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

 It is currently 17 Jul 2018, 08:30

### 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

# In the figure shown, what is the are of the triangular

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

### Hide Tags

Intern
Joined: 23 May 2012
Posts: 36
Location: India
Concentration: Strategy, Healthcare
GMAT 1: 760 Q50 V44
GPA: 3.3
In the figure shown, what is the are of the triangular [#permalink]

### Show Tags

Updated on: 09 Nov 2013, 06:34
16
50
00:00

Difficulty:

45% (medium)

Question Stats:

59% (00:27) correct 41% (00:42) wrong based on 973 sessions

### HideShow timer Statistics

Attachment:

image.png [ 3.8 KiB | Viewed 36174 times ]
In the figure shown, what is the are of the triangular region PRT?

(1) The area of rectangular region PQST is 24.
(2) The length of line segment RT is 5.

_________________

Please Kudos if you found my post useful

Originally posted by yuvrajsub on 29 Oct 2013, 04:14.
Last edited by yuvrajsub on 09 Nov 2013, 06:34, edited 5 times in total.
Veritas Prep GMAT Instructor
Joined: 23 Oct 2013
Posts: 144
Re: In the figure shown, what is the are of the triangular [#permalink]

### Show Tags

29 Oct 2013, 05:15
32
10
It statement 1, is it supposed to say "The area of the rectangular region PQST is 24? If so, statement 1 gives you enough information to prove that the area is 12. This is because the area of a quadrilateral is equal to base * height. Because the triangle is inscribed within the rectangle, we know that the base * height of the triangle must also equal 24. But the area of a triangle is equal to 1/2*base*height, so its area must equal 1/2*24 = 12.

Try some numbers to prove this to yourself. Say that the base of the rectangle is 24, and its height 1. That makes the base of the triangle 24 and its height 1, and 1/2*24*1 = 12. How about if the base is 6 and the height is 4? 1/2*6*4 = 12. The area of the triangle will always be 12.

Statement 2, on the other hand, provides neither the base nor the height, and is this insufficient.

This makes the correct answer A.

I hope this helps!!!
_________________

Brandon
Veritas Prep | GMAT Instructor

If you found this post helpful, please give me kudos!!!

Save \$100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

##### General Discussion
Intern
Joined: 23 May 2012
Posts: 36
Location: India
Concentration: Strategy, Healthcare
GMAT 1: 760 Q50 V44
GPA: 3.3
Re: In the figure shown, what is the are of the triangular [#permalink]

### Show Tags

29 Oct 2013, 05:21
Thanks a lot for the crystal clear explanation! Never ever question the official answers.
_________________

Please Kudos if you found my post useful

Intern
Joined: 08 Apr 2010
Posts: 1
Re: In the figure shown, what is the are of the triangular [#permalink]

### Show Tags

29 Oct 2013, 18:25
@ bunuel - pls help. Is it always that area of any quadrilateral will be its bxh?
Math Expert
Joined: 02 Sep 2009
Posts: 47037
Re: In the figure shown, what is the are of the triangular [#permalink]

### Show Tags

30 Oct 2013, 00:34
1
meenakshi1 wrote:
@ bunuel - pls help. Is it always that area of any quadrilateral will be its bxh?

No, that's not true. Please check here: math-polygons-87336.html

Hope it helps.
_________________
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 619
Re: In the figure shown, what is the are of the triangular [#permalink]

### Show Tags

09 Nov 2013, 04:48
yuvrajsub wrote:
Attachment:
image.png
In the figure shown, what is the are of the triangular region PRT?

(1) The area of rectangular region PQST is 24.
(2) The length of line segment RT is 5.

[spoiler=]Source: GMATPrep Exam Pack 1

OA: A

Theory: The area of any # of trianlge(s) between
A.2 fixed parallel lines, and
B.With the same base is ALWAYS the same.

The first point makes sure that the height of the given triangles is always the same;the second point mandates the base lenght to be the same for all of them.

From the given image, try sliding the point R towards Q till the line segment RP co-incides with the side QP of the rectangle and thus, RT becomes the diagonal.
Now, if we were told to find the area of the newly formed triangle PRT, it would be nothing but $$\frac{1}{2}*24$$

Hope this helps.
_________________
Intern
Joined: 24 Nov 2014
Posts: 1
Re: In the figure shown, what is the are of the triangular [#permalink]

### Show Tags

24 Nov 2014, 15:32
I'm sorry but I have a bit of a question on this:

(1) The are of PQST is 24 (.5*B*H) so that's the area of the triangular region: sufficient

(2) The length of the line segment RT is 5.

RT is 5
If you drop a perpendicular line down from R to PT that forms a 90 degree triangle. Let's call that point X.
Can we then assume a 3-4-5 triangle? I got 90 degrees and a 5 right?
Then triangle XRT is similar to XRP because they share the same side RX so you can set up proportions to find length PX and XT to get length PT and since you know RX is 4. b*h*.5 is the answer? thus sufficient???
Math Expert
Joined: 02 Sep 2009
Posts: 47037
Re: In the figure shown, what is the are of the triangular [#permalink]

### Show Tags

25 Nov 2014, 05:00
SweetiePi wrote:
I'm sorry but I have a bit of a question on this:

(1) The are of PQST is 24 (.5*B*H) so that's the area of the triangular region: sufficient

(2) The length of the line segment RT is 5.

RT is 5
If you drop a perpendicular line down from R to PT that forms a 90 degree triangle. Let's call that point X.
Can we then assume a 3-4-5 triangle? I got 90 degrees and a 5 right?
Then triangle XRT is similar to XRP because they share the same side RX so you can set up proportions to find length PX and XT to get length PT and since you know RX is 4. b*h*.5 is the answer? thus sufficient???

No, the red part is not correct. Hypotenuse of 5 does not necessarily means that the legs must be 3 and 4.
_________________
Manager
Joined: 26 May 2013
Posts: 61
Re: In the figure shown, what is the are of the triangular [#permalink]

### Show Tags

06 Mar 2015, 01:24
yuvrajsub wrote:
Attachment:
image.png
In the figure shown, what is the are of the triangular region PRT?

(1) The area of rectangular region PQST is 24.
(2) The length of line segment RT is 5.

You may also prove this algebraically. Area of the rectangle is the sum of the all three embedded triangles:

(1/2*RQ*ST) + (1/2*RS*ST) + (1/2*PT*ST). But, you will notice that RQ +RS = QS= PT; hence the sum of area of triangle PQR and RST is equal to the area of PRT. Thus, the area of triangle PRT is half of the rectangle.
Manager
Joined: 13 Dec 2013
Posts: 161
Location: United States (NY)
Concentration: Nonprofit, International Business
GMAT 1: 710 Q46 V41
GMAT 2: 720 Q48 V40
GPA: 4
WE: Consulting (Consulting)
Re: In the figure shown, what is the are of the triangular [#permalink]

### Show Tags

23 Mar 2017, 13:15
1
yuvrajsub wrote:
Attachment:
image.png
In the figure shown, what is the are of the triangular region PRT?

(1) The area of rectangular region PQST is 24.
(2) The length of line segment RT is 5.

Area of triangle = 1/2bh.
Area of rectangle = bh

1) Gives bh and is therefore suff.

2) Cannot get b or h. Insuff.

A

Kudos if you agree!
Intern
Joined: 30 Mar 2017
Posts: 3
Re: In the figure shown, what is the are of the triangular [#permalink]

### Show Tags

14 May 2017, 16:01
yuvrajsub wrote:
Attachment:
image.png
In the figure shown, what is the are of the triangular region PRT?

(1) The area of rectangular region PQST is 24.
(2) The length of line segment RT is 5.

I picked E because I thought we couldn't assume R was on QS since it is a Data Sufficiency Question and therefore, we don't know the height of the triangle. Just as we couldn't assume PQST was a quadrilateral until statement 1. I'm confused on what we can and cannot assume in these questions. Does anybody have any good advice on this?
Math Expert
Joined: 02 Sep 2009
Posts: 47037
Re: In the figure shown, what is the are of the triangular [#permalink]

### Show Tags

14 May 2017, 20:59
jwang1191 wrote:
yuvrajsub wrote:
Attachment:
image.png
In the figure shown, what is the are of the triangular region PRT?

(1) The area of rectangular region PQST is 24.
(2) The length of line segment RT is 5.

I picked E because I thought we couldn't assume R was on QS since it is a Data Sufficiency Question and therefore, we don't know the height of the triangle. Just as we couldn't assume PQST was a quadrilateral until statement 1. I'm confused on what we can and cannot assume in these questions. Does anybody have any good advice on this?

R is shown to be on QS so it is actually on QS. This will never be a trick on the GMAT.
_________________
Director
Joined: 12 Nov 2016
Posts: 774
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: In the figure shown, what is the are of the triangular [#permalink]

### Show Tags

05 Sep 2017, 20:00
yuvrajsub wrote:
Attachment:
image.png
In the figure shown, what is the are of the triangular region PRT?

(1) The area of rectangular region PQST is 24.
(2) The length of line segment RT is 5.

Tricky question ahhh

What the trap in this question is getting you to think that you need a particular hypotenuse length in order to calculate the respective areas- HOWEVER if you think about the question from a formulaic perspective then you will see that the area of a right triangle

1/2 BH essentially equals the area of the square

It doesn't actually matter what the height and length are- 6 and 4 or 8 and 3 because they will multiply to 24 which can just be substituted for BH in

1/2 BH

And will result in the same answer

A
CEO
Joined: 12 Sep 2015
Posts: 2631
Re: In the figure shown, what is the are of the triangular [#permalink]

### Show Tags

19 Apr 2018, 15:17
Top Contributor
yuvrajsub wrote:
Attachment:
image.png
In the figure shown, what is the are of the triangular region PRT?

(1) The area of rectangular region PQST is 24.
(2) The length of line segment RT is 5.

Target question: What is the area of triangular region PRT?

Statement 1: The area of rectangular region PQST is 24
The area of ∆PRT = (base)(height)/2
Statement 1 tells us that (base)(height) = 24
Since the base and the height of the rectangle are the SAME as the base and the height of the triangle PRT, we can use this information to find the area of ∆PRT.
The area of ∆PRT = (base)(height)/2 = 24/2 = 12
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The length of line segment RT is 5
The area of ∆PRT = (base)(height)/2
Statement 2 tells us NOTHING about the base and height, so we can't use this to find the area of ∆PRT.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Re: In the figure shown, what is the are of the triangular   [#permalink] 19 Apr 2018, 15:17
Display posts from previous: Sort by

# In the figure shown, what is the are of the triangular

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

# Events & Promotions

 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®.