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In the figure above, if PQRS is a parallelogram, then y  x
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15 Oct 2012, 04:25
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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
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Re: In the figure above, if PQRS is a parallelogram, then y  x
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15 Oct 2012, 04:25
In the figure above, if PQRS is a parallelogram, then y  x =(A) 30 (B) 35 (C) 40 (D) 70 (E) 100 In parallelogram corresponding angles are equal and consecutive angles are supplementary (supplementary angles are two angles that add up to 180°), thus: \(140=2y\) > \(y=70\); \(2y+x=180\) > \(140+x=180\) > \(x=40\); Therefore, \(yx=7040=30\). Answer: A. For more check Polygons chapter of Math Book: mathpolygons87336.html
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Re: In the figure above, if PQRS is a parallelogram, then y  x
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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
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Re: In the figure above, if PQRS is a parallelogram, then y  x
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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!
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Re: In the figure above, if PQRS is a parallelogram, then y  x
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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



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Re: In the figure above, if PQRS is a parallelogram, then y  x
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19 Oct 2012, 04:21
In the figure above, if PQRS is a parallelogram, then y  x =(A) 30 (B) 35 (C) 40 (D) 70 (E) 100 In parallelogram corresponding angles are equal and consecutive angles are supplementary (supplementary angles are two angles that add up to 180°), thus: \(140=2y\) > \(y=70\); \(2y+x=180\) > \(140+x=180\) > \(x=40\); Therefore, \(yx=7040=30\). Answer: A. For more check Polygons chapter of Math Book: mathpolygons87336.htmlKudos points given to everyone with correct solution. Let me know if I missed someone.
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Re: In the figure above, if PQRS is a parallelogram, then y  x
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02 May 2013, 10:59
180140= 40, x=40 140/2y= 70=y yx = 7040=30



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Re: In the figure above, if PQRS is a parallelogram, then y  x
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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.
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Re: In the figure above, if PQRS is a parallelogram, then y  x
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05 Jul 2017, 21:27
Answer is A
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In the figure above, if PQRS is a parallelogram, then y  x
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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
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Re: In the figure above, if PQRS is a parallelogram, then y  x
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Re: In the figure above, if PQRS is a parallelogram, then y  x
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