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

It is currently 20 Oct 2019, 00:15

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

In the figure above, what is the area of region PQRST ? (1) PQ = RS (

  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: 58446
In the figure above, what is the area of region PQRST ? (1) PQ = RS (  [#permalink]

Show Tags

New post 26 Apr 2019, 03:09
10
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

60% (02:09) correct 40% (01:52) wrong based on 418 sessions

HideShow timer Statistics

examPAL Representative
User avatar
P
Joined: 07 Dec 2017
Posts: 1153
In the figure above, what is the area of region PQRST ? (1) PQ = RS (  [#permalink]

Show Tags

New post Updated on: 04 May 2019, 10:42
2
The Logical approach to this question will the observation that the area we're looking for is of a shape which doesn't have a matching formula. Thus, we should either refer to it as the sum of or the difference between two familiar shapes. In this case, the sum of a rectangle and a triangle.
Statement (1) tells us that the sides of the rectangle are 6, which is enough to find the other side of the rectangle (using the pythagorean triplet 6,8,10). However, we don't have a height required to find the area of the triangle. Thus, answers (A) and (D) are eliminated.
Statement (2): Knowing that the triangle is an isosceles triangle is not enough to find its area. Answer choice (B) is eliminated.
Combining both statements, we now know that the triangle is an equilateral triangle, so the length of one side is enough to find its area.
The correct answer is (C).

Posted from my mobile device
_________________

Originally posted by DavidTutorexamPAL on 26 Apr 2019, 14:56.
Last edited by DavidTutorexamPAL on 04 May 2019, 10:42, edited 1 time in total.
Intern
Intern
avatar
S
Joined: 26 Apr 2017
Posts: 45
Re: In the figure above, what is the area of region PQRST ? (1) PQ = RS (  [#permalink]

Show Tags

New post 01 May 2019, 07:41
Please explain why statement 2 is insufficient:
Since we know the isosceles triangle. Side QT = RS, and Side QR can be found using Pythagorean theorem. Hence, it can be found. Thanks.
examPAL Representative
User avatar
P
Joined: 07 Dec 2017
Posts: 1153
In the figure above, what is the area of region PQRST ? (1) PQ = RS (  [#permalink]

Show Tags

New post 01 May 2019, 08:56
1
Valhalla wrote:
Please explain why statement 2 is insufficient:
Since we know the isosceles triangle. Side QT = RS, and Side QR can be found using Pythagorean theorem. Hence, it can be found. Thanks.


Hey Valhalla,

Knowing that QT= RS is insufficient to know their length. (In particular, it is also insufficient to calculate QR)
Try it!
Draw PT of length 6, build an isosceles triangle on top of it and build the square QRST off the side of that.
See how changing the lengths of the sides of the isosceles means that you will change the size of the square (because the diagonal must equal 10).
Then this is insufficient.
_________________
Intern
Intern
avatar
S
Joined: 26 Apr 2017
Posts: 45
Re: In the figure above, what is the area of region PQRST ? (1) PQ = RS (  [#permalink]

Show Tags

New post 01 May 2019, 17:14
Thanks. I have mistakenly taken PT = QT = 6, that is why I could not fathom how statement 2 alone is insufficient. Dear David, thanks for replying. Any pointers you would give to avoid such mistakes? Thanks.
examPAL Representative
User avatar
P
Joined: 07 Dec 2017
Posts: 1153
In the figure above, what is the area of region PQRST ? (1) PQ = RS (  [#permalink]

Show Tags

New post 02 May 2019, 02:29
1
Valhalla wrote:
Thanks. I have mistakenly taken PT = QT = 6, that is why I could not fathom how statement 2 alone is insufficient. Dear David, thanks for replying. Any pointers you would give to avoid such mistakes? Thanks.


Hey Valhalla,

The mistake you describe is what we classify as a 'silly mistake'.
In other words, it is not that you didn't know the material, but rather that you missed / misinterpreted a small piece of data and therefore got the rest of the question wrong.
Tip number 1: Take a few seconds after reading the question but before diving into calculations to make sure you've copied everything down / read everything correctly. This is the best way to avoid such mistakes.
Tip number 2: Build up a timing strategy which doesn't leave you feeling completely rushed. It is better to guess a few questions and have enough time to do the others properly than to do everything in a hurried manner.
Tip number 3: Practice! The more questions you solve, the more familiar with the GMAT you get, and consequently the better you are able to notice the 'important' and 'tricky' details.

Best of luck,
David
_________________
Intern
Intern
avatar
B
Joined: 10 Jun 2018
Posts: 13
Re: In the figure above, what is the area of region PQRST ? (1) PQ = RS (  [#permalink]

Show Tags

New post 03 May 2019, 11:10
Why is statement 1 insufficient?
We have diagonal as 10 and PQ=RS=6
So, we can find ST = 8
Since its a rectangle, we can directly find the area of this figure.
Similarly, for the triangle, we can take height which is divides QT in half and so by pythagoras, we can find the height of triangle as 5.

What have I considered wrong here?
examPAL Representative
User avatar
P
Joined: 07 Dec 2017
Posts: 1153
Re: In the figure above, what is the area of region PQRST ? (1) PQ = RS (  [#permalink]

Show Tags

New post 03 May 2019, 12:21
abannore wrote:
Why is statement 1 insufficient?
We have diagonal as 10 and PQ=RS=6
So, we can find ST = 8
Since its a rectangle, we can directly find the area of this figure.
Similarly, for the triangle, we can take height which is divides QT in half and so by pythagoras, we can find the height of triangle as 5.

What have I considered wrong here?


Hey abannore,

You're right about the rectangle but wrong about the triangle.
The height only divides QT in half if the triangle is isosceles (if PQ = PT).
One way to SEE that there are many options is to imagine different angles for PQT.
If angle PQT were exactly 90 degrees, then PQ itself would be the height!
Instead, if angle PQT was very close to 0 then the triangle would be very 'narrow', and the height would also be very close to 0.
Two different options --> insufficient.

Best,
David
_________________
Manager
Manager
avatar
B
Joined: 27 Nov 2015
Posts: 122
GMAT ToolKit User
Re: In the figure above, what is the area of region PQRST ? (1) PQ = RS (  [#permalink]

Show Tags

New post 03 May 2019, 22:36
1
DavidTutorexamPAL wrote:
The Logical approach to this question will the observation that the area we're looking for us of a shape which doesn't have a matching formula. Thus, we should either refer to it as the sum of or the difference between two familiar shapes. In this case, the sum of a rectangle and a triangle.
Statement (1) tells us that the sides of the rectangle are 6, which is enough to find the other side of the rectangle (using the pythagorean triplet 6,8,10).Yet, we don't have a height required to find the area of the rectangle. Thus, answers (A) and (D) are eliminated.
Statement (2): Knowing that the triangle is an isoscelous triangle is not enough to find its area. Answer choice (B) is eliminated.
Combining both statements, we now know that the triangle is an equilateral triangle, so one side is enough in order to find its area.
The correct answer is (C).

Posted from my mobile device


Hi David, do you mean triangle here?
examPAL Representative
User avatar
P
Joined: 07 Dec 2017
Posts: 1153
In the figure above, what is the area of region PQRST ? (1) PQ = RS (  [#permalink]

Show Tags

New post 04 May 2019, 10:40
rnn wrote:
DavidTutorexamPAL wrote:
The Logical approach to this question will the observation that the area we're looking for us of a shape which doesn't have a matching formula. Thus, we should either refer to it as the sum of or the difference between two familiar shapes. In this case, the sum of a rectangle and a triangle.
Statement (1) tells us that the sides of the rectangle are 6, which is enough to find the other side of the rectangle (using the pythagorean triplet 6,8,10).Yet, we don't have a height required to find the area of the rectangle. Thus, answers (A) and (D) are eliminated.
Statement (2): Knowing that the triangle is an isoscelous triangle is not enough to find its area. Answer choice (B) is eliminated.
Combining both statements, we now know that the triangle is an equilateral triangle, so one side is enough in order to find its area.
The correct answer is (C).

Posted from my mobile device


Hi David, do you mean triangle here?


Hey rnn,
You mean in (1)?
Yes! Thanks, fixed the typo.
_________________
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15287
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: In the figure above, what is the area of region PQRST ? (1) PQ = RS (  [#permalink]

Show Tags

New post 11 May 2019, 14:25
Hi All,

We're asked for the area of region PQRST. This question is based around a couple of Geometry rules. To properly find the area, we can break this shape into 2 pieces (a rectangle and a triangle), so we need to know the dimensions of the rectangle and the exact type of triangle - since we have one of the sides, we either need the 3 angles or the 2 missing sides - to calculate the overall area.

(1) PQ = RS

With the information in Fact 1, we know that the width of the rectangle is 6 and one of the two missing triangle sides is also 6. Along with the diagonal of the rectangle, we can now calculate its length (it's 8, since we have a 6/8/10 right triangle in the rectangle) but without the 3rd side of the triangle (or its 3 angles), we cannot calculate that other area.
Fact 1 is INSUFFICIENT

(2) PT = QT

The information in Fact 2 tells us that the triangle is either Isosceles or Equilateral, but we still do not know enough to determine its area and we don't know the length or width of the rectangle, so we cannot determine its area either.
Fact 2 is INSUFFICIENT

Combined, we know...
PQ = RS
PT = QT

With both Facts, we know that the triangle's sides are 6/6/6, so it's Equilateral and we can calculate its area. We also know the area of the rectangle (it's 6x8 = 48), so we CAN determine the area of PQRST.
Combined, SUFFICIENT

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 ★★★★★
GMAT Club Bot
Re: In the figure above, what is the area of region PQRST ? (1) PQ = RS (   [#permalink] 11 May 2019, 14:25
Display posts from previous: Sort by

In the figure above, what is the area of region PQRST ? (1) PQ = RS (

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





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