Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47006

In the figure above, if PQRS is a parallelogram, then y  x [#permalink]
Show Tags
15 Oct 2012, 04:25
Question Stats:
82% (00:46) correct 18% (00:59) wrong based on 833 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Sep 2009
Posts: 47006

Re: In the figure above, if PQRS is a parallelogram, then y  x [#permalink]
Show Tags
15 Oct 2012, 04:25



Senior Manager
Joined: 24 Aug 2009
Posts: 479
Schools: Harvard, Columbia, Stern, Booth, LSB,

Re: In the figure above, if PQRS is a parallelogram, then y  x [#permalink]
Show Tags
15 Oct 2012, 04:34
[quote="Bunuel"] The Official Guide for GMAT® Review, 13th Edition  Quantitative Questions ProjectAttachment: PQRS.png In the figure above, if PQRS is a parallelogram, then y  x = (A) 30 (B) 35 (C) 40 (D) 70 (E) 100 Note: 1) Any two continuous interior angles of a parallelogram are supplementary. 2) Opposite angles are equal. x= 180  140 = 40 x+2y = 180> 2y = 180 x > 2y = 180 40> y = 70 Thus y  x = 70  40 = 30 Answer A
_________________
If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth Game Theory
If you have any question regarding my post, kindly pm me or else I won't be able to reply



Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 616
Location: India
Concentration: Strategy, General Management
Schools: Olin  Wash U  Class of 2015
WE: Information Technology (Computer Software)

Re: In the figure above, if PQRS is a parallelogram, then y  x [#permalink]
Show Tags
15 Oct 2012, 11:08
In the figure shown, angle x= QRS = QPS (opposite angles in parallelogram) Also, intersecting lines PQ and PS, therefore QPS +Outerangle = 180 => QPS =180140 = 40 hence x =40 Also, Lines PQ and RS are parallel so angles they make with horizontal line PS are same. hence 2y =140 => y =70 Therefore, yx =7040 = 30 Ans A. Bunuel wrote: The Official Guide for GMAT® Review, 13th Edition  Quantitative Questions ProjectAttachment: PQRS.png In the figure above, if PQRS is a parallelogram, then y  x = (A) 30 (B) 35 (C) 40 (D) 70 (E) 100 Practice Questions Question: 62 Page: 160 Difficulty: 650 GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a solution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
_________________
Lets Kudos!!! Black Friday Debrief



Manager
Joined: 21 Sep 2012
Posts: 229

Re: In the figure above, if PQRS is a parallelogram, then y  x [#permalink]
Show Tags
16 Oct 2012, 03:30
since opposite sides and angles in a parallelogram are equal we know that
angle QRS = QPS = X angle RSP = RPQ = 2y
140 + angle QPS = 180 ( sum of 2 angles on a straight line)
so X=40
now 2 ways to proceed sum of angles in parellogram is 360
so we have 2X+4Y=360 4Y = 36080 ( 40*2) 4Y=280 Y=70 therefore YX=7040 = 30 Answer Choice A
The other way since opposite sides are parallel PQ ll RS hence 2Y=140 >>> y=70 and then Yx = 7040 = 30
In both cases Answer Choice is A



Math Expert
Joined: 02 Sep 2009
Posts: 47006

Re: In the figure above, if PQRS is a parallelogram, then y  x [#permalink]
Show Tags
19 Oct 2012, 04:21



Manager
Joined: 17 Jul 2010
Posts: 117

Re: In the figure above, if PQRS is a parallelogram, then y  x [#permalink]
Show Tags
02 May 2013, 10:59
180140= 40, x=40 140/2y= 70=y yx = 7040=30



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2669

Re: In the figure above, if PQRS is a parallelogram, then y  x [#permalink]
Show Tags
03 Jun 2016, 06:41
Bunuel wrote: Attachment: PQRS.png In the figure above, if PQRS is a parallelogram, then y  x = (A) 30 (B) 35 (C) 40 (D) 70 (E) 100 To solve we need to review some rules about parallelograms. In parallelograms there are two main rules about the relationships between the angles: 1) Opposite angles are equal Thus, angle P = angle R, and Angle Q = Angle S. 2) Consecutive angles are supplementary. That is, they add to 180 degrees. Thus, angles Q and P add up to 180 degrees, as do angles P and S, angles S and R, and angles R and Q. These rules can be used to solve the problem at hand. We start by determining the value for angle P. We see that angle P is part of a straight angle. Since the exterior angle of angle P = 140 degrees, angle P must equal 40 degrees (since the two angles must sum to 180 degrees). Using our first rule of parallelograms we see that angle R, which is equal to x, must also measure 40 degrees, since angles P and R are opposite angles. Using our second rule of parallelograms, we know that angles R and S must add up to 180 degrees because they are consecutive angles. We note that angle S is equal to 2y. Thus: 2y + x = 180 2y + 40 = 180 2y = 140 y = 70 Therefore, the value of y – x is 70 – 40 = 30. The answer is A.
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Manager
Joined: 22 Nov 2016
Posts: 236
Location: United States
Concentration: Leadership, Strategy
GPA: 3.4

Re: In the figure above, if PQRS is a parallelogram, then y  x [#permalink]
Show Tags
05 Jul 2017, 21:27
Answer is A
Attachments
x.jpg [ 46.5 KiB  Viewed 8024 times ]
_________________
Kudosity killed the cat but your kudos can save it.



CEO
Joined: 12 Sep 2015
Posts: 2630
Location: Canada

In the figure above, if PQRS is a parallelogram, then y  x [#permalink]
Show Tags
13 Sep 2017, 11:11
Bunuel wrote: Attachment: PQRS.png In the figure above, if PQRS is a parallelogram, then y  x = (A) 30 (B) 35 (C) 40 (D) 70 (E) 100 There are several ways to solve this question. Here's one approach; Since the two highlighted angles below share the same line, they must add to 180° So, ∠QPS = 40° Next, since the PQRS, we know that the two circled angles are corresponding angles, which means those two angles are equal If 2y° = 140°, then we know that y = 70°Finally, since the two angles (circled in blue below) are opposite angles in a parallelogram, we know that they are EQUAL. So, x = 40°This means y  x = 70  40 = 30 Answer: A Cheers, Brent
_________________
Brent Hanneson – Founder of gmatprepnow.com




In the figure above, if PQRS is a parallelogram, then y  x
[#permalink]
13 Sep 2017, 11:11






