It is currently 21 Oct 2017, 14:58

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

Events & Promotions in June
Open Detailed Calendar

In ∆ ABC above, what is the sum of p + q + r + s + t + u ?

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129160 [0], given: 12194

In ∆ ABC above, what is the sum of p + q + r + s + t + u ? [#permalink]

Show Tags

New post 06 Sep 2017, 04:40
Expert's post
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

83% (01:14) correct 18% (00:35) wrong based on 40 sessions

HideShow timer Statistics

Image
In ∆ ABC above, what is the sum of p + q + r + s + t + u ?

(A) 180
(B) 225
(C) 270
(D) 360
(E) 450


[Reveal] Spoiler:
Attachment:
2017-09-06_1535_002.png
2017-09-06_1535_002.png [ 11.77 KiB | Viewed 871 times ]
[Reveal] Spoiler: OA

_________________

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

Kudos [?]: 129160 [0], given: 12194

Senior Manager
Senior Manager
User avatar
G
Joined: 02 Jul 2017
Posts: 252

Kudos [?]: 59 [0], given: 60

Location: India
GMAT ToolKit User CAT Tests
Re: In ∆ ABC above, what is the sum of p + q + r + s + t + u ? [#permalink]

Show Tags

New post 06 Sep 2017, 04:49
Find : p + q + r + s + t + u

Let the angles of center triangle formed inside big triangle be x, y and z
=> x+y+z=180
Now as Sum of angles on 1 side of straight line = 180

=> p+u+x=180
=>q+r+y=180
=>s+t+z=180
adding all 3.. p+q+r+s+t+u+(x+y+z)= 540
p+q+r+s+t+u = 540 -(x+y+z) = 540-180 =360

Answer: D

Kudos [?]: 59 [0], given: 60

2 KUDOS received
BSchool Forum Moderator
User avatar
P
Joined: 26 Feb 2016
Posts: 1467

Kudos [?]: 597 [2], given: 16

Location: India
Concentration: General Management, Leadership
WE: Sales (Retail)
Premium Member CAT Tests
Re: In ∆ ABC above, what is the sum of p + q + r + s + t + u ? [#permalink]

Show Tags

New post 06 Sep 2017, 05:32
2
This post received
KUDOS
Attachment:
2017-09-06_1535_002.png
2017-09-06_1535_002.png [ 12.87 KiB | Viewed 592 times ]


There are 3 smaller triangles(∆ADE,∆BDF and ∆CEF) each which has a third angle(unmarked) - A,B and C
A + B + C = 180 degree(sum of the three angles of the triangle ABC total 180)

Similarly each of the smaller triangles also has a sum of angles equal to 180.
p + q + r + s + t + u + A + B + C = 540
p + q + r + s + t + u = 540 - 180 = 360(Option D)
_________________

Stay hungry, Stay foolish

2017-2018 MBA Deadlines

Class of 2020: Rotman Thread | Schulich Thread
Class of 2019: Sauder Thread

Kudos [?]: 597 [2], given: 16

1 KUDOS received
Manager
Manager
User avatar
S
Joined: 09 Mar 2017
Posts: 65

Kudos [?]: 34 [1], given: 161

Location: India
Concentration: Marketing, Organizational Behavior
WE: Information Technology (Computer Software)
Re: In ∆ ABC above, what is the sum of p + q + r + s + t + u ? [#permalink]

Show Tags

New post 06 Sep 2017, 09:16
1
This post received
KUDOS
Bunuel wrote:
Image
In ∆ ABC above, what is the sum of p + q + r + s + t + u ?

(A) 180
(B) 225
(C) 270
(D) 360
(E) 450


[Reveal] Spoiler:
Attachment:
2017-09-06_1535_002.png


A + B + C = 180
[180-(r+s) ] + [180-(q+p)] + [180 - (t+u)] = 180
3(180) - 180 = r+s +p+q+t+u
2(180) = r+s +p+q+t+u
=360
option D
_________________

------------------------------
"Trust the timing of your life"

Kudos [?]: 34 [1], given: 161

1 KUDOS received
Director
Director
avatar
P
Joined: 22 May 2016
Posts: 823

Kudos [?]: 266 [1], given: 553

Re: In ∆ ABC above, what is the sum of p + q + r + s + t + u ? [#permalink]

Show Tags

New post 06 Sep 2017, 11:54
1
This post received
KUDOS
Bunuel wrote:
Image
In ∆ ABC above, what is the sum of p + q + r + s + t + u ?

(A) 180
(B) 225
(C) 270
(D) 360
(E) 450


[Reveal] Spoiler:
Attachment:
The attachment 2017-09-06_1535_002.png is no longer available

Attachment:
triangles111.png
triangles111.png [ 31.82 KiB | Viewed 448 times ]


A, B, and C are interior angles of the larger ∆ ABC

So A + B + C = 180

(A + B + C) can be used to find p + q + r + s + t + u

Angles in each small triangle (yellow, purple, green) also sum to 180.

From diagram, write the equations -- and add them

r + s + A = 180
p + q + B = 180
t + u + C = 180____________________
r + s + A + p + q + B + t + u + C = 540, or

p + q + r + s + t + u + (A + B + C) = 540, or

p + q + r + s + t + u + 180 = 540

p + q + r + s + t + u = 360

Answer D

Kudos [?]: 266 [1], given: 553

Expert Post
Target Test Prep Representative
User avatar
S
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1648

Kudos [?]: 848 [0], given: 3

Location: United States (CA)
Re: In ∆ ABC above, what is the sum of p + q + r + s + t + u ? [#permalink]

Show Tags

New post 11 Sep 2017, 10:54
Bunuel wrote:
Image
In ∆ ABC above, what is the sum of p + q + r + s + t + u ?

(A) 180
(B) 225
(C) 270
(D) 360
(E) 450


[Reveal] Spoiler:
Attachment:
2017-09-06_1535_002.png


We see that the sum of the interior angles is 180. Let’s say each angle within the triangle is 60 degrees. Then s + t = r + q = p + u = 180 - 60 = 120.

So, p + q + r + s + t + u = 360.

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 848 [0], given: 3

Re: In ∆ ABC above, what is the sum of p + q + r + s + t + u ?   [#permalink] 11 Sep 2017, 10:54
Display posts from previous: Sort by

In ∆ ABC above, what is the sum of p + q + r + s + t + u ?

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.