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

 It is currently 18 Feb 2020, 10:30

### 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

# Is quadrilateral PQRS a parallelogram? (1) Adjacent sides PQ and QR

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 61283

### Show Tags

26 Apr 2019, 01:53
00:00

Difficulty:

35% (medium)

Question Stats:

59% (01:05) correct 41% (01:06) wrong based on 471 sessions

### HideShow timer Statistics

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

DS51602.01
OG2020 NEW QUESTION

_________________
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4325

### Show Tags

09 May 2019, 12:41
5
Top Contributor
1
Bunuel wrote:

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

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.

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.

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

Cheers,
Brent

RELATED VIDEO FROM MY COURSE

_________________
Test confidently with gmatprepnow.com
examPAL Representative
Joined: 07 Dec 2017
Posts: 1154

### Show Tags

26 Apr 2019, 14:36
4
7
The Logical approach to this question starts with the notion that the GMAC uses 5 different ways to tell us that a certain quadrilateral is a parallelogram:
1. We're given two pairs of equal opposite sides.
2. We're given two pairs of parallel sides.
3. We're given one pair of sides that are equal and parallel.
4. We're given two pairs of equal opposite angles.
5. The question states 'In the figure above, ABCD is a parallelogram...".
In this particular question it is the ADJACENT SIDES that are equal, which means that even if both statements are taken into account, all we know is that it is a deltoid. Can it be a parallelogram? Sure, if all 4 sides are equal (i.e. a rhombus), but it doesn't have to be.

Posted from my mobile device
_________________
##### General Discussion
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9426
Location: United States (CA)

### Show Tags

12 May 2019, 18:06
1
Bunuel wrote:

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

DS51602.01
OG2020 NEW QUESTION

Statement One Alone:

Adjacent sides PQ and QR have the same length.

Quadrilateral PQRS might or might not be a parallelogram. For example, if RS and SP also have the same length as PQ and QR (for example, PQ = QR = RS = SP = 4), then it’s a parallelogram (in fact, it’s a rhombus). On the other hand, if RS and SP don’t have the same length as PQ and QR (for example, PQ = QR = 4 and RS = SP = 5), then it’s not a parallelogram. Statement one alone is not sufficient.

Statement Two Alone:

Adjacent sides RS and SP have the same length.

Quadrilateral PQRS might or might not be a parallelogram. For example, if PQ and QR also have the same length as RS and SP (for example, RS = SP = PQ = QR = 4), then it’s a parallelogram (in fact, it’s a rhombus). On the other hand, if PQ and QR don’t have the same length as RS and SP (for example, RS = SP = 4 and PQ = QR = 5), then it’s not a parallelogram. Statement two alone is not sufficient.

Statements One and Two Together:

Even with two statements, quadrilateral PQRS might or might not be a parallelogram. If all 4 sides have the same length (for example, PQ = QR = RS = SP = 4), then it’s a parallelogram (in fact, it’s a rhombus). However, if PQ = QR = 4 and RS = SP = 5, then it’s not a parallelogram.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
181 Reviews

5-star rated online GMAT quant
self study course

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.

examPAL Representative
Joined: 07 Dec 2017
Posts: 1154

### Show Tags

26 Apr 2019, 14:37
The Logical approach to this question starts with the notion that the GMAC uses 5 different ways to tell us that a certain quadrilateral is a parallelogram:
1. We're given two pairs of equal opposite sides.
2. We're given two pairs of parallel sides.
3. We're given one pair of sides that are equal and parallel.
4. We're given two pairs of equal opposite angles.
5. The question states 'In the figure above, ABCD is a parallelogram...".
In this particular question it is the ADJACENT SIDES that are equal, which means that even if both statements are taken into account, all we know is that it is a deltoid. Can it be a parallelogram? Sure, if all 4 sides are equal (i.e. a rhombus), but it doesn't have to be.

Posted from my mobile device
_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16107
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170

### Show Tags

09 May 2019, 18:20
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

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Re: Is quadrilateral PQRS a parallelogram? (1) Adjacent sides PQ and QR   [#permalink] 09 May 2019, 18:20
Display posts from previous: Sort by