BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Is quadrilateral PQRS a parallelogram?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Thu May 02, 2019 2:20 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

AbeNeedsAnswers wrote:Is quadrilateral PQRS a parallelogram?

(1) Adjacent sides PQ and QR have the same length.
(2) Adjacent sides RS and SP have the same length.

E

Source: Official Guide 2020
For the quadrilateral PQRS to be a parallelogram, the opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Let's take each statement one by one.

(1) Adjacent sides PQ and QR have the same length.

The opposite sides may or may not be equal. Insufficient.

(2) Adjacent sides RS and SP have the same length.

The opposite sides may or may not be equal. Insufficient.

(1) and (2) together

Still, the opposite sides may or may not be equal. Insufficient.

The correct answer: E

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: GRE Manhattan | ACT Tutoring San Antonio | GRE Prep Courses Boston | Houston IELTS Tutoring | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Thu May 09, 2019 12:37 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

AbeNeedsAnswers wrote:Is quadrilateral PQRS a parallelogram?

(1) Adjacent sides PQ and QR have the same length.
(2) Adjacent sides RS and SP have the same length.

E

Source: Official Guide 2020
Target question: Is quadrilateral PQRS a parallelogram?
If you recognize that each statement on its own is not sufficient, we can jump straight to . . .


Statements 1 and 2 combined
There are infinitely-many quadrilaterals that satisfy BOTH statements. Here are two:

Case a: PQRS could be a square.
Image
Since a square is a type of parallelogram, the answer to the target question is YES, quadrilateral PQRS IS a parallelogram

Case b: PQRS could be kite-shaped.
Image
In this case, the answer to the target question is NO, quadrilateral PQRS is NOT a parallelogram

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Thu May 09, 2019 3:33 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Hi All,

We're asked if quadrilateral PQRS is a parallelogram? This is a YES/NO question can be answered with a bit of logic (and a couple of drawings). By definition, a parallelogram must have 4 sides and each pair of 'opposite' sides must be parallel.

1) Adjacent sides PQ and QR have the same length.

'Adjacent' sides refer to two sides that are next to one another (and meet at a point):
-A Square fits this description - and is a parallelogram, so the answer to the question is YES.
-Any other 4-sided shape with 2 equal sides that touch and 2 others sides that are NOT the same length as the first 2 - that's NOT a parallelogram, so the answer to the question is NO.
Brent's explanation provides a nice example of the second shape.
Fact 1 is INSUFFICIENT

2) Adjacent sides RS and SP have the same length.

Fact 2 essentially provides the same information that Fact 1 provides (but about the other 2 sides). The examples that fit Fact 1 also fit Fact 2 - and lead us to two different answers (one "YES" and one "NO").
Fact 2 is INSUFFICIENT

Combined, we know...
1) Adjacent sides PQ and QR have the same length.
2) Adjacent sides RS and SP have the same length.

Even with both Facts, we can end up with shapes that are parallelograms or not, so the answer to the question is inconsistent.
Combined, INSUFFICIENT

Final Answer: E

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Post new topic Post Reply
• Page 1 of 1