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

It is currently 12 Dec 2019, 01:22

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, angle PTQ = angle QRS = 70º, PT = 4, PR = 12, and

  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: 59685
In the figure above, angle PTQ = angle QRS = 70º, PT = 4, PR = 12, and  [#permalink]

Show Tags

New post 15 Mar 2015, 23:18
3
25
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

65% (03:15) correct 35% (03:36) wrong based on 132 sessions

HideShow timer Statistics

Image

In the figure above, angle PTQ = angle QRS = 70º, PT = 4, PR = 12, and the shaded region has an area of 48. What is the length of QW?

A. \(2\sqrt{2}\)

B. 3

C. \(\sqrt{10}\)

D. 3.2

E. 3.5

Kudos for a correct solution.

Attachment:
gpp-sgf_img6.png
gpp-sgf_img6.png [ 12.51 KiB | Viewed 4251 times ]

_________________
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59685
Re: In the figure above, angle PTQ = angle QRS = 70º, PT = 4, PR = 12, and  [#permalink]

Show Tags

New post 23 Mar 2015, 03:34
3
5
Bunuel wrote:
Image
In the figure above, angle PTQ = angle QRS = 70º, PT = 4, PR = 12, and the shaded region has an area of 48. What is the length of QW?

A. \(2\sqrt{2}\)

B. 3

C. \(\sqrt{10}\)

D. 3.2

E. 3.5

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

We know the larger and smaller triangles are similar, because they share the angle at P, and one other angle in each is 70º. What’s tricky is that they have different orientations, so that side PT actually corresponds to side PR. We know PR:PT = 3, so that’s the scale fact. Every length in triangle PRS is three times more than the corresponding side in triangle PTQ. If lengths are multiplied by 3, area is multiplied by 3 squared, or 9. Let’s say that the area of triangle PTQ is A. Then the area of triangle PRS is 9A. The shaded area is the difference of the two triangle areas, or 8A. If 8A = 48, this means A = 6, and that’s the area of triangle PTQ.

Well, PT = 4 is a base of PTQ, and QW is a corresponding altitude: call its length h.

A = 0.5bh

6 = 0.5(4)h

6 = 2h

3 = h

The length of QW is 3.

Answer = (B)
_________________
General Discussion
Manager
Manager
User avatar
Status: A mind once opened never loses..!
Joined: 05 Mar 2015
Posts: 186
Location: India
MISSION : 800
WE: Design (Manufacturing)
GMAT ToolKit User
Re: In the figure above, angle PTQ = angle QRS = 70º, PT = 4, PR = 12, and  [#permalink]

Show Tags

New post 16 Mar 2015, 00:57
3
1
Hi
this question basically tests the concept of similar triangles
plz have a look on the attached pic
Attachments

tri.png
tri.png [ 43.79 KiB | Viewed 3812 times ]

Manager
Manager
avatar
Joined: 17 Mar 2015
Posts: 113
Re: In the figure above, angle PTQ = angle QRS = 70º, PT = 4, PR = 12, and  [#permalink]

Show Tags

New post 23 Mar 2015, 04:01
It is probably worth mentioning that formula of 1/2*a*b*sin(a^b) is a good way to remember the relation between sides and the areas of triangles: as in, 1/2*PQ*PT*sin(P)/(1/2*PS*PR*sin(P) = PQ*PT/(PS*PR) = PQ*PT/(3*PQ*3*PT) = 1/3*1/3 = 1/9 in our case.
Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2491
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Reviews Badge
Re: In the figure above, angle PTQ = angle QRS = 70º, PT = 4, PR = 12, and  [#permalink]

Show Tags

New post 19 Feb 2016, 20:26
oh man..took me some time to solve..would definitely not solve on the actual test..spent about 10 minutes to solve it...
we know that angles PTQ and QRS are 70 degrees. we also know that angle P is shared by the triangle PQT and PRS.
since these 2 triangles have 2 similar angles, the triangles must be similar.
the "base", or the segment from the 70 degree angle to the P angle is 3 times greater than PT, thus, the height of the PRS triangle must be 3 times greater than QW.

ok, so the area of the shaded region is:
A(PRS)-A(PQT) = 48
area of PQT=4QW/2 = 2QW
area of PRS=12*3QW/2 = 18QW.

now, 18QW-2QW=16QW=48.
QW=3.
Director
Director
avatar
P
Joined: 24 Nov 2016
Posts: 955
Location: United States
Re: In the figure above, angle PTQ = angle QRS = 70º, PT = 4, PR = 12, and  [#permalink]

Show Tags

New post 02 Sep 2019, 12:34
Bunuel wrote:
Image
In the figure above, angle PTQ = angle QRS = 70º, PT = 4, PR = 12, and the shaded region has an area of 48. What is the length of QW?

A. \(2\sqrt{2}\)
B. 3
C. \(\sqrt{10}\)
D. 3.2
E. 3.5


Similarity between: PRS~PQT; \(\frac{side^2_a}{side^2_b}=\frac{area_a}{area_b}\)
\(\frac{12^2}{4^2}=\frac{48+x}{x}…144x=16(48)+16x…x=area_{pqt}=6\)
\(area_{pqt}=\frac{base•height}{2}=\frac{PT•QW}{2}=6…4QW=12…QW=3\)

Answer (B)
GMAT Club Bot
Re: In the figure above, angle PTQ = angle QRS = 70º, PT = 4, PR = 12, and   [#permalink] 02 Sep 2019, 12:34
Display posts from previous: Sort by

In the figure above, angle PTQ = angle QRS = 70º, PT = 4, PR = 12, and

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





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