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

 It is currently 20 Jun 2018, 09:43

### 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 rectangular region PQRS above, T is a point on side PS. If PS = 4,

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 46207
In rectangular region PQRS above, T is a point on side PS. If PS = 4, [#permalink]

### Show Tags

08 Oct 2015, 07:54
2
9
00:00

Difficulty:

65% (hard)

Question Stats:

59% (01:16) correct 41% (01:12) wrong based on 227 sessions

### HideShow timer Statistics

In rectangular region PQRS above, T is a point on side PS. If PS = 4, what is the area of region PQRS?

(1) Triangle QTR is equilateral.
(2) Segments PT and TS have equal length.

Kudos for a correct solution.

Attachment:

2015-10-08_1851.png [ 5.63 KiB | Viewed 7242 times ]

_________________
Director
Joined: 10 Mar 2013
Posts: 562
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Re: In rectangular region PQRS above, T is a point on side PS. If PS = 4, [#permalink]

### Show Tags

08 Oct 2015, 09:34
1
1
Bunuel wrote:

In rectangular region PQRS above, T is a point on side PS. If PS = 4, what is the area of region PQRS?

(1) Triangle QTR is equilateral.
(2) Segments PT and TS have equal length.

Kudos for a correct solution.

Attachment:
2015-10-08_1851.png

(1) QTR is equilateral means that point T is in the middle of PS - > qt=rt=long leg of the eq.triangle=4 and than from the pytgorean theorem we can find QP and the Area - SUFFICIENT
(2) Smae Info as above SUFFICIENT
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Share some Kudos, if my posts help you. Thank you !

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Intern
Joined: 09 Jul 2014
Posts: 6
Re: In rectangular region PQRS above, T is a point on side PS. If PS = 4, [#permalink]

### Show Tags

08 Oct 2015, 09:57
second statement is not sufficient. B'se QT may be equal to RT, but need not be equal to QR. so 2 is insufficient
So i believe answer will be 'A'
Verbal Forum Moderator
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2016
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
Re: In rectangular region PQRS above, T is a point on side PS. If PS = 4, [#permalink]

### Show Tags

08 Oct 2015, 13:31
1
1. PS=QR=4
Since , QTR is equilateral
QT=TR=QR=4
Triangles QTP and RTS are congruent(RHS)
=>PT=TS
Now using pythagorean theorem , we can find out QP or RS .
QT^2= QP^2 + PT^2
And calculate the area of rectangle PQRS.
Sufficient

2. PT=TS = 2
Triangles QTP and RTS are congruent (SAS)
=> QT=RT
But we have no can conclude whether QT/RT is equal to QR .
Hence, insufficient.

_________________

When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
+1 Kudos if you find this post helpful

Director
Joined: 10 Mar 2013
Posts: 562
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Re: In rectangular region PQRS above, T is a point on side PS. If PS = 4, [#permalink]

### Show Tags

08 Oct 2015, 14:17
1
Hmm... was too fast about B, missed the point... B is not sufficient
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Share some Kudos, if my posts help you. Thank you !

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Intern
Joined: 06 Oct 2013
Posts: 45
Re: In rectangular region PQRS above, T is a point on side PS. If PS = 4, [#permalink]

### Show Tags

08 Oct 2015, 14:33
2
Bunuel wrote:

In rectangular region PQRS above, T is a point on side PS. If PS = 4, what is the area of region PQRS?

(1) Triangle QTR is equilateral.
(2) Segments PT and TS have equal length.

Kudos for a correct solution.

Attachment:
2015-10-08_1851.png

SOLUTION:

Statement 1: If Triangle QTR is equilateral. then QR=QT=4, And also every angle of this Triangle is 60 degrees.
then Triangle QTP is 30-60-90 right triangle then the sides of triangle PQT are in ratio 1:$$\sqrt{3}$$:2.

if longest side QT=4, then PQ must be 2*$$\sqrt{3}$$.

we now know lengths of adjacent sides , we can calculate area of rectangle.

So , Statement 1 is SUFFICIENT.

Statement 2: we know PT, but we don't know anything about type of a triangle or lengths of PQ or QT.

So, Statement 2 is INSUFFICIENT.

ANS: A.

Hope i am not missing anything about Statement 2.
Math Expert
Joined: 02 Sep 2009
Posts: 46207
Re: In rectangular region PQRS above, T is a point on side PS. If PS = 4, [#permalink]

### Show Tags

11 Oct 2015, 07:57
3
Bunuel wrote:

In rectangular region PQRS above, T is a point on side PS. If PS = 4, what is the area of region PQRS?

(1) Triangle QTR is equilateral.
(2) Segments PT and TS have equal length.

Kudos for a correct solution.

Attachment:
2015-10-08_1851.png

VERITAS PREP OFFICIAL SOLUTION:

Question Type: What Is the Value? This question asks for the area of the rectangle PQRS.

Given information in the question stem or diagram: The diagram is given and importantly one side is defined with PS = 4, so both PS and QR = 4. To find the area you need to somehow determine either RS or PQ from the information in the statements. The question is really: What is RS or PQ?

Statement 1: QTR is an equilateral triangle. If this is true, then with QR as the base, the height of the equilateral triangle is equivalent to the side that you are trying to determine (PQ or RS). Since the base of QTR is 4 you can determine the necessary height with your knowledge of 30–60–90 triangles or simply with your knowledge that if you know one thing about an equilateral triangle, then you know everything! While you do not need to calculate it, the height would be 2√3 as it is the long leg in a 30–60–90 triangle formed by 1/2 the base of QTR (2), the hypotenuse QT (4) and the height ( 2√3 ) which is equivalent to PQ or RS. Statement 1 is sufficient, so the answer is A or D.

Statement 2: In this difficult statement, the testmakers are playing with a common trick. They have polluted your brain with the first statement and want you to assume that if “segments PT and TS have equal lengths,” then QTR must again be equilateral. However, this statement does nothing to help you determine the length of the sides (QP and RS) because it only proves that QTR is isosceles. There is no limit put on the lengths of PQ and RS (because you do not know the angle of TQR and TRQ) with this statement, so it is not sufficient. Remember: One of the keys to success in Data Sufficiency is to consciously avoid assumptions, but that can be hard when you are set up so nicely to make assumptions with the other statement. Statement 2 is not sufficient, so the correct answer is A.
_________________
Intern
Joined: 11 Dec 2013
Posts: 15
Location: India
Concentration: Finance, Technology
Schools: ISB '18
GMAT Date: 03-15-2015
WE: Operations (Telecommunications)
Re: In rectangular region PQRS above, T is a point on side PS. If PS = 4, [#permalink]

### Show Tags

06 Apr 2016, 00:06
The correct answer must be D
If PT = PS , then we already know QP=RS , Hence QT = RT . Therefore triangles QPT and RTS are congruent (RHS) .
Angles TQR and QRT are equal ( As QT=RT) .
Angles QTP and RTS are equal ( Congruent triangles) .
Angle QTR = 180 - 2(angle TQR) = 180 - 2(angle QTP)
Therefore angle TQR = QTP , which implies TQR=QTP=RTS
Therefore an equilateral triangle , Hence we can find the area .
Math Expert
Joined: 02 Sep 2009
Posts: 46207
Re: In rectangular region PQRS above, T is a point on side PS. If PS = 4, [#permalink]

### Show Tags

06 Apr 2016, 00:20
4d wrote:

In rectangular region PQRS above, T is a point on side PS. If PS = 4, what is the area of region PQRS?

(1) Triangle QTR is equilateral.
(2) Segments PT and TS have equal length.

The correct answer must be D
If PT = PS , then we already know QP=RS , Hence QT = RT . Therefore triangles QPT and RTS are congruent (RHS) .
Angles TQR and QRT are equal ( As QT=RT) .
Angles QTP and RTS are equal ( Congruent triangles) .
Angle QTR = 180 - 2(angle TQR) = 180 - 2(angle QTP)
Therefore angle TQR = QTP , which implies TQR=QTP=RTS
Therefore an equilateral triangle , Hence we can find the area .

The correct answer is given under the spoiler in the original post and it's A. For (2) all we k now is one side of the rectangle. Having T as the midpoint of PS gives us nothing.

Hope it helps.
_________________
Intern
Joined: 11 Dec 2013
Posts: 15
Location: India
Concentration: Finance, Technology
Schools: ISB '18
GMAT Date: 03-15-2015
WE: Operations (Telecommunications)
Re: In rectangular region PQRS above, T is a point on side PS. If PS = 4, [#permalink]

### Show Tags

06 Apr 2016, 23:09
Yes i have seen the answer .
But i proved that if T is the midpoint then the resulting triangle will be equilateral .
Math Expert
Joined: 02 Aug 2009
Posts: 5896
Re: In rectangular region PQRS above, T is a point on side PS. If PS = 4, [#permalink]

### Show Tags

07 Apr 2016, 04:51
4d wrote:
Yes i have seen the answer .
But i proved that if T is the midpoint then the resulting triangle will be equilateral .

Hi,
check the angles which are equal..
the Triangle is QRT
and your solution says

Quote:
Therefore angle TQR = QTP , which implies TQR=QTP=RTS
Therefore an equilateral triangle , Hence we can find the area .

The angle which has to be shown EQUAL are QRT = RTQ = TQR..
Statement 2 is not sufficient..
relook in your solution

Logically, I will give you ONE rectangle..
1) It has 100 as length and ONLY 1 as width..
try it out, it can never have all angles as 60 degree as the two equal sides will be CLOSE to 50-60 and the third side will be 100..

_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

GMAT online Tutor

Retired Moderator
Joined: 18 Sep 2014
Posts: 1174
Location: India
Re: In rectangular region PQRS above, T is a point on side PS. If PS = 4, [#permalink]

### Show Tags

07 Apr 2016, 12:34
OE wrote:
Statement 1) “QTR is an equilateral triangle” If this is true then with QR as the base and the height equivalent to the side PQ (or RS). Then the measure of the of the triangle is ½ of the measure of the rectangle since the triangle QTR would essentially be LW/ 2. You can determine the area of triangle QTR using the formula for the area of an equilateral triangle
“$$(s^2\sqrt{3})/4$$.”

(the facts tell you that “s = 4”) This is sufficient. The answer is A or D.

I got this right but I'm curios how it would help us if we find the area of QTR to find the area of the rectangle.
can some one address the query?
_________________

The only time you can lose is when you give up. Try hard and you will suceed.
Thanks = Kudos. Kudos are appreciated

http://gmatclub.com/forum/rules-for-posting-in-verbal-gmat-forum-134642.html
When you post a question Pls. Provide its source & TAG your questions
Avoid posting from unreliable sources.

My posts
http://gmatclub.com/forum/beauty-of-coordinate-geometry-213760.html#p1649924
http://gmatclub.com/forum/calling-all-march-april-gmat-takers-who-want-to-cross-213154.html
http://gmatclub.com/forum/possessive-pronouns-200496.html
http://gmatclub.com/forum/double-negatives-206717.html
http://gmatclub.com/forum/the-greatest-integer-function-223595.html#p1721773

Manager
Status: folding sleeves up
Joined: 26 Apr 2013
Posts: 148
Location: India
Concentration: Finance, Strategy
GMAT 1: 530 Q39 V23
GMAT 2: 560 Q42 V26
GPA: 3.5
WE: Consulting (Computer Hardware)
Re: In rectangular region PQRS above, T is a point on side PS. If PS = 4, [#permalink]

### Show Tags

16 Apr 2016, 08:34
Bunuel wrote:

In rectangular region PQRS above, T is a point on side PS. If PS = 4, what is the area of region PQRS?

(1) Triangle QTR is equilateral.
(2) Segments PT and TS have equal length.

Kudos for a correct solution.

Attachment:
2015-10-08_1851.png

For an equilateral triangle, all the angles are equal to 60 degree.
So ag(QRT)+ag(TRS)=90
ag(TRS)= 30degree

which means: ag(RTS) = 60 and ag(RST)=90

Sin 60 = root3/2

RS/RT=root3/2

RS=2root3

area= RS*PS

1 suff
Senior Manager
Joined: 05 Dec 2016
Posts: 260
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
In rectangular region PQRS above, T is a point on side PS. If PS = 4, [#permalink]

### Show Tags

02 May 2017, 00:28
(1) PQ=PS=4
Since QTR is equilateral then, knowing the value of one side we can easility calculate the altitude,using the followign formula:
h=a*3^1/2/2=4*3^1/2/2=2*3^1/2 Sufficient
(2) Defferent values are possible and since we are lacking any information about angles it's completely insufficient.
Non-Human User
Joined: 09 Sep 2013
Posts: 7007
Re: In rectangular region PQRS above, T is a point on side PS. If PS = 4, [#permalink]

### Show Tags

23 May 2018, 20:03
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 rectangular region PQRS above, T is a point on side PS. If PS = 4,   [#permalink] 23 May 2018, 20:03
Display posts from previous: Sort by

# In rectangular region PQRS above, T is a point on side PS. If PS = 4,

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.