It is currently 21 Oct 2017, 20:15

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is

  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 [?]: 129181 [0], given: 12194

In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is [#permalink]

Show Tags

New post 23 Feb 2015, 03:28
Expert's post
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

67% (01:08) correct 33% (01:28) wrong based on 129 sessions

HideShow timer Statistics

Image
In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is the length of FG?

(1) Ttriangle FGH has 9 times the area of triangle ABC
(2) HF = 9


Kudos for a correct solution.

[Reveal] Spoiler:
Attachment:
gsdsq_img1.png
gsdsq_img1.png [ 9.4 KiB | Viewed 1664 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 [?]: 129181 [0], given: 12194

1 KUDOS received
Manager
Manager
avatar
Joined: 25 Mar 2014
Posts: 167

Kudos [?]: 58 [1], given: 48

Location: India
Concentration: Operations, Finance
GMAT Date: 05-10-2015
GPA: 3.51
WE: Programming (Computer Software)
In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is [#permalink]

Show Tags

New post 23 Feb 2015, 03:54
1
This post received
KUDOS
OA must be D.
Triangles above are similar triangle. Since corresponding angles are equal:
A = F = 50
B=G=20
C= H =110
option A is sufficient since ratio of area is given, we can find the ratio of sides from this.
option B also sufficient, since one side in the ratio is provided.
_________________

Please give Kudos to the post if you liked.


Last edited by aniteshgmat1101 on 24 Feb 2015, 21:42, edited 1 time in total.

Kudos [?]: 58 [1], given: 48

Intern
Intern
avatar
Joined: 18 Apr 2014
Posts: 15

Kudos [?]: 29 [0], given: 4

Concentration: Strategy, Finance
GMAT Date: 03-30-2015
WE: Web Development (Computer Software)
Re: In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is [#permalink]

Show Tags

New post 23 Feb 2015, 04:14
Answer must be B

As both are similar Trianges If we know HF we can get FG

Kudos [?]: 29 [0], given: 4

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

Kudos [?]: 129181 [0], given: 12194

Re: In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is [#permalink]

Show Tags

New post 02 Mar 2015, 06:53
Expert's post
1
This post was
BOOKMARKED
Bunuel wrote:
Image
In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is the length of FG?

(1) Ttriangle FGH has 9 times the area of triangle ABC
(2) HF = 9


Kudos for a correct solution.

[Reveal] Spoiler:
Attachment:
gsdsq_img1.png


MAGOOSH OFFICIAL SOLUTION:

The information given implies that ∠C = 110° and ∠G = 20°, because the sum of the three angles in each triangle must be 180°, by Euclid’s well-known theorem. Thus, the two triangles have all the same angles, but they are different sizes — they are similar. We know the length of AB, so all we need is the scale factor to determine length of the corresponding side FG.

Statement #1: this statement tells us the ratio of areas is 9 —- this is the square of the scale factor, so k = 3, and from this we can calculate the length of FG. Statement #1, alone and by itself, is sufficient.

Statement #2: this statement gives us a third side, so we can set up a proportion:

AC/AB = FH/FG.

Since we now know three of the terms of that proportion, we can solve for the fourth, FG. Statement #2, alone and by itself, is sufficient.

Answer = D
_________________

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 [?]: 129181 [0], given: 12194

Manager
Manager
avatar
B
Joined: 26 May 2013
Posts: 98

Kudos [?]: 30 [0], given: 30

Premium Member
Re: In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is [#permalink]

Show Tags

New post 02 Mar 2015, 08:05
Bunuel wrote:
Bunuel wrote:
Image
In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is the length of FG?

(1) Ttriangle FGH has 9 times the area of triangle ABC
(2) HF = 9


Kudos for a correct solution.

[Reveal] Spoiler:
Attachment:
gsdsq_img1.png


MAGOOSH OFFICIAL SOLUTION:

The information given implies that ∠C = 110° and ∠G = 20°, because the sum of the three angles in each triangle must be 180°, by Euclid’s well-known theorem. Thus, the two triangles have all the same angles, but they are different sizes — they are similar. We know the length of AB, so all we need is the scale factor to determine length of the corresponding side FG.

Statement #1: this statement tells us the ratio of areas is 9 —- this is the square of the scale factor, so k = 3, and from this we can calculate the length of FG. Statement #1, alone and by itself, is sufficient.

Statement #2: this statement gives us a third side, so we can set up a proportion:

AC/AB = FH/FG.

Since we now know three of the terms of that proportion, we can solve for the fourth, FG. Statement #2, alone and by itself, is sufficient.

Answer = D


How do we know that the factor is 3 based off the area being 9 times greater? I'm having trouble making this connection without picking random values for the height of the triangle. On that note, is it possible to solve for the height? Using GMAT tested properties.

Posted from my mobile device

Kudos [?]: 30 [0], given: 30

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

Kudos [?]: 129181 [0], given: 12194

Re: In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is [#permalink]

Show Tags

New post 02 Mar 2015, 08:10
ak1802 wrote:
Bunuel wrote:
Bunuel wrote:
Image
In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is the length of FG?

(1) Ttriangle FGH has 9 times the area of triangle ABC
(2) HF = 9


Kudos for a correct solution.

[Reveal] Spoiler:
Attachment:
gsdsq_img1.png


MAGOOSH OFFICIAL SOLUTION:

The information given implies that ∠C = 110° and ∠G = 20°, because the sum of the three angles in each triangle must be 180°, by Euclid’s well-known theorem. Thus, the two triangles have all the same angles, but they are different sizes — they are similar. We know the length of AB, so all we need is the scale factor to determine length of the corresponding side FG.

Statement #1: this statement tells us the ratio of areas is 9 —- this is the square of the scale factor, so k = 3, and from this we can calculate the length of FG. Statement #1, alone and by itself, is sufficient.

Statement #2: this statement gives us a third side, so we can set up a proportion:

AC/AB = FH/FG.

Since we now know three of the terms of that proportion, we can solve for the fourth, FG. Statement #2, alone and by itself, is sufficient.

Answer = D


How do we know that the factor is 3 based off the area being 9 times greater? I'm having trouble making this connection without picking random values for the height of the triangle. On that note, is it possible to solve for the height? Using GMAT tested properties.

Posted from my mobile device


If two similar triangles have sides in the ratio \(\frac{x}{y}\), then their areas are in the ratio \(\frac{x^2}{y^2}\).

OR in another way: in two similar triangles, the ratio of their areas is the square of the ratio of their sides: \(\frac{AREA}{area}=\frac{SIDE^2}{side^2}\).
_________________

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 [?]: 129181 [0], given: 12194

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16589

Kudos [?]: 273 [0], given: 0

Premium Member
Re: In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is [#permalink]

Show Tags

New post 17 Sep 2017, 03:36
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 273 [0], given: 0

Re: In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is   [#permalink] 17 Sep 2017, 03:36
Display posts from previous: Sort by

In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is

  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®.