Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 16 Oct 2010
Posts: 86
Location: United States
Concentration: Finance, Entrepreneurship
WE: Information Technology (Investment Banking)

If x is a positive number, is x an even integer? [#permalink]
Show Tags
26 Aug 2012, 05:24
4
This post received KUDOS
16
This post was BOOKMARKED
Question Stats:
39% (00:38) correct 61% (00:24) wrong based on 500 sessions
HideShow timer Statistics
If x is a positive number, is x an even integer? (1) 3x is an even integer. (2) 5x is an even integer.
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 43894

Re: If x is a positive number, is x an even integer? [#permalink]
Show Tags
26 Aug 2012, 05:42
7
This post received KUDOS
Expert's post
10
This post was BOOKMARKED



Director
Joined: 22 Mar 2011
Posts: 608
WE: Science (Education)

Re: If x is a positive number, is x an even integer? [#permalink]
Show Tags
26 Aug 2012, 08:13
2
This post received KUDOS
2
This post was BOOKMARKED
syog wrote: If x is a positive number, is x an even integer? (1) 3x is an even integer. (2) 5x is an even integer. Neither (1) nor (2) alone is sufficient. (1) and (2) together: From (1) \(3x=2k,\) where \(k\) is a positive integer. From (2) \(5x=2m,\) where \(m\) is some positive integer. Necessarily \(\frac{2k}{3}=\frac{2m}{5}\) from which \(5k=3m.\) \(k\) and \(m\) being integers, necessarily \(k\) must be a multiple of 3 (because 5 is not divisible by 3), so \(k=3a\) for some positive integer \(a.\) It follows that \(x=\frac{2k}{3}=2a\) so \(x\) is even. Sufficient. Answer C
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Manager
Joined: 28 Feb 2012
Posts: 114
Concentration: Strategy, International Business
GPA: 3.9
WE: Marketing (Other)

Re: If x is a positive number, is x an even integer? [#permalink]
Show Tags
30 Aug 2012, 03:53
Bunuel wrote: If x is a positive number, is x an even integer?
Notice that we are not told that x is an integer. (1) 3x is an even integer. x could be ANY even number or some fraction (for example 2/3), so this statement is NOT sufficient.
(2) 5x is an even integer. The same here, x could be ANY even number or some fraction (for example 2/5). Not sufficient.
(1)+(2) We have that 3x=even and 5x=even. Subtract one from another: 5x3x=eveneven > 2x=even > x=even/2=integer. Now, x=integer and 3x=even (from 1) means that x must be an even integer. Sufficient.
Answer: C. My answer to this question was D, both sufficient, however my assumption was that in GMAT number and integer are interchangible words, but as i see i was wrong. Bunuel could you please remind what word was interchangible with word integer?
_________________
If you found my post useful and/or interesting  you are welcome to give kudos!



Math Expert
Joined: 02 Sep 2009
Posts: 43894

Re: If x is a positive number, is x an even integer? [#permalink]
Show Tags
30 Aug 2012, 04:18
ziko wrote: Bunuel wrote: If x is a positive number, is x an even integer?
Notice that we are not told that x is an integer. (1) 3x is an even integer. x could be ANY even number or some fraction (for example 2/3), so this statement is NOT sufficient.
(2) 5x is an even integer. The same here, x could be ANY even number or some fraction (for example 2/5). Not sufficient.
(1)+(2) We have that 3x=even and 5x=even. Subtract one from another: 5x3x=eveneven > 2x=even > x=even/2=integer. Now, x=integer and 3x=even (from 1) means that x must be an even integer. Sufficient.
Answer: C. My answer to this question was D, both sufficient, however my assumption was that in GMAT number and integer are interchangible words, but as i see i was wrong. Bunuel could you please remind what word was interchangible with word integer? I think you refer to Natural Numbers, which are nonnegative (or positive) integers but GMAT doesn't use words "Natural Number" in their questions. So, there is no interchangeable word for "integer" on the GMAT.
_________________
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



Intern
Joined: 11 Jul 2013
Posts: 43

Re: If x is a positive number, is x an even integer? [#permalink]
Show Tags
02 Sep 2013, 07:23
Bunuel wrote: ziko wrote: Bunuel wrote: If x is a positive number, is x an even integer?
Notice that we are not told that x is an integer. (1) 3x is an even integer. x could be ANY even number or some fraction (for example 2/3), so this statement is NOT sufficient.
(2) 5x is an even integer. The same here, x could be ANY even number or some fraction (for example 2/5). Not sufficient.
(1)+(2) We have that 3x=even and 5x=even. Subtract one from another: 5x3x=eveneven > 2x=even > x=even/2=integer. Now, x=integer and 3x=even (from 1) means that x must be an even integer. Sufficient.
Answer: C. My answer to this question was D, both sufficient, however my assumption was that in GMAT number and integer are interchangible words, but as i see i was wrong. Bunuel could you please remind what word was interchangible with word integer? I think you refer to Natural Numbers, which are nonnegative (or positive) integers but GMAT doesn't use words "Natural Number" in their questions. So, there is no interchangeable word for "integer" on the GMAT. I am a little confused. 1) 3x is an even integer. Let x=4/3; then 3x=4. But in this case x is not an even integer. Hence INSUFFICIENT. 2) 5x is an even integer. Let x=4/5; then 5x=4. But in this case x is not an even integer. Hence INSUFFICIENT. (1+2): 15x is an integer. Let x=4/15; then 15x=4. But in this case x is not an even integer. Hence INSUFFICIENT.



Math Expert
Joined: 02 Sep 2009
Posts: 43894

Re: If x is a positive number, is x an even integer? [#permalink]
Show Tags
02 Sep 2013, 07:42
domfrancondumas wrote: Bunuel wrote: ziko wrote: If x is a positive number, is x an even integer?
Notice that we are not told that x is an integer. (1) 3x is an even integer. x could be ANY even number or some fraction (for example 2/3), so this statement is NOT sufficient.
(2) 5x is an even integer. The same here, x could be ANY even number or some fraction (for example 2/5). Not sufficient.
(1)+(2) We have that 3x=even and 5x=even. Subtract one from another: 5x3x=eveneven > 2x=even > x=even/2=integer. Now, x=integer and 3x=even (from 1) means that x must be an even integer. Sufficient.
Answer: C.
My answer to this question was D, both sufficient, however my assumption was that in GMAT number and integer are interchangible words, but as i see i was wrong. Bunuel could you please remind what word was interchangible with word integer? I think you refer to Natural Numbers, which are nonnegative (or positive) integers but GMAT doesn't use words "Natural Number" in their questions. So, there is no interchangeable word for "integer" on the GMAT. I am a little confused. 1) 3x is an even integer. Let x=4/3; then 3x=4. But in this case x is not an even integer. Hence INSUFFICIENT. 2) 5x is an even integer. Let x=4/5; then 5x=4. But in this case x is not an even integer. Hence INSUFFICIENT. (1+2): 15x is an integer. Let x=4/15; then 15x=4. But in this case x is not an even integer. Hence INSUFFICIENT. Notice that x cannot be 4/15, because in this case 3x=12/15 which is NOT an even integer and 5x=20/15 which is also NOT an even integer, so in this case both statements are violated.
_________________
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



Intern
Joined: 13 Feb 2015
Posts: 9

Re: If x is a positive number, is x an even integer? [#permalink]
Show Tags
10 Jan 2017, 06:31
If it's given that "5 is a factor of x". Is it correct to assume that x is an integer? If yes, how and why? Please explain. Also explain if the answer to my question is No. Consider a case wherein x is 5/2. Isn't 5 a factor of x? Please address, thanks a lot in advance
_________________
Before getting into the options, have an idea of what you seek
Thanks & Regards, Vipul Chhabra



Math Expert
Joined: 02 Sep 2009
Posts: 43894

Re: If x is a positive number, is x an even integer? [#permalink]
Show Tags
10 Jan 2017, 09:12



VP
Joined: 26 Mar 2013
Posts: 1441

Re: If x is a positive number, is x an even integer? [#permalink]
Show Tags
11 Jan 2017, 02:48
x is positive Integer means we need to think only in positive fractions and integers.
(1) 3x is an even integer.
Let x= 2.....3x=6..........x is even integer
Let x=2/3....3x=2.........x is NOT even integer
Insufficient
(2) 5x is an even integer.
Let x= 2........5x=10..........x is even integer
Let x=2/5.......5x=2...........x is NOT even integer
Insufficient
Combining 1 +2 ,
There is not fraction could be multiplied simultaneously to 3 & 5 and give EVEN INTEGER. We left with that x=EVEN INTEGER to give make both 3x & 5x even integers.
As 3 & 5 are odd numbers then x needs to be EVEN Integer to make both statements Even integers.
Answer: C



Director
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 518
Location: India

Re: If x is a positive number, is x an even integer? [#permalink]
Show Tags
11 Jan 2017, 11:01
1
This post received KUDOS
Hi Ellipse, Whenever you combine two statements in a DS question, the best thing to do instead of plugging in values is to use one statement into the other or use a mathematical operation between the two statements. The mathematical operation(s) that you choose to perform must lead to your target question. In this case the target question is 'Is x an even integer'? Statement 1 : 3x is an even integerHere x can either be an even integer such as 2, 4, 6.... or it can be a fraction such as 2/3, 4/3..... So x can be an even integer or a fraction. Insufficient. Statement 2 : 5x is an even integerHere again x can be an even integer such as 2, 4, 6.... or it can be a fraction such as 2/5, 4/5.... So x again can either be an even integer or a fraction. Insufficient. Now instead of recycling the values it makes sense to use a mathematical operation (or mathematical operations) between the two statements. Let us multiply the first statement by 2, since 3x = even integer ; 3x * 2 = even integer * 2 > 6x = even integerStatement 2 says that 5x is an even integer and by multiplying statement 1 by 2 we have 6x to be an even integer. Subtracting the two we get 6x  5x = even integer  even integer > x = even integer. Sufficient. Answer : C
_________________
Join Free 4 part MBA Through GMAT Video Training Series here  https://gmat.crackverbal.com/mbathroughgmatvideo2018
Enroll for our GMAT Trial Course here  http://gmatonline.crackverbal.com/
For more info on GMAT and MBA, follow us on @AskCrackVerbal



Director
Joined: 12 Nov 2016
Posts: 790

Re: If x is a positive number, is x an even integer? [#permalink]
Show Tags
19 Apr 2017, 16:56
1
This post received KUDOS
Ellipse wrote: If x is a positive number, is x an even integer? (1) 3x is an even integer. (2) 5x is an even integer. Statement 1:3 (2/3) could be an even number the questin says x is a positive number...not necessarily an integer Insufficient Statement 25(2/5) btw again here were are using a counterexample to establish that x does not necessarily have to be an integer 10/5 =2 Insufficient Statement 1 and 2: Statement 1 and Statement 2Knowing from statement 1 and 2 that 3x and 5x are even integers we can use solve this question using algebra instead of imagining numbers and testing various cases an even integer minus an even integer is always an even integer so 5x3x=2x 5(4)3(4)=2(4)



Manager
Status: Math Tutor
Joined: 12 Aug 2017
Posts: 74
WE: Education (Education)

Re: If x is a positive number, is x an even integer? [#permalink]
Show Tags
22 Aug 2017, 11:36
Bunuel wrote: ziko wrote: Bunuel wrote: If x is a positive number, is x an even integer?
Notice that we are not told that x is an integer. (1) 3x is an even integer. x could be ANY even number or some fraction (for example 2/3), so this statement is NOT sufficient.
(2) 5x is an even integer. The same here, x could be ANY even number or some fraction (for example 2/5). Not sufficient.
(1)+(2) We have that 3x=even and 5x=even. Subtract one from another: 5x3x=eveneven > 2x=even > x=even/2=integer. Now, x=integer and 3x=even (from 1) means that x must be an even integer. Sufficient.
Answer: C. My answer to this question was D, both sufficient, however my assumption was that in GMAT number and integer are interchangible words, but as i see i was wrong. Bunuel could you please remind what word was interchangible with word integer? I think you refer to Natural Numbers, which are nonnegative (or positive) integers but GMAT doesn't use words "Natural Number" in their questions. So, there is no interchangeable word for "integer" on the GMAT. Dear, Natural numbers are not nonnegative numbers as 0 is a nonnegative Integer but 0 is not natural number. Natural numbers are positive integers.
_________________
Abhishek Parikh Math Tutor Whatsapp +919983944321 Mobile +971568653827 Website: http://www.holamaven.com



Math Expert
Joined: 02 Sep 2009
Posts: 43894

Re: If x is a positive number, is x an even integer? [#permalink]
Show Tags
22 Aug 2017, 12:04



Manager
Status: Math Tutor
Joined: 12 Aug 2017
Posts: 74
WE: Education (Education)

Re: If x is a positive number, is x an even integer? [#permalink]
Show Tags
22 Aug 2017, 12:18
Bunuel wrote: HolaMaven wrote: Bunuel wrote: I think you refer to Natural Numbers, which are nonnegative (or positive) integers but GMAT doesn't use words "Natural Number" in their questions.
So, there is no interchangeable word for "integer" on the GMAT. Dear, Natural numbers are not nonnegative numbers as 0 is a nonnegative Integer but 0 is not natural number. Natural numbers are positive integers. There are two definitions as mentioned in my post: https://en.wikipedia.org/wiki/Natural_numberhttp://mathworld.wolfram.com/NaturalNumber.htmlhttp://www.mathopenref.com/countingnumber.htmlhttps://www.wolframalpha.com/input/?i=natural+numbersThank you for your enlightenment on the topic. Do the definitions differ according to the area of usage? Like in Number Theory we have Natural Numbers starting from 1 and in Set Theory or Computer Science Natural Numbers includes 0.
_________________
Abhishek Parikh Math Tutor Whatsapp +919983944321 Mobile +971568653827 Website: http://www.holamaven.com



Director
Joined: 29 Jun 2017
Posts: 511
GPA: 4
WE: Engineering (Transportation)

Re: If x is a positive number, is x an even integer? [#permalink]
Show Tags
22 Aug 2017, 12:20
1) 3x is even with x=2 and x= 2/3 , hence A,D ruled out 2) 5x is even with x= 2 and x= 2/5 B ruled out 3x = 2,4,6,8,10,12..... x = 2/3, 4/3, 6/3,8/3,..... 5x = 2,4,6,8,10.... x= 2/5,4/5,6/5,8/5,10/5 taking common from above series x=2,4,6....and so on...hence even. sufficient and C is answer
_________________
Give Kudos for correct answer and/or if you like the solution.



Math Expert
Joined: 02 Sep 2009
Posts: 43894

Re: If x is a positive number, is x an even integer? [#permalink]
Show Tags
22 Aug 2017, 12:27
HolaMaven wrote: Bunuel wrote: HolaMaven wrote: Dear, Natural numbers are not nonnegative numbers as 0 is a nonnegative Integer but 0 is not natural number. Natural numbers are positive integers. There are two definitions as mentioned in my post: https://en.wikipedia.org/wiki/Natural_numberhttp://mathworld.wolfram.com/NaturalNumber.htmlhttp://www.mathopenref.com/countingnumber.htmlhttps://www.wolframalpha.com/input/?i=natural+numbersThank you for your enlightenment on the topic. Do the definitions differ according to the area of usage? Like in Number Theory we have Natural Numbers starting from 1 and in Set Theory or Computer Science Natural Numbers includes 0. Yes, there are different definitions: "The term "natural number" refers either to a member of the set of positive integers 1, 2, 3, ... (OEIS A000027) or to the set of nonnegative integers 0, 1, 2, 3, ... (OEIS A001477; e.g., Bourbaki 1968, Halmos 1974). Regrettably, there seems to be no general agreement about whether to include 0 in the set of natural numbers. In fact, Ribenboim states "Let P be a set of natural numbers; whenever convenient, it may be assumed that 0 element P." Luckily we don't have to worry about this at all. Not a single official GMAT question uses a term "natural number". GMAT questions use: integer, positive integer, negative integer, nonnegative integer.
_________________
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



Director
Joined: 29 Jun 2017
Posts: 511
GPA: 4
WE: Engineering (Transportation)

Re: If x is a positive number, is x an even integer? [#permalink]
Show Tags
22 Aug 2017, 12:50
Bunuelgood day Bunuel, let in case if a ques come in gmat then whether i have to include 0 in natural number or not. as u mentioned above that gmat has not asked natural numbers specifically in its questions. till today i was knowing that 0 is a whole number. and is not a natural number. P.S. thanks
_________________
Give Kudos for correct answer and/or if you like the solution.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11063
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: If x is a positive number, is x an even integer? [#permalink]
Show Tags
10 Dec 2017, 14:24
Hi All, We're told that X is a POSITIVE number (meaning that X > 0). We're asked if X is an EVEN INTEGER. This is a YES/NO question. This question can be solved by TESTing VALUES. 1) 3X is an even integer. IF.... X = 2/3, then 3X = 2 and the answer to the question is NO. X = 2, then 3X = 6 and the answer to the question is YES. Fact 1 is INSUFFICIENT 2) 5X is an even integer. X = 2/5, then 5X = 2 and the answer to the question is NO. X = 2, then 5X = 10 and the answer to the question is YES. Fact 2 is INSUFFICIENT Combined, the various 'fractional' answers that fit one of the Facts will NOT fit the other (since multiplying the same fraction by 3 and by 5 won't 'cancel out' the denominator and lead to an integer result for both calculations). Thus, the only possible values for X must be INTEGERS. In addition, since 3 and 5 are both ODD integers, for the 3X and 5X to both be EVEN integers, the X MUST be EVEN. Combined, SUFFICIENT Final Answer: 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!***********************




Re: If x is a positive number, is x an even integer?
[#permalink]
10 Dec 2017, 14:24






