• NEW! FREE Beat The GMAT Quizzes  Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## (35^2 - 1)/k is an integer ##### This topic has 5 expert replies and 6 member replies ### GMAT/MBA Expert If k is an integer, and (35^2 - 1)/k is an integer, then k could be each of the following, EXCEPT (A) 8 (B) 9 (C) 12 (D) 16 (E) 17 Source: http://readyforgmat.com _________________ The mind is everything. What you think you become. –Lord Buddha Sanjeev K Saxena Quantitative Instructor The Princeton Review - Manya Abroad Lucknow-226001 www.manyagroup.com Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 11 Apr 2010 Posted: 1179 messages Followed by: 88 members Upvotes: 447 (35^2 - 1)/k = (35 - 1)(35 + 1)/k = (34)(36)/k We can clearly see that if k = 17, 12, 9 or 8, then (35^2 - 1)/k will give an integer value. But if k = 16, then 35^2 - 1)/k will not give an integer value. The correct answer is (D). _________________ Rahul Lakhani Quant Expert Gurome, Inc. https://www.GuroMe.com On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits 1-800-566-4043 (USA) +91-99201 32411 (India) ### GMAT/MBA Expert GMAT Instructor Joined 03 Jul 2008 Posted: 1031 messages Followed by: 253 members Upvotes: 716 GMAT Score: 750 Hey everyone, Rahul's solution above is terrific, but let me point out a few strategic things here. 1) When you see that (35^2 - 1) setup, or any version of (x^2 - y^2), you HAVE TO think about the Difference of Squares rule: x^2 - y^2 = (x+y)(x-y). That rule sets up quite a bit for you - namely, it allows you to turn ugly subtraction into multiplication, which should allow you to factor. 2) Pursuant to the above, when you see addition/subtraction of exponents, there's an overwhelming likelihood that you'll need to factor somehow to turn that into multiplication (broken record for those of you reading my posts today, but I can't stress this enough). Difference of Squares is a great tool to have in your arsenal for that. 3) You may find it helpful to break down the resulting divisibility problem (34*36/k) into prime factors: 2*2*2*3*3*17 is divisible by k. Since the answer choices are: 8 = 2*2*2 (divisible) 9 = 3*3 (divisible) 12 = 2*2*3 (divisible) 16 = 2*2*2*2 (we're one 2 short, so this is NOT divisible) 17 = 17 (divisible) You can attack these systematically. When divisibility is in question, prime factorization helps you to have a system for checking divisibility without needing to treat each division as individual. _________________ Brian Galvin GMAT Instructor Director of Academic Programs Veritas Prep Looking for GMAT practice questions? Try out the Veritas Prep Question Bank. Learn More. Last edited by Brian@VeritasPrep on Tue Sep 14, 2010 11:59 am; edited 1 time in total Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! Master | Next Rank: 500 Posts Joined 31 Mar 2010 Posted: 261 messages Followed by: 3 members Upvotes: 11 Test Date: 23rd April, 2011 Target GMAT Score: 700 GMAT Score: NA Brian@VeritasPrep wrote: Hey everyone, Rahul's solution above is terrific, but let me point out a few strategic things here. 1) When you see that (35^2 - 1) setup, or any version of (x^2 - y^2), you HAVE TO think about the Difference of Squares rule: x^2 - y^2 = (x+y)(x-y). That rule sets up quite a bit for you - namely, it allows you to turn ugly subtraction into multiplication, which should allow you to factor. 2) Pursuant to the above, when you see addition/subtraction of exponents, there's an overwhelming likelihood that you'll need to factor somehow to turn that into multiplication (broken record for those of you reading my posts today, but I can't stress this enough). Difference of Squares is a great tool to have in your arsenal for that. 3) You may find it helpful to break down the resulting divisibility problem (34*36/k) into prime factors: 2*2*2*3*3*17 is divisible by k. Since the answer choices are: 8 = 2*2*2 (divisible) 9 = 3*3*3 (divisible) 12 = 2*2*3 (divisible) 16 = 2*2*2*2 (we're one 2 short, so this is NOT divisible) 17 = 17 (divisible) You can attack these systematically. When divisibility is in question, prime factorization helps you to have a system for checking divisibility without needing to treat each division as individual. Thx Brian not only for solving the problems but also for giving us deeper insights. Master | Next Rank: 500 Posts Joined 31 Mar 2010 Posted: 261 messages Followed by: 3 members Upvotes: 11 Test Date: 23rd April, 2011 Target GMAT Score: 700 GMAT Score: NA [quote="Brian@VeritasPrep"]Hey everyone, Rahul's solution above is terrific, but let me point out a few strategic things here. 1) When you see that (35^2 - 1) setup, or any version of (x^2 - y^2), you HAVE TO think about the Difference of Squares rule: x^2 - y^2 = (x+y)(x-y). That rule sets up quite a bit for you - namely, it allows you to turn ugly subtraction into multiplication, which should allow you to factor. 2) Pursuant to the above, when you see addition/subtraction of exponents, there's an overwhelming likelihood that you'll need to factor somehow to turn that into multiplication (broken record for those of you reading my posts today, but I can't stress this enough). Difference of Squares is a great tool to have in your arsenal for that. 3) You may find it helpful to break down the resulting divisibility problem (34*36/k) into prime factors: 2*2*2*3*3*17 is divisible by k. Since the answer choices are: 8 = 2*2*2 (divisible) 9 = 3*3*3 (divisible) 12 = 2*2*3 (divisible) 16 = 2*2*2*2 (we're one 2 short, so this is NOT divisible) 17 = 17 (divisible) You can attack these systematically. When divisibility is in question, prime factorization helps you to have a system for checking divisibility without needing to treat each division as individual. how did u write 9= 3*3*3 above. ### GMAT/MBA Expert GMAT Instructor Joined 03 Jul 2008 Posted: 1031 messages Followed by: 253 members Upvotes: 716 GMAT Score: 750 [quote="ankur.agrawal"] Brian@VeritasPrep wrote: Hey everyone, Rahul's solution above is terrific, but let me point out a few strategic things here. 1) When you see that (35^2 - 1) setup, or any version of (x^2 - y^2), you HAVE TO think about the Difference of Squares rule: x^2 - y^2 = (x+y)(x-y). That rule sets up quite a bit for you - namely, it allows you to turn ugly subtraction into multiplication, which should allow you to factor. 2) Pursuant to the above, when you see addition/subtraction of exponents, there's an overwhelming likelihood that you'll need to factor somehow to turn that into multiplication (broken record for those of you reading my posts today, but I can't stress this enough). Difference of Squares is a great tool to have in your arsenal for that. 3) You may find it helpful to break down the resulting divisibility problem (34*36/k) into prime factors: 2*2*2*3*3*17 is divisible by k. Since the answer choices are: 8 = 2*2*2 (divisible) 9 = 3*3*3 (divisible) 12 = 2*2*3 (divisible) 16 = 2*2*2*2 (we're one 2 short, so this is NOT divisible) 17 = 17 (divisible) You can attack these systematically. When divisibility is in question, prime factorization helps you to have a system for checking divisibility without needing to treat each division as individual. how did u write 9= 3*3*3 above. Typo...the 3 key must have stuck! Sorry about that...just fixed it. _________________ Brian Galvin GMAT Instructor Director of Academic Programs Veritas Prep Looking for GMAT practice questions? Try out the Veritas Prep Question Bank. Learn More. Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! Senior | Next Rank: 100 Posts Joined 05 Sep 2010 Posted: 74 messages Upvotes: 3 {[(35^2) -1]/k}=integer integer= (35-1)*(35+1)/k =1224/k only when you divide by 16 the divisor is not an integer so ans D ### GMAT/MBA Expert GMAT Instructor Joined 21 Jan 2009 Posted: 3650 messages Followed by: 82 members Upvotes: 267 GMAT Score: 760 klmehta03 wrote: {[(35^2) -1]/k}=integer integer= (35-1)*(35+1)/k =1224/k only when you divide by 16 the divisor is not an integer so ans D very laborious _________________ The mind is everything. What you think you become. –Lord Buddha Sanjeev K Saxena Quantitative Instructor The Princeton Review - Manya Abroad Lucknow-226001 www.manyagroup.com Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. Master | Next Rank: 500 Posts Joined 23 Nov 2010 Posted: 123 messages Followed by: 4 members Upvotes: 5 Target GMAT Score: 800 Brian@VeritasPrep wrote: Hey everyone, Rahul's solution above is terrific, but let me point out a few strategic things here. 1) When you see that (35^2 - 1) setup, or any version of (x^2 - y^2), you HAVE TO think about the Difference of Squares rule: x^2 - y^2 = (x+y)(x-y). That rule sets up quite a bit for you - namely, it allows you to turn ugly subtraction into multiplication, which should allow you to factor. 2) Pursuant to the above, when you see addition/subtraction of exponents, there's an overwhelming likelihood that you'll need to factor somehow to turn that into multiplication (broken record for those of you reading my posts today, but I can't stress this enough). Difference of Squares is a great tool to have in your arsenal for that. 3) You may find it helpful to break down the resulting divisibility problem (34*36/k) into prime factors: 2*2*2*3*3*17 is divisible by k. Since the answer choices are: 8 = 2*2*2 (divisible) 9 = 3*3 (divisible) 12 = 2*2*3 (divisible) 16 = 2*2*2*2 (we're one 2 short, so this is NOT divisible) 17 = 17 (divisible) You can attack these systematically. When divisibility is in question, prime factorization helps you to have a system for checking divisibility without needing to treat each division as individual. Nice! Thanks Brian! You mentioned Difference of Square Rule, if there is a "+" sign, can we still break it up as (x^2 + y^2)? In the OG-12 Maths review is this rule mentioned...I don't remember it seeing in the book nor in the Gmat Prep! Can you share/mention more of such essential concepts which we will definitely need to apply? This will be a HUGE help! Thanks! ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 Another (more theoretical) approach: (It is what is "behind" Brian´s (3) item, watch out!) When you are told that a and b are integers such that a/b is an integer (b implicitly non-zero, for sure), that means that b is a divisor of a. Therefore, from the question stem we know that k must be a divisor of 35^2-1 = (34)(36) = 2^3*3^2*17. (A) 2^3 is a divisor of the "red thing", for sure. (B) 3^2 also (C) 2^2*3 also (D) 2^4 is NOT, because we have only three 2´s and we "would need" four 2´s. PUFF! Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br Junior | Next Rank: 30 Posts Joined 22 Jul 2011 Posted: 25 messages Upvotes: 1 i don't think that we can "clearly" see that if k = 17, 12, 9, or 8, then (35^2-1)/k will give an integer value. for (34)(36)/k, i think we can clearly see that 17, 12, and 9 all result in integer values (they are factors of either 34 or 36). However, neither 8 nor 16 are factors of 34 or 36, and the math required to multiply 34 by 36 then divide out 8 and 16 would be too time consuming (we could factor a 2 out, leaving 17*72, but that isn't necessarily clear on first glance either). What we are left with is both options A (8) and D (16). Because 8 is a factor of 16, if the number is divisible by 16, then it must also be divisible by 8, however, the converse is not true (a number divisible by 8 is not necessarily divisible by 16). Therefore, 16 must be the number which results in a non-integer result. Rahul@gurome wrote: (35^2 - 1)/k = (35 - 1)(35 + 1)/k = (34)(36)/k We can clearly see that if k = 17, 12, 9 or 8, then (35^2 - 1)/k will give an integer value. But if k = 16, then 35^2 - 1)/k will not give an integer value. The correct answer is (D). Newbie | Next Rank: 10 Posts Joined 18 Sep 2013 Posted: 1 messages D)16 • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for \$0

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

### Top First Responders*

1 Ian Stewart 41 first replies
2 Brent@GMATPrepNow 36 first replies
3 Scott@TargetTestPrep 33 first replies
4 Jay@ManhattanReview 30 first replies
5 GMATGuruNY 23 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

159 posts
2 Max@Math Revolution

Math Revolution

91 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

56 posts
4 Ian Stewart

GMATiX Teacher

50 posts
5 GMATGuruNY

The Princeton Review Teacher

35 posts
See More Top Beat The GMAT Experts