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

It is currently 11 Dec 2018, 19:06

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
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Free GMAT Prep Hour

     December 11, 2018

     December 11, 2018

     09:00 PM EST

     10:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

In the figure shown, QS is an altitude of right triangle PQR, PS = 16,

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51100
In the figure shown, QS is an altitude of right triangle PQR, PS = 16,  [#permalink]

Show Tags

New post 25 Mar 2018, 23:17
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

62% (03:17) correct 38% (02:42) wrong based on 43 sessions

HideShow timer Statistics

Image

In the figure shown, QS is an altitude of right triangle PQR, PS = 16, and RS = 4. Find the perimeter of PQR.


A. \(20 + 4\sqrt{5}\)

B. \(20 + 6\sqrt{5}\)

C. \(20 + 8\sqrt{5}\)

D. \(20 + 12\sqrt{5}\)

E. \(32\sqrt{5}\)


Attachment:
2018-03-26_1113.png
2018-03-26_1113.png [ 9.37 KiB | Viewed 728 times ]

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

examPAL Representative
User avatar
G
Joined: 07 Dec 2017
Posts: 841
Re: In the figure shown, QS is an altitude of right triangle PQR, PS = 16,  [#permalink]

Show Tags

New post 26 Mar 2018, 01:34
Bunuel wrote:

In the figure shown, QS is an altitude of right triangle PQR, PS = 16, and RS = 4. Find the perimeter of PQR.


A. \(20 + 4\sqrt{5}\)

B. \(20 + 6\sqrt{5}\)

C. \(20 + 8\sqrt{5}\)

D. \(20 + 12\sqrt{5}\)

E. \(32\sqrt{5}\)




As the answers are close together we can't estimate and need to rely on specific geometric rules for an exact solution.
This is a Precise approach.

Since the larger triangle is right-angle then angle P and angle R sum to 90.
Since the two smaller triangle are also right-angle then angle SQP and angle P sum to 90 as do angles R and angle SRQ.
That is, angle SQP = angle R and angle SQR = angle P.
So our small triangles are similar both to each other and to the larger triangle.
Then using similarity of the two smaller triangles: SQ/SP = SR/SQ --> SQ^2 = 16*4 = 64 --> SQ = 8.
Then the hypotenuse of the small internal triangle can be calculated as \(\sqrt{8^2 + 4^2}=\sqrt{4^2(2^2+1)}=4\sqrt{5}\)
Then the hypotenuse of the large internal triangle can be calculated as the \(\sqrt{8^2 + 16^2}=\sqrt{8^2(1+2^2)}=8\sqrt{5}\)
Then our total perimeter is \(16 + 4 + 4\sqrt{5} + 8\sqrt{5} = 20 +12\sqrt{5}\)

(D) is our answer.
_________________

Image
Sign up for 7-day free trial
Image

Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3325
Location: India
GPA: 3.12
Premium Member CAT Tests
In the figure shown, QS is an altitude of right triangle PQR, PS = 16,  [#permalink]

Show Tags

New post 26 Mar 2018, 01:53
2
Attachment:
2018-03-26_1113.png
2018-03-26_1113.png [ 11.74 KiB | Viewed 589 times ]


In Triangle PQS, \(PQ^2 = PS^2 + QS^2\) -> \(PQ^2 = 16^2 + x^2 = 256 + x^2\)

In Triangle RQS, \(RQ^2 = SR^2 + QS^2\) -> \(RQ^2 = 4^2 + x^2 = 16 + x^2\)

In Triangle PQR, \(PR^2 = PQ^2 + RQ^2\) -> \(20^2 = 256 + x^2 + 16 + x^2\) -> \(2x^2 = 400 - 272 = 128\) -> \(x^2 = 64\) -> \(x = 8\)

Perimeter = \(20 + \sqrt{256 + 64} + \sqrt{16 + 64} = 20 + \sqrt{320} + \sqrt{80} = 20 + 2\sqrt{80} + \sqrt{80} = 20 + 3\sqrt{2^4*5} = 20 + 12\sqrt{5}\)

Therefore, the perimeter of triangle PQR is \(20 + 12\sqrt{5}\)(Option D)
_________________

You've got what it takes, but it will take everything you've got

GMAT Club Bot
In the figure shown, QS is an altitude of right triangle PQR, PS = 16, &nbs [#permalink] 26 Mar 2018, 01:53
Display posts from previous: Sort by

In the figure shown, QS is an altitude of right triangle PQR, PS = 16,

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.