), (3, 5)$$ and $$(1, 5)$$ as $$4$$ vertices and another quadrilateral $$Q$$ has $$(-1, -1), (-5, -1), (-5, -5)$$ and $$(-1, -5)$$ as $$4$$ vertices. A line divides these two quadrilaterals evenly at the same time. What is this line?

A. $$y = \frac{- 1}{6}x + \frac{5}{6 }$$

B. $$y = \frac{- 5}{6}x + \frac{1}{6}$$

C. $$y = \frac{ 6}{5}x + \frac{3}{5}$$

D. $$y = \frac{1}{3}x + \frac{5}{6}$$

E. $$y = \frac{- 1}{6}x + \frac{7}{5}$$

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" AWA Forum Moderator Status: Manager Joined: 27 Oct 2018 Posts: 866 Location: Egypt Concentration: Strategy, International Business GPA: 3.67 WE: Pharmaceuticals (Health Care) A quadrilateral P has (1, 1), (3, 1), (3, 5) and (1, 5) as 4 vertices [#permalink] ### Show Tags 09 Jan 2020, 02:33 By visualizing the two quadrilaterals, we find that one is in the first quadrant, and the other is in the fourth, so for a line that can pass through them, the slope must be positive ---> this eliminates A,B,E By trying D, the starting point of the line will be (3 , 1.833) which can't be possibly dividing the quadrilateral in the first quadrant. By trying C, the starting point of the line will be (3 , 4.166) which can possibly do the trick C Attachments aaa.png [ 14.89 KiB | Viewed 398 times ] Director Joined: 04 Aug 2010 Posts: 546 Schools: Dartmouth College Re: A quadrilateral P has (1, 1), (3, 1), (3, 5) and (1, 5) as 4 vertices [#permalink] ### Show Tags 09 Jan 2020, 03:43 MathRevolution wrote: [GMAT math practice question] A quadrilateral $$P$$ has $$(1, 1), (3, 1), (3, 5)$$ and $$(1, 5)$$ as $$4$$ vertices and another quadrilateral $$Q$$ has $$(-1, -1), (-5, -1), (-5, -5)$$ and $$(-1, -5)$$ as $$4$$ vertices. A line divides these two quadrilaterals evenly at the same time. What is this line? A. $$y = \frac{- 1}{6}x + \frac{5}{6 }$$ B. $$y = \frac{- 5}{6}x + \frac{1}{6}$$ C. $$y = \frac{ 6}{5}x + \frac{3}{5}$$ D. $$y = \frac{1}{3}x + \frac{5}{6}$$ E. $$y = \frac{- 1}{6}x + \frac{7}{5}$$ Each quadrilateral is a rectangle. To divide a rectangle in half, a line must pass through the CENTER of the rectangle. Center of P = (midpoint of the x-values, midpoint of the y-values) $$= (\frac{1+3}{2}, \frac{1+5}{2}) = (2, 3)$$ Center of Q = (midpoint of the x-values, midpoint of the y-values) $$= (\frac{-1+(-5)}{2}, \frac{-1+(-5)}{2}) = (-3, -3)$$ The correct answer must pass through the two centers (2, 3) and (-3, -3). Slope of the line that passes through (2, 3) and (-3, -3) $$= \frac{∆y}{∆x} = \frac{-3-3}{-3-2} = \frac{6}{5}$$ _________________ GMAT and GRE Tutor New York, NY Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8722 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: A quadrilateral P has (1, 1), (3, 1), (3, 5) and (1, 5) as 4 vertices [#permalink] ### Show Tags 12 Jan 2020, 17:49 => Attachment: 1.9ps(a).png [ 29.51 KiB | Viewed 277 times ] The quadrilaterals are rectangles, and bisecting lines of rectangles pass through the center of the rectangles. Thus we have to find the line passing through the centers of those two rectangles. The centers of the rectangles are $$(2, 3)$$ and $$(-3, -3).$$ The slope of the line passing through $$(2, 3)$$ and $$(-3, -3)$$ is $$\frac{(3- (-3)) }{ (2 - (-3))}$$ $$=\frac{ 6}{5}$$. The line passing through them is $$y – 3 = (\frac{6}{5})(x - 2)$$ or $$y = (\frac{6}{5})x + (\frac{3}{5}).$$ Therefore, C is the answer. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Re: A quadrilateral P has (1, 1), (3, 1), (3, 5) and (1, 5) as 4 vertices   [#permalink] 12 Jan 2020, 17:49
Display posts from previous: Sort by