GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 21 Nov 2019, 03:24

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59224
Is quadrilateral PQRS a parallelogram? (1) Adjacent sides PQ and QR  [#permalink]

Show Tags

New post 26 Apr 2019, 02:53
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

60% (01:05) correct 40% (01:05) wrong based on 400 sessions

HideShow timer Statistics

Most Helpful Expert Reply
examPAL Representative
User avatar
P
Joined: 07 Dec 2017
Posts: 1155
Re: Is quadrilateral PQRS a parallelogram? (1) Adjacent sides PQ and QR  [#permalink]

Show Tags

New post 26 Apr 2019, 15:36
2
6
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.
The correct answer is (E).

Posted from my mobile device
_________________
General Discussion
examPAL Representative
User avatar
P
Joined: 07 Dec 2017
Posts: 1155
Re: Is quadrilateral PQRS a parallelogram? (1) Adjacent sides PQ and QR  [#permalink]

Show Tags

New post 26 Apr 2019, 15:37
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.
The correct answer is (E).

Posted from my mobile device
_________________
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4074
Location: Canada
Is quadrilateral PQRS a parallelogram? (1) Adjacent sides PQ and QR  [#permalink]

Show Tags

New post 09 May 2019, 13:41
2
Top Contributor
Bunuel 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.


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

RELATED VIDEO FROM MY COURSE

_________________
Test confidently with gmatprepnow.com
Image
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15498
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Is quadrilateral PQRS a parallelogram? (1) Adjacent sides PQ and QR  [#permalink]

Show Tags

New post 09 May 2019, 19:20
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

Final Answer:

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


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8453
Location: United States (CA)
Re: Is quadrilateral PQRS a parallelogram? (1) Adjacent sides PQ and QR  [#permalink]

Show Tags

New post 12 May 2019, 19:06
1
Bunuel 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.


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.

Answer: E
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 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.

GMAT Club Bot
Re: Is quadrilateral PQRS a parallelogram? (1) Adjacent sides PQ and QR   [#permalink] 12 May 2019, 19:06
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne