December 20, 2018 December 20, 2018 10:00 PM PST 11:00 PM PST This is the most inexpensive and attractive price in the market. Get the course now! December 22, 2018 December 22, 2018 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
Author 
Message 
TAGS:

Hide Tags

VP
Joined: 21 Jul 2006
Posts: 1390

If x is a positive integer, is x prime?
[#permalink]
Show Tags
Updated on: 02 Apr 2014, 03:52
Question Stats:
71% (01:27) correct 29% (01:35) wrong based on 421 sessions
HideShow timer Statistics
If x is a positive integer, is x prime? (1) x has the same number of factors as y^2, where y is a positive integer greater than 2. (2) x has the same number of factors as z, where z is a positive integer greater than 2.
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by tarek99 on 24 Nov 2007, 07:07.
Last edited by Bunuel on 02 Apr 2014, 03:52, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.




Math Expert
Joined: 02 Sep 2009
Posts: 51301

Re: If X is a positive integer, is x prime? (1) x has the same
[#permalink]
Show Tags
02 Apr 2014, 03:58




Current Student
Joined: 28 Dec 2004
Posts: 3227
Location: New York City
Schools: Wharton'11 HBS'12

I will go with A..
all prime factors have even number of factors i.e 2
any square of a positive integer will give you odd factors..sufficient..x is not a prime.



Senior Manager
Joined: 06 Aug 2007
Posts: 312

Re: Is x prime?
[#permalink]
Show Tags
24 Nov 2007, 08:15
tarek99 wrote: If X is a positive integer, is x prime?
(1) x has the same number of factors as y^2, where y is a positive integer greater than 2.
(2) x has the same number of factors as z, where z is a positive integer greater than 2.
When choosing your answer, please provide your explanation.
Its A for me too..It cant be a prime number....
X = has the same factors as y^2..
y = Y*Y so the factors of Y^2 = are 1, y and Y*Y for a number to be prime the only factors are 1 and itself.



VP
Joined: 28 Dec 2005
Posts: 1444

said A for this one.
y^2 = 9,16,25,36 and so on.
All these numbers have more than two factors, and so x cannot be prime.
B says z=3,4,5,6 and so on. Some of the numbers are prime, and some are not, so this statement by itself is insufficient.



SVP
Joined: 29 Mar 2007
Posts: 2423

Re: Is x prime?
[#permalink]
Show Tags
17 Dec 2007, 10:19
tarek99 wrote: If X is a positive integer, is x prime?
(1) x has the same number of factors as y^2, where y is a positive integer greater than 2.
(2) x has the same number of factors as z, where z is a positive integer greater than 2.
When choosing your answer, please provide your explanation.
A.
1) an integer^2 that is greater than 1 will always have more factors than a prime. So X is not a prime.
2) could be prime or could not be. Insuff.



Senior Manager
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 482
Location: India
GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GMAT 3: 790 Q51 V49
GPA: 3.3

Re: If X is a positive integer, is x prime? (1) x has the same
[#permalink]
Show Tags
02 Apr 2014, 00:29
Bunuel, I am still not clear with the questions solution. Can you Please throw Insight. Thanks!
_________________
Like my post Send me a Kudos It is a Good manner. My Debrief: http://gmatclub.com/forum/howtoscore750and750imovedfrom710to189016.html



Manager
Joined: 03 Jan 2015
Posts: 61
Concentration: Strategy, Marketing
WE: Research (Pharmaceuticals and Biotech)

Re: If x is a positive integer, is x prime?
[#permalink]
Show Tags
16 Jan 2015, 06:06
Bunuel wrote: honchos wrote: Bunuel,
I am still not clear with the questions solution. Can you Please throw Insight. Thanks! If x is a positive integer, is x prime? (1) x has the same number of factors as y^2, where y is a positive integer greater than 2. y^2 is a perfect square. The number of distinct factors of a positive perfect square is ALWAYS ODD, while the number of factors of a prime is two (1 and itself). Thus since x has the same number of factors as a perfect square it cannot be a prime. Sufficient. (2) x has the same number of factors as z, where z is a positive integer greater than 2. Clearly insufficient. Answer: A. Hi there, Can you please explain the statement "The number of distinct factors of a positive perfect square is ALWAYS ODD"? e.g. distinct factors of 36 are 2 and 3 (=even). Likewise for 100 are 2 and 5 ( = even). Thank you, TO



Math Expert
Joined: 02 Sep 2009
Posts: 51301

If x is a positive integer, is x prime?
[#permalink]
Show Tags
16 Jan 2015, 06:38
thorinoakenshield wrote: Bunuel wrote: honchos wrote: Bunuel,
I am still not clear with the questions solution. Can you Please throw Insight. Thanks! If x is a positive integer, is x prime? (1) x has the same number of factors as y^2, where y is a positive integer greater than 2. y^2 is a perfect square. The number of distinct factors of a positive perfect square is ALWAYS ODD, while the number of factors of a prime is two (1 and itself). Thus since x has the same number of factors as a perfect square it cannot be a prime. Sufficient. (2) x has the same number of factors as z, where z is a positive integer greater than 2. Clearly insufficient. Answer: A. Hi there, Can you please explain the statement "The number of distinct factors of a positive perfect square is ALWAYS ODD"? e.g. distinct factors of 36 are 2 and 3 (=even). Likewise for 100 are 2 and 5 ( = even). Thank you, TO It says distinct factors, not distinct prime factors. So, for example, distinct factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36: 9 factors. Distinct factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100: 9 factors. Distinct factors of 4 are 1, 2, and 4: 3 factors. Does this make sense?
_________________
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: 19 Jul 2017
Posts: 34

Re: If x is a positive integer, is x prime?
[#permalink]
Show Tags
29 Jun 2018, 03:40
tarek99 wrote: If x is a positive integer, is x prime?
(1) x has the same number of factors as y^2, where y is a positive integer greater than 2.
(2) x has the same number of factors as z, where z is a positive integer greater than 2. 1) SUFF.: If x has the same number of factors as y2, then x cannot be prime. A prime number is a number that has only itself and 1 as factors. But a square has at least 3 prime factors. For example, if y is prime, y = 2, then y2 = 4, which has 1, 2, and 4 as factors. If the root (in this case y) is not prime, then the square will have more than 3 factors. For example, if y = 4, then y2 = 16, which has 1, 2, 4, 8, and 16 as factors. In either case, x will have at least 3 factors, establishing it as nonprime. (2) INSUFF.: If z is prime, then x will have only two factors, making it prime. But if z is nonprime, it will have either one (if z = 1) or more than two factors, which means x will have either one or more than two factors, making x nonprime. Since we do not know which case we have, we cannot tell whether x is prime
_________________
You never FAIL until you stop TRYING [wrapimg=][/wrapimg]




Re: If x is a positive integer, is x prime? &nbs
[#permalink]
29 Jun 2018, 03:40






