It is currently 18 Nov 2017, 16:42

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

The area of the right triangle ABC is 4 times greater than

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

Hide Tags

4 KUDOS received
Intern
Intern
avatar
Joined: 30 Apr 2010
Posts: 24

Kudos [?]: 18 [4], given: 8

Location: Texas
Schools: University of Texas - TEMBA
GMAT ToolKit User
The area of the right triangle ABC is 4 times greater than [#permalink]

Show Tags

New post 10 May 2010, 20:48
4
This post received
KUDOS
6
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

55% (00:55) correct 45% (01:00) wrong based on 276 sessions

HideShow timer Statistics

Image
The area of the right triangle ABC is 4 times greater than the area of the right triangle KLM. If the hypotenuse KL is 10 inches, what is the length of the hypotenuse AB?

(1) Angles ABC and KLM are each equal to 55 degrees.

(2) LM is 6 inches.

[Reveal] Spoiler:
I thought the answer was D because Statement 1 tells us that the triangles are similar and statement 2 tells us that KLM = a right 6-8-10 triangle. So the area of KLM is 24 which would make ABC’s area = 96 and which makes ABC = 12-16-20 triangle.


OPEN DISCUSSION OF THIS QUESTION IS HERE: the-area-of-the-right-triangle-abc-is-4-times-greater-than-127070.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 12 Jul 2013, 02:23, edited 1 time in total.
Edited the question and added the OA

Kudos [?]: 18 [4], given: 8

Expert Post
11 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132617 [11], given: 12326

Re: MGMAT DS Help [#permalink]

Show Tags

New post 11 May 2010, 04:34
11
This post received
KUDOS
Expert's post
5
This post was
BOOKMARKED
TXTDryFly wrote:
The area of the right triangle ABC is 4 times greater than the area of the right triangle KLM. If the hypotenuse KL is 10 inches, what is the length of the hypotenuse AB?

“INSERT A DRAWING OF TWO RIGHT TRIANGLES”

(1) Angles ABC and KLM are each equal to 55 degrees.

(2) LM is 6 inches.

“INSERT A DRAWING OF TWO RIGHT TRIANGLES”

[Reveal] Spoiler:
A

I thought the answer was D because Statement 1 tells us that the triangles are similar and statement 2 tells us that KLM = a right 6-8-10 triangle. So the area of KLM is 24 which would make ABC’s area = 96 and which makes ABC = 12-16-20 triangle.


The above solution is not right.

Properties of Similar Triangles:

• Corresponding angles are the same.
• Corresponding sides are all in the same proportion.
• It is only necessary to determine that two sets of angles are identical in order to conclude that two triangles are similar; the third set will be identical because all of the angles of a triangle always sum to 180º.
• In similar triangles, the sides of the triangles are in some proportion to one another. For example, a triangle with lengths 3, 4, and 5 has the same angle measures as a triangle with lengths 6, 8, and 10. The two triangles are similar, and all of the sides of the larger triangle are twice the size of the corresponding legs on the smaller triangle.
• 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: \(\frac{AREA}{area}=\frac{SIDE^2}{side^2}\).

For more on triangles please check Triangles chapter of the Math Book (link in my signature).

Back to original question:
The area of the right triangle ABC is 4 times greater than the area of the right triangle KLM. If the hypotenuse KL is 10 inches, what is the length of the hypotenuse AB?

(1) Angles ABC and KLM are each equal to 55 degrees --> ABC and KLM are similar triangles --> \(\frac{AREA_{ABC}}{area_{KLM}}=\frac{4}{1}\), so the sides are in ratio 2/1 --> hypotenuse KL=10 --> hypotenuse AB=2*10=20. Sufficient.

(2) LM is 6 inches --> KM=8 --> \(area_{KLM}=24\) --> \(AREA_{ABC}=96\). But just knowing the are of ABC is not enough to determine hypotenuse AB. For instance: legs of ABC can be 96 and 2 OR 48 and 4 and you'll get different values for hypotenuse. Not sufficient.

Answer: A.

Hope it helps.
_________________

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 [?]: 132617 [11], given: 12326

1 KUDOS received
Manager
Manager
avatar
Joined: 20 Apr 2010
Posts: 151

Kudos [?]: 19 [1], given: 16

Location: I N D I A
Re: MGMAT DS Help [#permalink]

Show Tags

New post 10 May 2010, 22:47
1
This post received
KUDOS
TXTDryFly wrote:
The area of the right triangle ABC is 4 times greater than the area of the right triangle KLM. If the hypotenuse KL is 10 inches, what is the length of the hypotenuse AB?

“INSERT A DRAWING OF TWO RIGHT TRIANGLES”

(1) Angles ABC and KLM are each equal to 55 degrees.

(2) LM is 6 inches.

“INSERT A DRAWING OF TWO RIGHT TRIANGLES”

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

[Reveal] Spoiler:
A





I thought the answer was D because Statement 1 tells us that the triangles are similar and statement 2 tells us that KLM = a right 6-8-10 triangle. So the area of KLM is 24 which would make ABC’s area = 96 and which makes ABC = 12-16-20 triangle.


First of all Triangles ABC & KLM are right angled at C & M resp as KL is hypot..
Area of ABC = 1/2 * AC * CB = 4 * Area of KLM = 4 * 1/2 * KM * ML

Therefore AC * CB = 4 KM * ML

1. Angles ABC and KLM = 55 deg
Therefore AC = KM as similar triangles and sides opp equal angles..

Above equation becomes CB = 4 ML or CB / ML = 4 / 1 which is further = AB / KL
as triangles are similar.. As KL is 10 , therefore AB = 40.. sufficient..

2. LM = 6 inches . Therefore KM = 8 by pythogorus theorem.. ( 10^2 - 6^2 )
But no option to find out hypot AB.. Therefore , insufficient..

Ans : A..

Kudos [?]: 19 [1], given: 16

Manager
Manager
avatar
Joined: 20 Apr 2010
Posts: 151

Kudos [?]: 19 [0], given: 16

Location: I N D I A
Re: MGMAT DS Help [#permalink]

Show Tags

New post 11 May 2010, 05:31
Thanks Bunuel for Correct n Nice explanation... +1...

Kudos [?]: 19 [0], given: 16

Manager
Manager
avatar
Joined: 16 Feb 2010
Posts: 179

Kudos [?]: 34 [0], given: 17

Re: MGMAT DS Help [#permalink]

Show Tags

New post 15 May 2010, 12:29
nice explanation bunuel....... kudos !!

Kudos [?]: 34 [0], given: 17

VP
VP
avatar
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1283

Kudos [?]: 286 [0], given: 10

Re: MGMAT DS Help [#permalink]

Show Tags

New post 04 May 2011, 02:01
a.(AB/ KL)^2 = Area (abc)/ Area (klm)

AB/KL = 2 Hence AB = 20 Thus sufficient.

b. km = 8 area ABC = 4 * area (klm) = 4*24 = 96.

thus ac *bc = 196 will give different values for AB. Hence not sufficient.

A.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Kudos [?]: 286 [0], given: 10

TOEFL Forum Moderator
avatar
Joined: 16 Nov 2010
Posts: 1602

Kudos [?]: 600 [0], given: 40

Location: United States (IN)
Concentration: Strategy, Technology
Reviews Badge
Re: MGMAT DS Help [#permalink]

Show Tags

New post 04 May 2011, 03:50
(1) ABC and KLM are similar

Area of ABC AB^2
----------- = ------
Area of KLM KL^2

Sufficient

(2)

KM can be found.

No information about ABC, so not sufficient.

Answer - A
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 600 [0], given: 40

Re: MGMAT DS Help   [#permalink] 04 May 2011, 03:50
Display posts from previous: Sort by

The area of the right triangle ABC is 4 times greater than

  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®.