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:

how many factors of 80 are greater than square_root 80?

a)5

No need to find all factors of 80.

\(\sqrt{80}\) is more than 8 and less than 9. So we are asked to find # of factors of 80 which are more than 8.

Now, \(80=16*5=2^4*5\) --> # of factors of 80 is \((4+1)(1+1)=10\) (see below how to find the # of factors of an integer). Out of these 10, following 5 factors are less or equal to 8: 1, 2, 4, 5, and 8. So other 5 factors are more than 8.

Answer: 5.

Finding the Number of Factors of an Integer

First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.

The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)

Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.

Re: How many factors of 80 are greater than square_root 80? [#permalink]

Show Tags

16 Oct 2010, 00:18

8. How many different positive integers are factors of 342? A. 9 B. 11 C. 12 D. 20 E. 22

Bunuel logic gave me only 7 but the andser says 12 .. here the explaination given :

C. From the answers we can see that the list of factors will be relatively small, so it’s easiest just to list them out. The pairs of factors are 1 and 342, 2 and 171, 3 and 114, 6 and 57, 9 and 38, and 18 and 19. That makes 12 factors.

8. How many different positive integers are factors of 342? A. 9 B. 11 C. 12 D. 20 E. 22

Bunuel logic gave me only 7 but the andser says 12 .. here the explaination given :

C. From the answers we can see that the list of factors will be relatively small, so it’s easiest just to list them out. The pairs of factors are 1 and 342, 2 and 171, 3 and 114, 6 and 57, 9 and 38, and 18 and 19. That makes 12 factors.

It's not MY logic, it's MATH.

According to the formula in my previous post as \(342=2*3^2*19\) then # of factors of 342 equals to \((1+1)(2+1)(1+1)=12\).

Re: How many factors of 80 are greater than square_root 80? [#permalink]

Show Tags

10 Nov 2014, 21:31

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.
_________________

Re: How many factors of 80 are greater than square_root 80? [#permalink]

Show Tags

07 Jan 2015, 08:38

Bunuel wrote:

vanidhar wrote:

how many factors of 80 are greater than square_root 80?

a)5

No need to find all factors of 80.

\(\sqrt{80}\) is more than 8 and less than 9. So we are asked to find # of factors of 80 which are more than 8.

Now, \(80=16*5=2^4*5\) --> # of factors of 80 is \((4+1)(1+1)=10\) (see below how to find the # of factors of an integer). Out of these 10, following 5 factors are less or equal to 8: 1, 2, 4, 5, and 8. So other 5 factors are more than 8.

Answer: 5.

Finding the Number of Factors of an Integer

First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.

The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)

Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.

Hope it helps.

Bunuel, Did not get the part where you said root 80 is between 8 and 9..the value of root 80 is 4 root 5..Am i missing something here?

how many factors of 80 are greater than square_root 80?

a)5

No need to find all factors of 80.

\(\sqrt{80}\) is more than 8 and less than 9. So we are asked to find # of factors of 80 which are more than 8.

Now, \(80=16*5=2^4*5\) --> # of factors of 80 is \((4+1)(1+1)=10\) (see below how to find the # of factors of an integer). Out of these 10, following 5 factors are less or equal to 8: 1, 2, 4, 5, and 8. So other 5 factors are more than 8.

Answer: 5.

Finding the Number of Factors of an Integer

First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.

The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)

Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.

Hope it helps.

Bunuel, Did not get the part where you said root 80 is between 8 and 9..the value of root 80 is 4 root 5..Am i missing something here?

Thanks in Advance.

\(4\sqrt{5}\approx{8.94}\).

\(\sqrt{81}=9\), thus \(\sqrt{80}\) is a bit less than 9.
_________________

Re: How many factors of 80 are greater than square_root 80? [#permalink]

Show Tags

31 Jul 2015, 23:16

Honestly it's not really necessary to look at actual factors or even check the square root of \(80\) once you count factors (as Bunuel explained, \(80=2^4*5^1\) and thus has \((4+1)*(1+1)=10\) factors).

Since factors pair off, every integer will always have exactly half of its factors less than its square root. (Round down in the case of an odd number of factors -- i.e. a perfect square.)

Re: How many factors of 80 are greater than square_root 80? [#permalink]

Show Tags

03 Aug 2015, 02:16

IMHO, what you are writing is true only if the number is a non perfect square. If I change the question like - How many factors of 100 will be less than \sqrt{100, answer would be equal to ((total number of factors of 100)-1/2). Total number of factors of 100 is 9. Hence total number of factors which are less than or greater than square root of 100 will be (9-1)/2which is equal to 4.

Bunuel wrote:

vanidhar wrote:

how many factors of 80 are greater than square_root 80?

a)5

No need to find all factors of 80.

\([square_root]80}\) is more than 8 and less than 9. So we are asked to find # of factors of 80 which are more than 8.

Now, \(80=16*5=2^4*5\) --> # of factors of 80 is \((4+1)(1+1)=10\) (see below how to find the # of factors of an integer). Out of these 10, following 5 factors are less or equal to 8: 1, 2, 4, 5, and 8. So other 5 factors are more than 8.

Answer: 5.

Finding the Number of Factors of an Integer

First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.

The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)

Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.

Re: How many factors of 80 are greater than square_root 80? [#permalink]

Show Tags

03 Aug 2015, 05:09

gmatcrackerindia wrote:

IMHO, what you are writing is true only if the number is a non perfect square. If I change the question like - How many factors of 100 will be less than \sqrt{100, answer would be equal to ((total number of factors of 100)-1/2). Total number of factors of 100 is 9. Hence total number of factors which are less than or greater than square root of 100 will be (9-1)/2which is equal to 4.

Bunuel wrote:

vanidhar wrote:

how many factors of 80 are greater than square_root 80?

a)5

No need to find all factors of 80.

\([square_root]80}\) is more than 8 and less than 9. So we are asked to find # of factors of 80 which are more than 8.

Now, \(80=16*5=2^4*5\) --> # of factors of 80 is \((4+1)(1+1)=10\) (see below how to find the # of factors of an integer). Out of these 10, following 5 factors are less or equal to 8: 1, 2, 4, 5, and 8. So other 5 factors are more than 8.

Answer: 5.

Finding the Number of Factors of an Integer

First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.

The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)

Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.

Hope it helps.

You can't generalise it....

Bunnuel gave the easiest solution possible.

Lets take an example of 144.

As per the factors - 2^4*3^2 = Total factors including 1 & 144 = (4+1)(2+1) = 15.

Now go to the factors less than root 144 i.e. 12 = 2^2*3^1 = 6..

Re: How many factors of 80 are greater than square_root 80? [#permalink]

Show Tags

03 Aug 2015, 08:33

Quote:

You can't generalise it....

Bunnuel gave the easiest solution possible.

Lets take an example of 144.

As per the factors - 2^4*3^2 = Total factors including 1 & 144 = (4+1)(2+1) = 15.

Now go to the factors less than root 144 i.e. 12 = 2^2*3^1 = 6..

Where is your (n-1)/2 logic in this???

This is a perfect example of exactly why taking half of the total factors (as noted, round down in the case of a perfect square) is better than trying to list them all by hand.

Actually, the seven factors of \(144\) that are less than \(\sqrt{144}\) are: \(1\), \(2\), \(3\), \(4\), \(6\), \(8\), and \(9\). Not all factors of \(144\) that are less than \(12\) are necessarily factors of \(12\).

Re: How many factors of 80 are greater than square_root 80? [#permalink]

Show Tags

04 Aug 2015, 00:03

1

This post received KUDOS

Cadaver wrote:

gmatcrackerindia wrote:

IMHO, what you are writing is true only if the number is a non perfect square. If I change the question like - How many factors of 100 will be less than [square_root]100, answer would be equal to ((total number of factors of 100)-1/2). Total number of factors of 100 is 9. Hence total number of factors which are less than or greater than square root of 100 will be (9-1)/2which is equal to 4.

You can't generalise it....

Bunnuel gave the easiest solution possible.

Lets take an example of 144.

As per the factors - 2^4*3^2 = Total factors including 1 & 144 = (4+1)(2+1) = 15.

Now go to the factors less than root 144 i.e. 12 = 2^2*3^1 = 6..

Where is your (n-1)/2 logic in this???

What I am trying to say is:

(a)If the number is not a perfect square, then exactly half of the factors will be smaller than the square root of the number, and other half will be greater than the square root of the number. (b) If the number is a Perfect Square, then half of (total factors - 1) will be smaller than the square root of the number, and half of (total factors - 1) will be greater than the square root of the number. One of the factors will be equal to the square root of the number.

Re: How many factors of 80 are greater than square_root 80? [#permalink]

Show Tags

21 Oct 2016, 18:50

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...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...