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In the figure above, if PQRS is a parallelogram, then y - x

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In the figure above, if PQRS is a parallelogram, then y - x [#permalink] New post 15 Oct 2012, 03:25
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Attachment:
PQRS.png
PQRS.png [ 10.9 KiB | Viewed 5014 times ]
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
[Reveal] Spoiler: OA

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Re: In the figure above, if PQRS is a parallelogram, then y - x [#permalink] New post 15 Oct 2012, 03:25
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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

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, y-x=70-40=30.

Answer: A.

For more check Polygons chapter of Math Book: math-polygons-87336.html
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: In the figure above, if PQRS is a parallelogram, then y - x [#permalink] New post 15 Oct 2012, 03:34
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[quote="Bunuel"]The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

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

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 [#permalink] New post 15 Oct 2012, 10:08
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In the figure shown, angle x= QRS = QPS (opposite angles in parallelogram)
Also, intersecting lines PQ and PS, therefore QPS +Outerangle = 180
=> QPS =180-140 = 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, y-x =70-40 = 30

Ans A.

Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

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

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 [#permalink] New post 16 Oct 2012, 02:30
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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 = 360-80 ( 40*2)
4Y=280
Y=70 therefore Y-X=70-40 = 30 Answer Choice A

The other way since opposite sides are parallel PQ ll RS
hence 2Y=140 >>> y=70 and then Y-x = 70-40 = 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 [#permalink] New post 19 Oct 2012, 03:21
Expert's post
Image
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, y-x=70-40=30.

Answer: A.

For more check Polygons chapter of Math Book: math-polygons-87336.html

Kudos points given to everyone with correct solution. Let me know if I missed someone.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: In the figure above, if PQRS is a parallelogram, then y - x [#permalink] New post 02 May 2013, 09:59
180-140= 40, x=40
140/2y= 70=y
y-x =
70-40=30
Re: In the figure above, if PQRS is a parallelogram, then y - x   [#permalink] 02 May 2013, 09:59
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