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

 It is currently 25 May 2020, 00:55 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # In the figure above, if PQRS is a parallelogram, then y - x

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 64073
In the figure above, if PQRS is a parallelogram, then y - x  [#permalink]

### Show Tags

1
7 00:00

Difficulty:   5% (low)

Question Stats: 85% (01:04) correct 15% (01:23) wrong based on 860 sessions

### HideShow timer Statistics

Attachment: PQRS.png [ 10.9 KiB | Viewed 41507 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

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 64073
Re: In the figure above, if PQRS is a parallelogram, then y - x  [#permalink]

### Show Tags

3
1
4 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
_________________
##### General Discussion
Senior Manager  B
Joined: 24 Aug 2009
Posts: 429
Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: In the figure above, if PQRS is a parallelogram, then y - x  [#permalink]

### Show Tags

2
[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
Director  Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 552
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

3
1
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!
Manager  Joined: 21 Sep 2012
Posts: 188
Re: In the figure above, if PQRS is a parallelogram, then y - x  [#permalink]

### Show Tags

3
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
Math Expert V
Joined: 02 Sep 2009
Posts: 64073
Re: In the figure above, if PQRS is a parallelogram, then y - x  [#permalink]

### Show Tags 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.
_________________
Manager  Joined: 17 Jul 2010
Posts: 107
Re: In the figure above, if PQRS is a parallelogram, then y - x  [#permalink]

### Show Tags

180-140= 40, x=40
140/2y= 70=y
y-x =
70-40=30
Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2800
Re: In the figure above, if PQRS is a parallelogram, then y - x  [#permalink]

### Show Tags

1
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.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager  G
Joined: 22 Nov 2016
Posts: 245
Re: In the figure above, if PQRS is a parallelogram, then y - x  [#permalink]

### Show Tags

Attachments x.jpg [ 46.5 KiB | Viewed 17876 times ]

GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4871
GMAT 1: 770 Q49 V46
In the figure above, if PQRS is a parallelogram, then y - x  [#permalink]

### Show Tags

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

Cheers,
Brent
_________________
Non-Human User Joined: 09 Sep 2013
Posts: 14971
Re: In the figure above, if PQRS is a parallelogram, then y - x  [#permalink]

### Show Tags

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.
_________________ Re: In the figure above, if PQRS is a parallelogram, then y - x   [#permalink] 29 Mar 2020, 16:04

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