January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. January 19, 2019 January 19, 2019 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
Author 
Message 
TAGS:

Hide Tags

Director
Joined: 01 May 2007
Posts: 771

Which of the following is a possible length for side AB of triangle AB
[#permalink]
Show Tags
Updated on: 16 Sep 2014, 23:40
Question Stats:
56% (01:12) correct 44% (01:11) wrong based on 828 sessions
HideShow timer Statistics
Which of the following is a possible length for side AB of triangle ABC if AC = 6 and BC = 9? I. 3 II. 9 √3 III. 13.5 (A) I only (B) II only (C) III only (D) II and III (E) I, II, and III
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by jimmyjamesdonkey on 21 May 2008, 08:25.
Last edited by Bunuel on 16 Sep 2014, 23:40, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.



Director
Joined: 10 Sep 2007
Posts: 883

Re: Which of the following is a possible length for side AB of triangle AB
[#permalink]
Show Tags
21 May 2008, 09:17
Should be II and III. Sum to two sides of triangle should be greater than third side. I is not possible because 3 + 6 = 9 which is not greater than 9 (length of third side). For Both II and III you add any two pairs and the sum of pairs is greater than the length of third side.



Manager
Joined: 27 Apr 2008
Posts: 110

Re: Which of the following is a possible length for side AB of triangle AB
[#permalink]
Show Tags
05 Jun 2008, 10:33
The answer is III.
It cant be II because 9*3^(0.5)>15, and the thirs side must be less than 15.



Manager
Joined: 21 Mar 2008
Posts: 209

Re: Which of the following is a possible length for side AB of triangle AB
[#permalink]
Show Tags
05 Jun 2008, 13:05
The third side of a triangle should be less than the sum of the other 2 sides and greater than the mod(difference of 2 sides)
so, x should lie between mod(yz)<x<y+z (96)<x<9+6 3<x<15
only value is 13.5



VP
Joined: 28 Dec 2005
Posts: 1444

Re: Which of the following is a possible length for side AB of triangle AB
[#permalink]
Show Tags
05 Jun 2008, 14:10
2 and 3 for me as well .... we need the third side to be between 3 and 15, i.e. 3<x<15
Both 2 and 3 fit this requirement



Manager
Joined: 21 Mar 2008
Posts: 209

Re: Which of the following is a possible length for side AB of triangle AB
[#permalink]
Show Tags
05 Jun 2008, 14:34
9(3^1/2) = 15.58>15 ...only 3.



VP
Joined: 28 Dec 2005
Posts: 1444

Re: Which of the following is a possible length for side AB of triangle AB
[#permalink]
Show Tags
05 Jun 2008, 15:01
yes, how silly of me



VP
Joined: 18 May 2008
Posts: 1100

Re: Which of the following is a possible length for side AB of triangle AB
[#permalink]
Show Tags
05 Jun 2008, 22:54
Rules for a triangle (1)Third side is always greater than the difference of two other sides (2) Third side is always less than the sum of two other sides Going by above rules only 13.5 satisfies the condition. jimmyjamesdonkey wrote: Which of the following is a possible length of the side AB of the triangle ABC if AC = 6 and BC = 9?
I. 3 II. 9(sqrt3) III. 13.5



Math Expert
Joined: 02 Sep 2009
Posts: 52161

Re: Which of the following is a possible length for side AB of triangle AB
[#permalink]
Show Tags
16 Sep 2014, 23:44



Intern
Joined: 23 May 2015
Posts: 5

Re: Which of the following is a possible length for side AB of triangle AB
[#permalink]
Show Tags
23 May 2015, 22:22
Its still not convincing for me to consider C as the correct answer because no where the question states AB is the third side or the longest side.. If for example we consider the AB = 3 (answer Choice A), The side of the triangle would be 3,6 and 9.. Now 9 becomes the third side and satisfies all the constraints of the third side.. The same is applicable for the rest two choices.. I feel answer in E.. Can someone explain whats the assumption am missing here ?



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13326
Location: United States (CA)

Re: Which of the following is a possible length for side AB of triangle AB
[#permalink]
Show Tags
23 May 2015, 22:31
Hi ragunandan, You have to be very careful with the logic here. If you have sides of 3, 6 and 9, then you DO NOT actually have a triangle  you have a line segment with a length of 9 "on top of" another line segment with a length of 9. You can use a ruler and physically draw it on a piece of paper if that will help you to visualize the issue. From a "math" standpoint, if 9 is the longest side, then the other two sides have to SUM to a value that is GREATER than 9 (otherwise you don't have a triangle) and a DIFFERENCE that is LESS than 9. GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



SVP
Joined: 26 Mar 2013
Posts: 1998

Re: Which of the following is a possible length for side AB of triangle AB
[#permalink]
Show Tags
23 May 2015, 22:57
EMPOWERgmatRichC wrote: Hi ragunandan,
You have to be very careful with the logic here.
If you have sides of 3, 6 and 9, then you DO NOT actually have a triangle  you have a line segment with a length of 9 "on top of" another line segment with a length of 9. You can use a ruler and physically draw it on a piece of paper if that will help you to visualize the issue.
From a "math" standpoint, if 9 is the longest side, then the other two sides have to SUM to a value that is GREATER than 9 (otherwise you don't have a triangle) and a DIFFERENCE that is LESS than 9.
GMAT assassins aren't born, they're made, Rich Hi Rich, Thanks for your nice explanations you provide but I did not understand 'you have a line segment with a length of 9 "on top of" another line segment with a length of 9. You can use a ruler and physically draw it on a piece of paper if that will help you to visualize the issue.' I tried to draw it but it is just incomplete triangle. is that the result you mean? Also I want to know if you cover those tactics and tricks for geometry in your courses. Thanks in advance for your help



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2438

Re: Which of the following is a possible length for side AB of triangle AB
[#permalink]
Show Tags
23 May 2015, 23:44
ragunandan wrote: Its still not convincing for me to consider C as the correct answer because no where the question states AB is the third side or the longest side.. If for example we consider the AB = 3 (answer Choice A), The side of the triangle would be 3,6 and 9.. Now 9 becomes the third side and satisfies all the constraints of the third side.. The same is applicable for the rest two choices.. I feel answer in E.. Can someone explain whats the assumption am missing here ? Hi ragunandan, Which of the following is a possible length for side AB of triangle ABC if AC = 6 and BC = 9?1. It's mentioned in the question statement that AB is the side of triangle ABC. Since we have been given two sides AC and BC, AB has to the third side. 2. Secondly since the question asks the possible length of side AB, we need to consider all possible values of AB i.e. AB can be the shortest side or the longest side of triangle ABC. 3. Lastly AB = 3 is not a legible value of the 3rd side of triangle ABC with the other two sides as AC = 6 and BC = 9. In a triangle the sum of two sides should be greater than the 3rd side. In this case AB + AC = 9 = BC. Similarly AB = 15√3 is also not a legible value. Among the given options AB = 13.5 is the only value for which we can form a triangle with the other two sides being 6 and 9. Let me know in case you still have any trouble in the explanation Regards Harsh
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2  Remainders1  Remainders2 Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line  Inequalities Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13326
Location: United States (CA)

Re: Which of the following is a possible length for side AB of triangle AB
[#permalink]
Show Tags
24 May 2015, 09:26
Hi Mo2men, You've discovered another variation on 'problem' of having sides of 3, 6 and 9  if you tried to form a triangle, then the 3 and the 6 would NOT touch, so you would NOT have a triangle. This all stems from a math rule called the Triangle Inequality Theorem; it's relatively rare on the GMAT (you might not even see it on Test Day; if you do see it, you'll probably see it just once). Thus, the concept is not a big pointgainer on the GMAT, so unless you're already scoring at a really high level in the Quant, you should be focused on other subjects. To answer your last question: yes, we do cover it (and a couple of variants of it) in the EMPOWERgmat Course. GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



Intern
Joined: 23 May 2015
Posts: 5

Re: Which of the following is a possible length for side AB of triangle AB
[#permalink]
Show Tags
04 Jun 2015, 19:50
Hi Rich, Thanks for the detailed explanation. #Helpful



Intern
Joined: 23 May 2015
Posts: 5

Re: Which of the following is a possible length for side AB of triangle AB
[#permalink]
Show Tags
04 Jun 2015, 19:53
Hi Harsh,Thanks for the explanation.. It was simpler and neat..



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2722
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: Which of the following is a possible length for side AB of triangle AB
[#permalink]
Show Tags
05 Jun 2015, 04:46
jimmyjamesdonkey wrote: Which of the following is a possible length for side AB of triangle ABC if AC = 6 and BC = 9?
I. 3 II. 9 √3 III. 13.5
(A) I only (B) II only (C) III only (D) II and III (E) I, II, and III POINT : The effort here is to make the rule of triangle more precise and less time consumingWe know the rule in different forms however we only need to know the rule in just one line i.e. SUM OF TWO SHORTER SIDES > LONGEST SIDE OF THE TRIANGLE
FOR THE TRIANGLE TO EXISTLet's apply this in this case For Finding the range of values of the Third side For minimum value of the third side AB, We must consider the given BC = 9 as the longest sideHence AB (Min) + AC > BC i.e. AB (Min) + 6 > 9 i.e. AB (Min) > 3For Maximum value of the third side AB, We must consider the given BC = 9 and Ac=6 as the two shorter sidesHence AC + BC > AB (Max.) i.e. 6 + 9 > AB (Max.) i.e. AB (Max.) < 15i.e. the range of AB becomes 3 < AB < 15I. 3 NOT ACCEPTABLEII. 9 √3  9x1.73 = 15.3 NOT ACCEPTABLEIII. 13.5 ACCEPTABLEAnswer: Option
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Director
Joined: 26 Oct 2016
Posts: 637
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE: Education (Education)

Re: Which of the following is a possible length for side AB of triangle AB
[#permalink]
Show Tags
30 Dec 2016, 02:15
The third side of a triangle must be less than the sum of the other two sides and greater than their difference (i.e. y  z < x < y + z). In this question: BC  AC < AB < BC + AC 9  6 < AB < 9 + 6 3 < AB < 15 Only 13.5 is in this range. 9sqrt3 is approximately equal to 9(1.7) or 15.3. The correct answer is C.
_________________
Thanks & Regards, Anaira Mitch



Director
Joined: 12 Nov 2016
Posts: 731
Location: United States
GPA: 2.66

Re: Which of the following is a possible length for side AB of triangle AB
[#permalink]
Show Tags
19 Apr 2017, 21:32
jimmyjamesdonkey wrote: Which of the following is a possible length for side AB of triangle ABC if AC = 6 and BC = 9?
I. 3 II. 9 √3 III. 13.5
(A) I only (B) II only (C) III only (D) II and III (E) I, II, and III We can approach this problem with triangle properties in mind; though, first it is important to note that the stem does not state that this triangle is a right triangle so the Pythagorean Theorem cannot be applied: (I) The sums of the two smaller sides of a triangle must be larger than the hypotenuse or greatest side "3" fails this test and is therefore not a viable option (II) If considered 9 √3 as 9(1.7) = 15.3 which is larger than 6 + 9 and thus not a viable option (III) 13.5 is smaller than the sum of 9 and 6 and therefore a viable option The correct answer is (C)



Intern
Joined: 24 May 2016
Posts: 19
Location: Germany
Concentration: International Business, General Management

Which of the following is a possible length for side AB of triangle AB
[#permalink]
Show Tags
03 Jun 2017, 04:38
As pointed out earlier, the question is based on the triangle inequality theorem: In that case AB has to be smaller than the sum of the two given sides 9+6=15 and be bigger than their difference 96=3 Thus you can write the inequality as follows: 3<AB<15. If you now test the options only Roman Numeral III fits in that range, so the answer is C.




Which of the following is a possible length for side AB of triangle AB &nbs
[#permalink]
03 Jun 2017, 04:38



Go to page
1 2
Next
[ 23 posts ]



