Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 3001:30 AM EDT
-02:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 2912:30 AM EDT
-01:30 AM EDT
Learn how Kamakshi achieved a GMAT 675 with an impressive 96th %ile in Data Insights. Discover the unique methods and exam strategies that helped her excel in DI along with other sections for a balanced and high score.
May 0111:00 AM PDT
-12:00 PM PDT
Free- full-length test + 15 concept videos + 150+ short videos + study plan!
May 0306:30 AM PDT
-08:30 AM PDT
Verbal trouble on GMAT? Fix it NOW! Join Sunita Singhvi for a focused webinar on actionable strategies to boost your Verbal score and take your performance to the next level.
09 Jun 2015, 07:49
Kudos
Bookmarks
What is the least positive integer that is not a factor of 30! and is not a prime number?
A. 31
B. 32
C. 33
D. 62
E. 64
A. 31
B. 32
C. 33
D. 62
E. 64
09 Jun 2015, 07:50
Kudos
Bookmarks
Official Solution:
What is the least positive integer that is not a factor of 30! and is not a prime number?
A. 31
B. 32
C. 33
D. 62
E. 64
We are looking for a number that is not a factor of 30! and is also not a prime number.
The smallest prime which is not a factor of 30! is obviously 31. So, the smallest positive integer that is not a factor of 30! and is not a prime number is 2*31=62. Notice that all numbers between 30 and 62 are either primes (and we know that x is NOT a prime) or factors of 30! (because 30! has all its primes in higher powers). For example:
31 is a prime, hence \(x\) cannot be 31.
\(32 = 2^5\). Since 30! surely has 2 raised to a power greater than 5, 32 IS a factor of 30!.
\(33 = 3*11\). Both 3 and 11 are factors of 30!, hence 33 IS a factor of 30!
...
\(64 = 2^6\). Since 30! surely has 2 raised to a power greater than 6, 64 IS a factor of 30!.
Answer: D
What is the least positive integer that is not a factor of 30! and is not a prime number?
A. 31
B. 32
C. 33
D. 62
E. 64
We are looking for a number that is not a factor of 30! and is also not a prime number.
The smallest prime which is not a factor of 30! is obviously 31. So, the smallest positive integer that is not a factor of 30! and is not a prime number is 2*31=62. Notice that all numbers between 30 and 62 are either primes (and we know that x is NOT a prime) or factors of 30! (because 30! has all its primes in higher powers). For example:
31 is a prime, hence \(x\) cannot be 31.
\(32 = 2^5\). Since 30! surely has 2 raised to a power greater than 5, 32 IS a factor of 30!.
\(33 = 3*11\). Both 3 and 11 are factors of 30!, hence 33 IS a factor of 30!
...
\(64 = 2^6\). Since 30! surely has 2 raised to a power greater than 6, 64 IS a factor of 30!.
Answer: D
30 Aug 2023, 01:40
Kudos
Bookmarks
I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
