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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Statement 1: K^2 has one more factor. Let's say if K was a 4 (non-prime ) then it will have 4 factors. [1,2,4]. If you square 4, 16 has 5[1,2,4,8,16] factors. The factors increased by 2. The only way for a factor to increase by 1 is if the number is prime. 13 has 2 factors [1,13]. 169 has 3 factors [1,13,169].

This mean K is a prime. The only 2 numbers that can multiple to 13 is 13 and 1. Therefore we know the answer for the question is NO.

I think the question lacks a bit of information. It mentions that both the integers should be greater than 1 but does not mention that both integers should be different. However, still, when prime numbers are squared, the number of different factors increases by 1 which is a product of the prime no multiplied by the prime number.
_________________

"Nowadays, people know the price of everything, and the value of nothing."Oscar Wilde

Can the positive integer k be expressed as the product of two integers, each of which is greater than 1?

Question basically asks whether k is a prime number. If it is, then it cannot be expressed as the product of two integers, each of which is greater than 1 (definition of a prime number).

(1) k^2 has one more positive factor than k --> if k is a prime then it has 2 factors: 1, and k --> k^2 will have one more, so 3 factors: 1, k, and k^2. If k is some composite number greater than 1, then it has more than 2 factors and # of factors of k^2 will increase by more than just by 1 (try any composite number to check this). If k=1 then k^2 will have the same # of factor as k: one. Hence k=prime. Sufficient.

(2) 11 < k < 19. k can be 13, so prime, as well as 14 so not a prime. Not sufficient.

Re: Can the positive integer k be expressed as the product of [#permalink]

Show Tags

13 Feb 2012, 15:57

Can the positive integer k be expressed as the product of two integers, each of which is greater than 1?

Question basically asks whether k is a prime number. If it is, then it cannot be expressed as the product of two integers, each of which is greater than 1 (definition of a prime number).

Bunuel - I take it you mean product of two DIFFERENT integers, each of which is greater than 1.
_________________

Re: Can the positive integer k be expressed as the product of [#permalink]

Show Tags

13 Feb 2012, 16:02

If k is some composite number greater than 1, then it has more than 2 factors --> So K will be prime or not? Am I reading something wrong Bunuel?
_________________

If k is some composite number greater than 1, then it has more than 2 factors --> So K will be prime or not? Am I reading something wrong Bunuel?

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.

So, composite numbers are not primes.

We are considering 3 cases for (1): k=prime; k=composite>1; K=1;

And get that k can be only a prime number.

enigma123 wrote:

Can the positive integer k be expressed as the product of two integers, each of which is greater than 1?

Question basically asks whether k is a prime number. If it is, then it cannot be expressed as the product of two integers, each of which is greater than 1 (definition of a prime number).

Bunuel - I take it you mean product of two DIFFERENT integers, each of which is greater than 1.

It doesn't really matter. Can you express a prime as the product of two same integers?
_________________

Can the positive integer [m]k[/m] be expressed [#permalink]

Show Tags

28 Oct 2012, 07:47

Can the positive integer \(k\) be expressed as the product of two integers, each of which is greater than 1? (1) \(k^2\) has one more positive factor than k. (2) \(11 < k < 19\)

I don't understand well this explanation of the OE. Please, your help: The only types of numbers k such that k2 has exactly one more positive factor than k are primes. Prime numbers have two factors and their squares have three. If k had more than two factors, the number of factors would increase by more than 1 when squared. Thus, k must be prime, answering the question.

Re: Can the positive integer [m]k[/m] be expressed [#permalink]

Show Tags

28 Oct 2012, 18:59

danzig wrote:

Can the positive integer \(k\) be expressed as the product of two integers, each of which is greater than 1? (1) \(k^2\) has one more positive factor than k. (2) \(11 < k < 19\)

I don't understand well this explanation of the OE. Please, your help: The only types of numbers k such that k2 has exactly one more positive factor than k are primes. Prime numbers have two factors and their squares have three. If k had more than two factors, the number of factors would increase by more than 1 when squared. Thus, k must be prime, answering the question.

Note, for a number K the factors are K,1 and 'few other' depending upon whether it is prime or not for number k^2 - the factors are 1, k and k^2 and 'few other'

The 'few other' factors depend on the fact whether K is divisible by a number or not.

For example: factors of 5 : 1, 5 and ? - nothing else factors of 6: 1, 6 and ? - (2,3)

Similarly, factors of 25: 1,5, 25 and ? - nothing else ( because 5 is not divisible by anything else and hence can not be broken into any other number) factors of 36: 1,6,36 and ? - (2,3,4,9, 12,18)

Therefore if you notice the pattern only for a prime number, number of factors of k^2 is one more than number of factors for k.

Now with this concept target the question stem 1 : it shows us k is prime using above mentioned concept. can a prime number be a product of 2 integers each greather than 1? no. So we have a sufficient statement to say No. stem 2: K could be anything from 12 to 18. So ans would be if k is 12 then yes, but if k is 13 then no. hence insufficient.

Therefore ans A (only statement 1 is sufficient) it is.

Re: Can the positive integer [m]k[/m] be expressed [#permalink]

Show Tags

28 Oct 2012, 22:28

danzig wrote:

Can the positive integer \(k\) be expressed as the product of two integers, each of which is greater than 1? (1) \(k^2\) has one more positive factor than k. (2) \(11 < k < 19\)

I don't understand well this explanation of the OE. Please, your help: The only types of numbers k such that k2 has exactly one more positive factor than k are primes. Prime numbers have two factors and their squares have three. If k had more than two factors, the number of factors would increase by more than 1 when squared. Thus, k must be prime, answering the question.

Basically, what the question asks is whether k is not a prime number.

1)k is prime. Sufficient. 2)k can be 12,13,14,15,16,17,18. Both primes and non primes appear in this set. Insufficient

Answer is A.

Kudos Please... If my post helped.
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Can the positive integer \(k\) be expressed as the product of two integers, each of which is greater than 1? (1) \(k^2\) has one more positive factor than k. (2) \(11 < k < 19\)

I don't understand well this explanation of the OE. Please, your help: The only types of numbers k such that k2 has exactly one more positive factor than k are primes. Prime numbers have two factors and their squares have three. If k had more than two factors, the number of factors would increase by more than 1 when squared. Thus, k must be prime, answering the question.

Merging similar topics. Please refer to the solutions above.
_________________

Re: Can the positive integer k be expressed as the product of [#permalink]

Show Tags

07 Oct 2015, 16:59

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Happy 2017! Here is another update, 7 months later. With this pace I might add only one more post before the end of the GSB! However, I promised that...