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:

Re: Which of the following is not a perfect square [#permalink]

Show Tags

04 Nov 2009, 00:44

1

This post received KUDOS

A perfect square will have exactly an even number of each of its factors. 81 for example: 81 = 9x9 = 3x3x3x3 which is essentially 2 sets of 3x3 Or: 36 = 6x6 = 2x3x2x3 which is 2 sets of 2x3

1. 100856 2. 325137 3. 945729 4. All of these

You mention option 2 is not correct, so neither is option 4. Statement 1: 100856 You can only factor it by 2 three times. This is not an even amount of 2s so it cannot be a perfect square. Statement 3: 945729 You can factor 3 three times. This is not an even amount of 3s so it cannot be a perfect square

So if I’m not wrong then none of these are perfect square? Which seems odd as that’s not an answer option. Or I could be wrong

Re: Which of the following is not a perfect square [#permalink]

Show Tags

04 Nov 2009, 00:52

Ans is optn 4 as it says 'all of these' meaning all of these r not perfect squares

yangsta8 wrote:

A perfect square will have exactly an even number of each of its factors. 81 for example: 81 = 9x9 = 3x3x3x3 which is essentially 2 sets of 3x3 Or: 36 = 6x6 = 2x3x2x3 which is 2 sets of 2x3

1. 100856 2. 325137 3. 945729 4. All of these

You mention option 2 is not correct, so neither is option 4. Statement 1: 100856 You can only factor it by 2 three times. This is not an even amount of 2s so it cannot be a perfect square. Statement 3: 945729 You can factor 3 three times. This is not an even amount of 3s so it cannot be a perfect square

So if I’m not wrong then none of these are perfect square? Which seems odd as that’s not an answer option. Or I could be wrong

Re: Which of the following is not a perfect square [#permalink]

Show Tags

04 Nov 2009, 01:31

Ahh yes you are right I didn't read it properly. Also to answer your original question I guess there is no need to factor all prime factors, just factor a few until you find that there are not an even number.

A perfect square will have exactly an even number of each of its factors. 81 for example: 81 = 9x9 = 3x3x3x3 which is essentially 2 sets of 3x3 Or: 36 = 6x6 = 2x3x2x3 which is 2 sets of 2x3

I think the red part needs some clarification:

A perfect square will have exactly an even number of each of its factors.

That's not true.

I think you meant that perfect square n^2, has even number of prime factors of n or in other words prime factors of n have even powers.

In your example: 81=3*3*3*3=3^4, but 81 has the factor 27, what about it? There are three 27 in 81. Or 36=6*6=2^2*3^2 but what about 12 which is factor of 36? There are three 12 in 36.

There are some tips about the perfect square though:

1. The number of distinct factors of a perfect square is ALWAYS ODD. 2. The sum of distinct factors of a perfect square is ALWAYS ODD. 4. A perfect square ALWAYS has an ODD number of Odd-factors, and EVEN number of Even-factors. 5. Perfect square always has even number of powers of prime factors.

Re: Which of the following is not a perfect square [#permalink]

Show Tags

02 Jan 2011, 08:38

Bunuel, is the concept of a perfect square tested on the GMAT? I have come across it several times on this forum, but I am not sure if it is tested on the GMAT. Thank you.

Bunuel, is the concept of a perfect square tested on the GMAT? I have come across it several times on this forum, but I am not sure if it is tested on the GMAT. Thank you.

What do you mean by "the concept of a perfect square"??? A perfect square, is just an integer that can be written as the square of some other integer, for example 16=4^2, is a perfect square.
_________________

Re: Which of the following is not a perfect square [#permalink]

Show Tags

02 Jan 2011, 08:55

What I mean is that I've come across several questions here on the forum that have a phrase "perfect square", and I have never heard of it before. So the reason I'm asking is if I have to pay attention to these questions (and read about some useful properties of perfect squares) or not?

What I mean is that I've come across several questions here on the forum that have a phrase "perfect square", and I have never heard of it before. So the reason I'm asking is if I have to pay attention to these questions (and read about some useful properties of perfect squares) or not?

Again: a perfect square, is just an integer that can be written as the square of some other integer, for example 16=4^2, is a perfect square. So perfect square is just a name of such integers as 1, 4, 9, 16, ... There are several properties of a perfect square, which might be useful while solving specific GMAT questions. Now, it's up to you to decide whether to study these question and properties or not.
_________________

Re: Which of the following is not a perfect square [#permalink]

Show Tags

09 Aug 2017, 12:21

Bunuel wrote:

yangsta8 wrote:

A perfect square will have exactly an even number of each of its factors. 81 for example: 81 = 9x9 = 3x3x3x3 which is essentially 2 sets of 3x3 Or: 36 = 6x6 = 2x3x2x3 which is 2 sets of 2x3

I think the red part needs some clarification:

A perfect square will have exactly an even number of each of its factors.

That's not true.

I think you meant that perfect square n^2, has even number of prime factors of n or in other words prime factors of n have even powers.

In your example: 81=3*3*3*3=3^4, but 81 has the factor 27, what about it? There are three 27 in 81. Or 36=6*6=2^2*3^2 but what about 12 which is factor of 36? There are three 12 in 36.

There are some tips about the perfect square though:

1. The number of distinct factors of a perfect square is ALWAYS ODD. 2. The sum of distinct factors of a perfect square is ALWAYS ODD. 4. A perfect square ALWAYS has an ODD number of Odd-factors, and EVEN number of Even-factors. 5. Perfect square always has even number of powers of prime factors.

Hope it helps.

Could you please prove these rules?

I know only that the total number of factors (of a perfect square) is odd. Could you clarify the others?