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 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2601:30 AM EDT
-02:30 AM EDT
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and more.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
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.
15 Nov 2021, 02:00
Kudos
Bookmarks
If \(k\) is a positive integer, is \(\sqrt{k}\) an integer?
(1) The number of positive factors of \(k\) is a prime number
(2) \(k\) has a factor \(p\) such that \(1 < p < k\)
(1) The number of positive factors of \(k\) is a prime number
(2) \(k\) has a factor \(p\) such that \(1 < p < k\)
15 Nov 2021, 02:00
Kudos
Bookmarks
Official Solution:
If \(k\) is a positive integer, is \(\sqrt{k}\) an integer?
Notice that the question asks whether \(k\) is a perfect square (the square of an integer). Recall that the number of distinct factors of a perfect square is ALWAYS ODD. The reverse is also true: if a number has the odd number of distinct factors then it's a perfect square.
(1) The number of positive factors of \(k\) is a prime number
If the number of factors of \(k\) is 2, then that would mean that \(k\) is a prime, so \(\sqrt{k}\) will NOT be an integer.
If the number of factors of \(k\) is any other prime, then that would mean that the number of factors of \(k\) is odd, and therefore \(k\) is perfect square, so \(\sqrt{k}\) will be an integer.
Not sufficient.
(2) \(k\) has a factor \(p\) such that \(1 < p < k\)
This is another way of saying that \(k\) is NOT a prime number (because if \(k\) were a prime, it would not have any other factor but 1 and itself). Still not sufficient, consider \(k = 4\) and \(k = 6.\)
(1)+(2) From (2) we have that \(k\) is NOT a prime number, so we are left with second case from (1): the number of factors of \(k \) is odd, and therefore \(k\) is a perfect square, so \(\sqrt{k}\) is an integer. Sufficient.
Answer: C
If \(k\) is a positive integer, is \(\sqrt{k}\) an integer?
Notice that the question asks whether \(k\) is a perfect square (the square of an integer). Recall that the number of distinct factors of a perfect square is ALWAYS ODD. The reverse is also true: if a number has the odd number of distinct factors then it's a perfect square.
(1) The number of positive factors of \(k\) is a prime number
If the number of factors of \(k\) is 2, then that would mean that \(k\) is a prime, so \(\sqrt{k}\) will NOT be an integer.
If the number of factors of \(k\) is any other prime, then that would mean that the number of factors of \(k\) is odd, and therefore \(k\) is perfect square, so \(\sqrt{k}\) will be an integer.
Not sufficient.
(2) \(k\) has a factor \(p\) such that \(1 < p < k\)
This is another way of saying that \(k\) is NOT a prime number (because if \(k\) were a prime, it would not have any other factor but 1 and itself). Still not sufficient, consider \(k = 4\) and \(k = 6.\)
(1)+(2) From (2) we have that \(k\) is NOT a prime number, so we are left with second case from (1): the number of factors of \(k \) is odd, and therefore \(k\) is a perfect square, so \(\sqrt{k}\) is an integer. Sufficient.
Answer: C
15 Nov 2021, 20:46
Kudos
Bookmarks
Bunuel
In other words the question is: Is k a perfect square?
(1) The number of positive factors of \(k\) is a prime number
So, the number of factors can be 2 or some odd number.
2 factors: k is prime number
Odd number of factors: k is a perfect square. Perfect squares have odd number of factors.
Insufficient
(2) \(k\) has a factor \(p\) such that \(1 < p < k\)
Clearly insufficient.
Just tells us that k is NOT a prime because there is at least one more factor p other than 1 and k.
Combined
From statement I, we know that k is either a prime or a perfect square.
Statement II tells us that k is not a prime.
Thus, k has to be a perfect square.
Sufficient
C
