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# GMAT Maths Book Question (Perfect Squares P.6)

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Intern
Joined: 09 Sep 2014
Posts: 4
GMAT Maths Book Question (Perfect Squares P.6)  [#permalink]

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09 Oct 2017, 03:52
1
Hii guys..
Greetings..
I'm currently using the GMAT club maths book to prepare for the GMAT and I had a question regarding perfect squares in P6 of the maths book..
I tried applying these rules to a perfect square (ex 144) and some of them didn't work.. Would you please illustrate using an example how these rules "always" hold as the book says..
Rules:
" A perfect square, is an integer that can be written as the square of some other integer. For example 16=4^2, is an
perfect square.

There are some tips about the perfect square:
• The number of distinct factors of a perfect square is ALWAYS ODD.
• The sum of distinct factors of a perfect square is ALWAYS ODD.
• A perfect square ALWAYS has an ODD number of Odd-factors, and EVEN number of Even-factors.
• Perfect square always has even number of powers of prime factors. "

Ex. 144= (3^2)*(2^4)
Rules 2 and 4 don't apply here..

Thanks and have a great day!
Best Regards,
Reem
Math Expert
Joined: 02 Sep 2009
Posts: 49913
Re: GMAT Maths Book Question (Perfect Squares P.6)  [#permalink]

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09 Oct 2017, 04:00
reemel3bd wrote:
Hii guys..
Greetings..
I'm currently using the GMAT club maths book to prepare for the GMAT and I had a question regarding perfect squares in P6 of the maths book..
I tried applying these rules to a perfect square (ex 144) and some of them didn't work.. Would you please illustrate using an example how these rules "always" hold as the book says..
Rules:
" A perfect square, is an integer that can be written as the square of some other integer. For example 16=4^2, is an
perfect square.

There are some tips about the perfect square:
• The number of distinct factors of a perfect square is ALWAYS ODD.
• The sum of distinct factors of a perfect square is ALWAYS ODD.
• A perfect square ALWAYS has an ODD number of Odd-factors, and EVEN number of Even-factors.
• Perfect square always has even number of powers of prime factors. "

Ex. 144= (3^2)*(2^4)
Rules 2 and 4 don't apply here..

Thanks and have a great day!
Best Regards,
Reem

Why not???

144= (3^2)*(2^4), the powers of primes are even.

144 has 15 factors: 1 | 2 | 3 | 4 | 6 | 8 | 9 | 12 | 16 | 18 | 24 | 36 | 48 | 72 | 144. The sum = 403 = odd.
_________________
Intern
Joined: 09 Sep 2014
Posts: 4
Re: GMAT Maths Book Question (Perfect Squares P.6)  [#permalink]

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11 Oct 2017, 14:25
Bunuel wrote:
reemel3bd wrote:
Hii guys..
Greetings..
I'm currently using the GMAT club maths book to prepare for the GMAT and I had a question regarding perfect squares in P6 of the maths book..
I tried applying these rules to a perfect square (ex 144) and some of them didn't work.. Would you please illustrate using an example how these rules "always" hold as the book says..
Rules:
" A perfect square, is an integer that can be written as the square of some other integer. For example 16=4^2, is an
perfect square.

There are some tips about the perfect square:
• The number of distinct factors of a perfect square is ALWAYS ODD.
• The sum of distinct factors of a perfect square is ALWAYS ODD.
• A perfect square ALWAYS has an ODD number of Odd-factors, and EVEN number of Even-factors.
• Perfect square always has even number of powers of prime factors. "

Ex. 144= (3^2)*(2^4)
Rules 2 and 4 don't apply here..

Thanks and have a great day!
Best Regards,
Reem

Why not???

144= (3^2)*(2^4), the powers of primes are even.

144 has 15 factors: 1 | 2 | 3 | 4 | 6 | 8 | 9 | 12 | 16 | 18 | 24 | 36 | 48 | 72 | 144. The sum = 403 = odd.

Now I get it.. Thanks..
Is there a faster way to check if a number is a perfect square ??
If such question shows up on the exam, that would be very time-consuming to do..
Thank you..
Math Expert
Joined: 02 Sep 2009
Posts: 49913
Re: GMAT Maths Book Question (Perfect Squares P.6)  [#permalink]

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11 Oct 2017, 20:44
reemel3bd wrote:
Bunuel wrote:
reemel3bd wrote:
Hii guys..
Greetings..
I'm currently using the GMAT club maths book to prepare for the GMAT and I had a question regarding perfect squares in P6 of the maths book..
I tried applying these rules to a perfect square (ex 144) and some of them didn't work.. Would you please illustrate using an example how these rules "always" hold as the book says..
Rules:
" A perfect square, is an integer that can be written as the square of some other integer. For example 16=4^2, is an
perfect square.

There are some tips about the perfect square:
• The number of distinct factors of a perfect square is ALWAYS ODD.
• The sum of distinct factors of a perfect square is ALWAYS ODD.
• A perfect square ALWAYS has an ODD number of Odd-factors, and EVEN number of Even-factors.
• Perfect square always has even number of powers of prime factors. "

Ex. 144= (3^2)*(2^4)
Rules 2 and 4 don't apply here..

Thanks and have a great day!
Best Regards,
Reem

Why not???

144= (3^2)*(2^4), the powers of primes are even.

144 has 15 factors: 1 | 2 | 3 | 4 | 6 | 8 | 9 | 12 | 16 | 18 | 24 | 36 | 48 | 72 | 144. The sum = 403 = odd.

Now I get it.. Thanks..
Is there a faster way to check if a number is a perfect square ??
If such question shows up on the exam, that would be very time-consuming to do..
Thank you..

You should prime factorise a number a check the powers of its primes. It's not that hard to do.
_________________
Re: GMAT Maths Book Question (Perfect Squares P.6) &nbs [#permalink] 11 Oct 2017, 20:44
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