November 18, 2018 November 18, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. November 18th, 7 AM PST November 20, 2018 November 20, 2018 09:00 AM PST 10:00 AM PST The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 30 Aug 2007
Posts: 62

If k and t are integers and k^2 – t^2 is an odd integer
[#permalink]
Show Tags
02 Oct 2007, 12:27
Question Stats:
75% (01:45) correct 25% (01:53) wrong based on 570 sessions
HideShow timer Statistics
If k and t are integers and k^2 – t^2 is an odd integer, which of the following must be an even integer? I. k + t + 2 II. k^2 + 2kt + t^2 III. k^2 + t^2 A. None B. I only C. II only D. III only E. I, II, and III
Official Answer and Stats are available only to registered users. Register/ Login.



Director
Joined: 08 Jun 2007
Posts: 552

Re: GMAT Prep 2: PS Q25
[#permalink]
Show Tags
02 Oct 2007, 12:33
avenger wrote: Q25) If k and t are integers and k^2 – t^2 is an odd integer, which of the following must be an even integer?
I. k + t + 2 II. k^2 + 2kt + t^2 III. k^2 + t^2
(a) None (b) I only (c) II only (d) III only (e) I, II, and III
For k^2 – t^2 to be odd , I guess either k or t must be odd .
So lets assume k= even t = odd
I. k + t + 2
even + odd + 2 = even + odd = odd
II. k^2 + 2kt + t^2
even + even + odd = even + odd = odd
III. k^2 + t^2
even + odd = odd .
So I guess NONE



Senior Manager
Joined: 18 Jul 2006
Posts: 486

none..i.e E
take any example.. 3 & 4 and plug it in each option.



Manager
Joined: 30 Aug 2007
Posts: 62

OA is A i.e. (None).
Thanks



Manager
Joined: 21 Feb 2012
Posts: 78
Location: India
Concentration: Finance, General Management
GPA: 3.8
WE: Information Technology (Computer Software)

Re: Q25) If k and t are integers and k^2 t^2 is an odd
[#permalink]
Show Tags
07 May 2012, 07:42
avenger wrote: Q25) If k and t are integers and k^2 – t^2 is an odd integer, which of the following must be an even integer?
I. k + t + 2 II. k^2 + 2kt + t^2 III. k^2 + t^2
(a) None (b) I only (c) II only (d) III only (e) I, II, and III I have a doubt regarding option(III) of the stem,below is my explanation: Given : K^2t^2> odd it means (k+t)(kt) both are odd. take option 3 we have to chek whether k^2+t^2 is odd or even. k^2+t^2=(k+t)^2(kt)^2 = k^2+t^2+2ktk^2t^2+2kt =4kt Here as 4 is an even number, and any odd number multiplied by an even results in an even number. Please let me know whether this is correct as i had interpreted or not. and provide a suitable explanation.



Math Expert
Joined: 02 Sep 2009
Posts: 50621

Re: Q25) If k and t are integers and k^2 t^2 is an odd
[#permalink]
Show Tags
07 May 2012, 08:23
piyushksharma wrote: avenger wrote: Q25) If k and t are integers and k^2 – t^2 is an odd integer, which of the following must be an even integer?
I. k + t + 2 II. k^2 + 2kt + t^2 III. k^2 + t^2
(a) None (b) I only (c) II only (d) III only (e) I, II, and III I have a doubt regarding option(III) of the stem,below is my explanation: Given : K^2t^2> odd it means (k+t)(kt) both are odd. take option 3 we have to chek whether k^2+t^2 is odd or even. k^2+t^2=(k+t)^2(kt)^2 = k^2+t^2+2ktk^2t^2+2kt =4ktHere as 4 is an even number, and any odd number multiplied by an even results in an even number. Please let me know whether this is correct as i had interpreted or not. and provide a suitable explanation. The red part is not correct. k^2+t^2 does not equal to 4kt. If k and t are integers and k^2 – t^2 is an odd integer, which of the following must be an even integer?I. k + t + 2 II. k^2 + 2kt + t^2 III. k^2 + t^2 A. None B. I only C. II only D. III only E. I, II, and III k^2–t^2 is an odd integer means that either k is even and t is odd or k is odd and t is even. Check all options: I. k + t + 2 > even+odd+even=odd or odd+even+even=odd. Discard; II. k^2 + 2kt + t^2 > even+even+odd=odd or odd+even+even=odd. Discard; III. k^2 + t^2 > even+odd=odd or odd+even=odd. Discard. Answer: A.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 21 Feb 2012
Posts: 78
Location: India
Concentration: Finance, General Management
GPA: 3.8
WE: Information Technology (Computer Software)

Re: Q25) If k and t are integers and k^2 t^2 is an odd
[#permalink]
Show Tags
07 May 2012, 09:54
Bunuel wrote: piyushksharma wrote: avenger wrote: Q25) If k and t are integers and k^2 – t^2 is an odd integer, which of the following must be an even integer?
I. k + t + 2 II. k^2 + 2kt + t^2 III. k^2 + t^2
(a) None (b) I only (c) II only (d) III only (e) I, II, and III I have a doubt regarding option(III) of the stem,below is my explanation: Given : K^2t^2> odd it means (k+t)(kt) both are odd. take option 3 we have to chek whether k^2+t^2 is odd or even. k^2+t^2=(k+t)^2(kt)^2 = k^2+t^2+2ktk^2t^2+2kt =4ktHere as 4 is an even number, and any odd number multiplied by an even results in an even number. Please let me know whether this is correct as i had interpreted or not. and provide a suitable explanation. The red part is not correct. k^2+t^2 does not equal to 4kt. If k and t are integers and k^2 – t^2 is an odd integer, which of the following must be an even integer?I. k + t + 2 II. k^2 + 2kt + t^2 III. k^2 + t^2 A. None B. I only C. II only D. III only E. I, II, and III k^2–t^2 is an odd integer means that either k is even and t is odd or k is odd and t is even. Check all options: I. k + t + 2 > even+odd+even=odd or odd+even+even=odd. Discard; II. k^2 + 2kt + t^2 > even+even+odd=odd or odd+even+even=odd. Discard; III. k^2 + t^2 > even+odd=odd or odd+even=odd. Discard. Answer: A. Thanks, i misinterpreted the option (III),rather i solved it for k^2  t^2.



Intern
Joined: 14 Aug 2012
Posts: 10

Re: If k and t are integers and k^2 – t^2 is an odd integer
[#permalink]
Show Tags
27 Mar 2013, 03:51
i have chosen to solve using fact that since k^2  t^2 is odd, both K+T and KT should be odd. Making this choice, i get that both options 1 and 2 are odd 1) k+t+2 means odd number + 2 = odd number 2) (k+t)^2 means (odd)^2 = odd number 3) k^2 + t^2 = ((k+t)^2 + (kt)^2)/2 => (odd + odd)/2 = even
so, result is (1) and (2) are odd while (3) is even, since this combination is not part of any answer, chose NONE.
Is this approach correct?



Math Expert
Joined: 02 Sep 2009
Posts: 50621

Re: If k and t are integers and k^2 – t^2 is an odd integer
[#permalink]
Show Tags
27 Mar 2013, 05:36



Intern
Joined: 22 Jan 2010
Posts: 24
Location: India
Concentration: Finance, Technology
GPA: 3.5
WE: Programming (Telecommunications)

Re: If k and t are integers and k^2 – t^2 is an odd integer
[#permalink]
Show Tags
27 Mar 2013, 05:50
If k and t are integers and k^2 – t^2 is an odd integer, which of the following must be an even integer? I. k + t + 2 II. k^2 + 2kt + t^2 III. k^2 + t^2 A. None B. I only C. II only D. III only E. I, II, and III k^2 t^2 = odd so,if k is even,t will be odd. I. k+t+2 = even+odd+2 = odd II. k^2 + 2kt+t^2 = even + even + odd = odd III. k^2 + t^2 = even + odd = odd Hence answer will be option A. _________________________________________ Press KUDOS if you like my post. :
_________________
Please press +1 KUDOS if you like my post.



Intern
Status: Currently Preparing the GMAT
Joined: 15 Feb 2013
Posts: 29
Location: United States
GPA: 3.7
WE: Analyst (Consulting)

Re: If k and t are integers and k^2 – t^2 is an odd integer
[#permalink]
Show Tags
27 Mar 2013, 07:28
This problem mobilizes addition, substraction and multiplication rules of odd and even integers so knowing your rules will be the key to helping you solve this correctly. First of all, \(k^2  t^2\) can be rewritten as \((kt)*(k+t)\) If you're unsure about the notation, just develop \((kt)*(k+t)\). Now, assuming that \(k^2  t^2\) = \((kt)*(k+t)\) is odd, then according to the following rule : odd * odd = odd (1) We'll get \(kt\) is odd and \(k+t\) is odd, which is extremely helpful since, if you notice the answer choices, all of them revolve around \(k+t\). So let's go through them one by one : I. \(k+t+2\). Using parenthesis to isolate \(k+t\), we get \((k+t)+2\) which is a sum involving an odd number and an even number. So, according to the following rule : odd + even = odd (2) Which means that \(k+t+2\) is odd. So answer I is not possible. (Since we're looking for an even result) II. \(k^2 + 2kt + t^2\) Now this answer choice may seem intimidating, but it actually isn't. Since \(k^2 + 2kt + t^2\) is equal to \((k+t)^2\). And since \(k+t\) is odd, then its square will be odd as well (rule 1). So answer II is also not possible. III.\(k^2 + t^2\) Once again, this answer choice may seem intimidating since you have no data on k nor t. But, looking at answer choice II., \(k^2+t^2\) is actually equal to \((k+t)^2  2kt\). This is a difference between an odd number \((k+t)^2\) and an even number \(2kt\), so according to rule 2, the result will be odd. So answer III. is also not possible. As such, the only correct answer to this question is answer A. Hope that helped.



Current Student
Joined: 31 Mar 2013
Posts: 66
Location: India
GPA: 3.02

Re: Q25) If k and t are integers and k^2 t^2 is an odd
[#permalink]
Show Tags
04 Sep 2013, 03:18
Bunuel wrote: piyushksharma wrote: avenger wrote: Q25) If k and t are integers and k^2 – t^2 is an odd integer, which of the following must be an even integer?
I. k + t + 2 II. k^2 + 2kt + t^2 III. k^2 + t^2
(a) None (b) I only (c) II only (d) III only (e) I, II, and III I have a doubt regarding option(III) of the stem,below is my explanation: Given : K^2t^2> odd it means (k+t)(kt) both are odd. take option 3 we have to chek whether k^2+t^2 is odd or even. k^2+t^2=(k+t)^2(kt)^2 = k^2+t^2+2ktk^2t^2+2kt =4ktHere as 4 is an even number, and any odd number multiplied by an even results in an even number. Please let me know whether this is correct as i had interpreted or not. and provide a suitable explanation. The red part is not correct. k^2+t^2 does not equal to 4kt. If k and t are integers and k^2 – t^2 is an odd integer, which of the following must be an even integer?I. k + t + 2 II. k^2 + 2kt + t^2 III. k^2 + t^2 A. None B. I only C. II only D. III only E. I, II, and III k^2–t^2 is an odd integer means that either k is even and t is odd or k is odd and t is even. Check all options: I. k + t + 2 > even+odd+even=odd or odd+even+even=odd. Discard; II. k^2 + 2kt + t^2 > even+even+odd=odd or odd+even+even=odd. Discard; III. k^2 + t^2 > even+odd=odd or odd+even=odd. Discard. Answer: A. Hi Bunuel, You've mentioned that if k^2–t^2 is an odd integer means that either k is even and t is odd or k is odd and t is even. Isn't a 3rd case also possible where K is odd and T is 0?



Math Expert
Joined: 02 Sep 2009
Posts: 50621

Re: Q25) If k and t are integers and k^2 t^2 is an odd
[#permalink]
Show Tags
04 Sep 2013, 03:26
emailmkarthik wrote: Bunuel wrote: piyushksharma wrote: If k and t are integers and k^2 – t^2 is an odd integer, which of the following must be an even integer?
I. k + t + 2 II. k^2 + 2kt + t^2 III. k^2 + t^2
(a) None (b) I only (c) II only (d) III only (e) I, II, and III
I have a doubt regarding option(III) of the stem,below is my explanation: Given : K^2t^2> odd it means (k+t)(kt) both are odd. take option 3 we have to chek whether k^2+t^2 is odd or even. k^2+t^2=(k+t)^2(kt)^2 = k^2+t^2+2ktk^2t^2+2kt =4kt Here as 4 is an even number, and any odd number multiplied by an even results in an even number.
Please let me know whether this is correct as i had interpreted or not. and provide a suitable explanation. The red part is not correct. k^2+t^2 does not equal to 4kt. If k and t are integers and k^2 – t^2 is an odd integer, which of the following must be an even integer?I. k + t + 2 II. k^2 + 2kt + t^2 III. k^2 + t^2 A. None B. I only C. II only D. III only E. I, II, and III k^2–t^2 is an odd integer means that either k is even and t is odd or k is odd and t is even. Check all options: I. k + t + 2 > even+odd+even=odd or odd+even+even=odd. Discard; II. k^2 + 2kt + t^2 > even+even+odd=odd or odd+even+even=odd. Discard; III. k^2 + t^2 > even+odd=odd or odd+even=odd. Discard. Answer: A. Hi Bunuel, You've mentioned that if k^2–t^2 is an odd integer means that either k is even and t is odd or k is odd and t is even. Isn't a 3rd case also possible where K is odd and T is 0? Well, since 0 is an even number, then this scenario falls into the case when k=odd and t=even.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Current Student
Joined: 31 Mar 2013
Posts: 66
Location: India
GPA: 3.02

Re: If k and t are integers and k^2 – t^2 is an odd integer
[#permalink]
Show Tags
07 Sep 2013, 23:50
Thank you, Bunuel.



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4212
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: If k and t are integers and k^2 – t^2 is an odd integer
[#permalink]
Show Tags
21 Oct 2016, 10:29
avenger wrote: If k and t are integers and k^2 – t^2 is an odd integer, which of the following must be an even integer?
I. k + t + 2 II. k^2 + 2kt + t^2 III. k^2 + t^2
A. None B. I only C. II only D. III only E. I, II, and III Plug in some no's and check k = 7 , t = 4 I. k + t + 2 = 7 + 4 + 2 = 13 ( Odd ) II. k^2 + 2kt + t^2 = 7^2 + 2*7*4 + 4^2 = 121 ( Odd ) III. k^2 + t^2 = 7^2 + 4^2 = 65 ( Odd ) k = 6 , t = 3 I. k + t + 2 = 6 + 3 + 2 = 11 ( Odd ) II. k^2 + 2kt + t^2 = 6^2 + 2*6*3 + 3^2 = 81 ( Odd ) III. k^2 + t^2 = 6^2 + 3^2 = 45 ( Odd ) Check in all the cases the answer will be ODD, hence we will not get even number.. Answer will be (A) None...
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club  Rules for Posting in QA forum  Writing Mathematical Formulas Rules for Posting in VA forum  Request Expert's Reply ( VA Forum Only )



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2203

If k and t are integers and k^2 – t^2 is an odd integer
[#permalink]
Show Tags
07 Nov 2016, 04:06
avenger wrote: If k and t are integers and k^2 – t^2 is an odd integer, which of the following must be an even integer?
I. k + t + 2 II. k^2 + 2kt + t^2 III. k^2 + t^2
A. None B. I only C. II only D. III only E. I, II, and III Here is a methodical approach to solve this question: Given Info: \(k^2 – t^2\) is odd. Inferences: \(k^2 – t^2\) can be written as \((k – t)*(k + t)\) Since the product is odd, both \((k – t)\) and \((k + t)\) must be odd. So, \((k – t)\) is odd ……. (1) \((k + t)\) is odd …… (2) The above also implies that exactly one of {\(k\), \(t\)} is odd and the other is even …… (3) Approach: We’ll use the above inferences to identify the evenodd nature of each of the given expressions. Working Out: (I) \(k + t + 2\)We already determined that \((k + t)\)is odd. So, adding an even number (\(2\)) to \((k + t)\) won’t change its evenodd nature. Think: \(3\)is odd. \(3+2 = 5\) is also odd.(II) \(k^2 + 2kt + t^2\) This is simply \((k + t)^2\) Since \((k + t)\) is odd, its square is also odd. Think: \(3\) is odd. \(3^2 = 9\) is odd). (You can also look at this case as: product of two odd integers is always odd). (III) \(k^2 + t^2\) \(k^2 + t^2\) will have the same evenodd nature as\(k^2 – t^2\). So, \(k^2 + t^2\) is also odd. Think: \((a + b)\) will have the same evenodd nature as\((a – b)\). Eg: \(52 = 3\) (odd) \(5 + 2 = 7\) (odd)Since none of the given expressions are even, the correct answer is option A. Hope this helps. Cheers, Krishna
_________________
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 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



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830

Re: If k and t are integers and k^2 – t^2 is an odd integer
[#permalink]
Show Tags
03 Sep 2018, 18:00
avenger wrote: If k and t are integers and k^2 – t^2 is an odd integer, which of the following must be an even integer?
I. k + t + 2 II. k^2 + 2kt + t^2 III. k^2 + t^2
A. None B. I only C. II only D. III only E. I, II, and III We can see that k^2  t^2 = odd or (k  t)(k + t) = odd. Thus, (k  t) is odd, and (k + t) is odd. Let’s consider each Roman numeral. I. Since(k + t) is odd, k + t + 2 = odd + 2 = odd. II. Since k^2 + 2kt + t^2 = (k + t)^2 = (odd)^2 = odd, k^2 + 2kt + t^2 is odd. III. Since k^2 – t^2 is odd, k^2 + t^2 is also odd. Answer: A
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: If k and t are integers and k^2 – t^2 is an odd integer &nbs
[#permalink]
03 Sep 2018, 18:00






