It is currently 23 Sep 2017, 15:13

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124654 [0], given: 12079

In the figure above, if PQRS is a parallelogram, then y - x [#permalink]

### Show Tags

15 Oct 2012, 04:25
Expert's post
4
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

84% (00:47) correct 16% (01:00) wrong based on 706 sessions

### HideShow timer Statistics

Attachment:

PQRS.png [ 10.9 KiB | Viewed 20120 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

_________________

Kudos [?]: 124654 [0], given: 12079

Math Expert
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124654 [2], given: 12079

Re: In the figure above, if PQRS is a parallelogram, then y - x [#permalink]

### Show Tags

15 Oct 2012, 04:25
2
KUDOS
Expert's post

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, $$y-x=70-40=30$$.

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

Kudos [?]: 124654 [2], given: 12079

Director
Joined: 24 Aug 2009
Posts: 502

Kudos [?]: 826 [2], given: 276

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
2
KUDOS
[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
_________________

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

Kudos [?]: 826 [2], given: 276

Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 639

Kudos [?]: 644 [3], given: 23

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
3
KUDOS
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

GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Each 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:
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

Kudos [?]: 644 [3], given: 23

Manager
Joined: 21 Sep 2012
Posts: 236

Kudos [?]: 402 [3], given: 63

Re: In the figure above, if PQRS is a parallelogram, then y - x [#permalink]

### Show Tags

16 Oct 2012, 03:30
3
KUDOS
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

Kudos [?]: 402 [3], given: 63

Math Expert
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124654 [0], given: 12079

Re: In the figure above, if PQRS is a parallelogram, then y - x [#permalink]

### Show Tags

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, $$y-x=70-40=30$$.

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.
_________________

Kudos [?]: 124654 [0], given: 12079

Manager
Joined: 17 Jul 2010
Posts: 124

Kudos [?]: 54 [0], given: 43

Re: In the figure above, if PQRS is a parallelogram, then y - x [#permalink]

### Show Tags

02 May 2013, 10:59
180-140= 40, x=40
140/2y= 70=y
y-x =
70-40=30

Kudos [?]: 54 [0], given: 43

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 17624

Kudos [?]: 271 [0], given: 0

Re: In the figure above, if PQRS is a parallelogram, then y - x [#permalink]

### Show Tags

23 Dec 2014, 05:43
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.
_________________

Kudos [?]: 271 [0], given: 0

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 17624

Kudos [?]: 271 [0], given: 0

Re: In the figure above, if PQRS is a parallelogram, then y - x [#permalink]

### Show Tags

08 May 2016, 01:24
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.
_________________

Kudos [?]: 271 [0], given: 0

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1414

Kudos [?]: 762 [1], given: 5

Re: In the figure above, if PQRS is a parallelogram, then y - x [#permalink]

### Show Tags

03 Jun 2016, 06:41
1
KUDOS
Expert's post
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.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 762 [1], given: 5

Manager
Joined: 22 Nov 2016
Posts: 187

Kudos [?]: 32 [0], given: 36

Location: United States
GPA: 3.4
Re: In the figure above, if PQRS is a parallelogram, then y - x [#permalink]

### Show Tags

05 Jul 2017, 21:27
Attachments

x.jpg [ 46.5 KiB | Viewed 1173 times ]

_________________

Kudosity killed the cat but your kudos can save it.

Kudos [?]: 32 [0], given: 36

SVP
Joined: 12 Sep 2015
Posts: 1753

Kudos [?]: 2296 [0], given: 355

Re: In the figure above, if PQRS is a parallelogram, then y - x [#permalink]

### Show Tags

13 Sep 2017, 11:11
Top Contributor
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 PQ||RS, 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

[Reveal] Spoiler:
A

RELATED VIDEOS FROM OUR COURSE

_________________

Brent Hanneson – Founder of gmatprepnow.com

Kudos [?]: 2296 [0], given: 355

Re: In the figure above, if PQRS is a parallelogram, then y - x   [#permalink] 13 Sep 2017, 11:11
Similar topics Replies Last post
Similar
Topics:
In ∆ PQR above, y = 6 19 Aug 2017, 22:02
2 If the figure above is a parallelogram, what is the value of 8 10 Sep 2013, 22:44
3 In the above figure, PQRS is a square with side x + 4. Each of the 4 20 Sep 2017, 11:26
In the figure above, if angle PQR = twice angle STU, then x/y = 3 19 Jul 2017, 09:23
In the above figure, PQRS is a parallelogram. Then y = 2 20 Sep 2017, 11:42
Display posts from previous: Sort by