Last visit was: 17 May 2026, 15:54 It is currently 17 May 2026, 15:54
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
655-705 (Hard)|   Arithmetic|      
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,063
Own Kudos:
20,091
 [11]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,063
Kudos: 20,091
 [11]
Is a positive integer x a prime number? 04 Aug 2016, 19:25
Kudos
Add Kudos
11
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

57% (01:36) correct 43% (01:37) wrong based on 395 sessions

History

Date
Time
Result
Not Attempted Yet
Is a positive integer x a prime number?
1) All the prime factors of x are greater than √x
2) All the prime factors of x are 1 and itself

*An answer will be posted in 2 days.
ShowHide Answer
Official Answer
D
User avatar
acegmat123
User avatar
Joined: 28 Jun 2016
Last visit: 25 Oct 2021
Posts: 146
Own Kudos:
220
Given Kudos: 99
Location: Canada
Concentration: Operations, Entrepreneurship
Posts: 146
Kudos: 220
Is a positive integer x a prime number? 05 Aug 2016, 04:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think the second point should be, "All the factors of x are 1 and itself". Since 1 is not a prime.


Sent from my iPhone using GMAT Club Forum mobile app
User avatar
abhimahna
User avatar
Board of Directors
Joined: 18 Jul 2015
Last visit: 06 Jul 2024
Posts: 3,481
Own Kudos:
5,780
 [4]
Given Kudos: 346
Status:Emory Goizueta Alum
Products:
My Reviews
Expert
Expert reply
Posts: 3,481
Kudos: 5,780
 [4]
Is a positive integer x a prime number? 05 Aug 2016, 10:39
1
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
MathRevolution
Is a positive integer x a prime number?
1) All the prime factors of x are greater than √x
2) All the prime factors of x are 1 and itself

*An answer will be posted in 2 days.
Show more

Answer is D.

1) For every non prime number, its prime factors are either < or = or > then its root. Take any non prime no. , lets say 10. Prime factors are 2 and 5. sqrt(10) >3, but 2 is less than 3. Hence proved. Thus, Statement 1 is sufficient.

2) This is the definition of prime numbers.

Hence, D.
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,063
Own Kudos:
20,091
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,063
Kudos: 20,091
Is a positive integer x a prime number? 08 Aug 2016, 18:19
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The original condition has 1 variable (x) and there is a high chance that D is the correct answer. Con 1) and con 2) both are the definition of prime number. Hence, the correct answer is D.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
User avatar
stonecold
User avatar
Joined: 12 Aug 2015
Last visit: 09 Apr 2024
Posts: 2,230
Own Kudos:
3,648
Given Kudos: 893
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Posts: 2,230
Kudos: 3,648
Is a positive integer x a prime number? 16 Oct 2016, 03:55
Kudos
Add Kudos
Bookmarks
Bookmark this Post
abhimahna
MathRevolution
Is a positive integer x a prime number?
1) All the prime factors of x are greater than √x
2) All the prime factors of x are 1 and itself

*An answer will be posted in 2 days.

Answer is D.

1) For every non prime number, its prime factors are either < or = or > then its root. Take any non prime no. , lets say 10. Prime factors are 2 and 5. sqrt(10) >3, but 2 is less than 3. Hence proved. Thus, Statement 1 is sufficient.

2) This is the definition of prime numbers.

Hence, D.
Show more

Isn't statement no.2 just ridiculous ?
How on earth can 1 be regarded as a "PRIME NUMBER"

One is neither Prime nor Composite.
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 17 Dec 2025
Posts: 5,896
Own Kudos:
5,466
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,896
Kudos: 5,466
Is a positive integer x a prime number? 16 Oct 2016, 04:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
stonecold
Isn't statement no.2 just ridiculous ?
How on earth can 1 be regarded as a "PRIME NUMBER"

One is neither Prime nor Composite.
Show more

No, it is not at all ridiculous

Definition of Prime Number

A Prime number is a natural number with exactly two distinct natural number divisors: 1 and itself. Otherwise a number is called a composite number. Therefore, 1 is not a prime, since it only has one divisor, namely 1. A number n>1 is prime if it cannot be written as a product of two factors a and b, both of which are greater than 1: n = ab.

Statement 2 is sufficient to state the x is a prime number...
User avatar
stonecold
User avatar
Joined: 12 Aug 2015
Last visit: 09 Apr 2024
Posts: 2,230
Own Kudos:
3,648
Given Kudos: 893
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Posts: 2,230
Kudos: 3,648
Is a positive integer x a prime number? 16 Oct 2016, 04:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Abhishek009
stonecold
Isn't statement no.2 just ridiculous ?
How on earth can 1 be regarded as a "PRIME NUMBER"

One is neither Prime nor Composite.

No, it is not at all ridiculous

Definition of Prime Number

A Prime number is a natural number with exactly two distinct natural number divisors: 1 and itself. Otherwise a number is called a composite number. Therefore, 1 is not a prime, since it only has one divisor, namely 1. A number n>1 is prime if it cannot be written as a product of two factors a and b, both of which are greater than 1: n = ab.

Statement 2 is sufficient to state the x is a prime number...
Show more


Completely Disagree..!!!

How can someone say that 1 is a prime factor of a number.
One is neither prime nor composite.
In a way your statement is supporting my claim :)

statement 2 states => All the prime factors of x are 1 and itself.
How can one be a prime factor
The statement should be => All the factors of x are 1 and itself.
Big Difference :)
User avatar
abhimahna
User avatar
Board of Directors
Joined: 18 Jul 2015
Last visit: 06 Jul 2024
Posts: 3,481
Own Kudos:
5,780
Given Kudos: 346
Status:Emory Goizueta Alum
Products:
My Reviews
Expert
Expert reply
Posts: 3,481
Kudos: 5,780
Is a positive integer x a prime number? 16 Oct 2016, 10:22
Kudos
Add Kudos
Bookmarks
Bookmark this Post
stonecold
Abhishek009
stonecold
Isn't statement no.2 just ridiculous ?
How on earth can 1 be regarded as a "PRIME NUMBER"

One is neither Prime nor Composite.

No, it is not at all ridiculous

Definition of Prime Number

A Prime number is a natural number with exactly two distinct natural number divisors: 1 and itself. Otherwise a number is called a composite number. Therefore, 1 is not a prime, since it only has one divisor, namely 1. A number n>1 is prime if it cannot be written as a product of two factors a and b, both of which are greater than 1: n = ab.

Statement 2 is sufficient to state the x is a prime number...


Completely Disagree..!!!

How can someone say that 1 is a prime factor of a number.
One is neither prime nor composite.
In a way your statement is supporting my claim :)

statement 2 states => All the prime factors of x are 1 and itself.
How can one be a prime factor
The statement should be => All the factors of x are 1 and itself.
Big Difference :)
Show more

Yes, I agree. I missed that point. My Bad.

1 is a factor of a prime number BUT NOT a prime factor. 1 is neither prime nor composite.

Either the OA marked is incorrect or the question is incorrect.

Thanks stonecold :-D
avatar
SWAPNILP
avatar
Joined: 13 Mar 2018
Last visit: 04 Sep 2021
Posts: 12
Own Kudos:
2
Given Kudos: 183
Posts: 12
Kudos: 2
Is a positive integer x a prime number? 22 Dec 2018, 05:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
abhimahna
MathRevolution
Is a positive integer x a prime number?
1) All the prime factors of x are greater than √x
2) All the prime factors of x are 1 and itself

*An answer will be posted in 2 days.

Answer is D.

1) For every non prime number, its prime factors are either < or = or > then its root. Take any non prime no. , lets say 10. Prime factors are 2 and 5. sqrt(10) >3, but 2 is less than 3. Hence proved. Thus, Statement 1 is sufficient.

2) This is the definition of prime numbers.

Hence, D.
Show more

Hi abhimahna

Request you to please elaborate with one more example. I am not able to understand this solution. Many thanks
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,086
Own Kudos:
1,125
Posts: 39,086
Kudos: 1,125
Is a positive integer x a prime number? 30 May 2023, 04:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
110522 posts
kingbucky
498 posts
Gmat860sanskar
263 posts