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GMAT Maths Book Question (Perfect Squares P.6)

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

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New post 09 Oct 2017, 03:52
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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

Kudos [?]: 1 [0], given: 12

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Joined: 02 Sep 2009
Posts: 42338

Kudos [?]: 133141 [0], given: 12415

Re: GMAT Maths Book Question (Perfect Squares P.6) [#permalink]

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New post 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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 133141 [0], given: 12415

Intern
Intern
avatar
B
Joined: 09 Sep 2014
Posts: 5

Kudos [?]: 1 [0], given: 12

Re: GMAT Maths Book Question (Perfect Squares P.6) [#permalink]

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New post 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..

Kudos [?]: 1 [0], given: 12

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42338

Kudos [?]: 133141 [0], given: 12415

Re: GMAT Maths Book Question (Perfect Squares P.6) [#permalink]

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New post 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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 133141 [0], given: 12415

Re: GMAT Maths Book Question (Perfect Squares P.6)   [#permalink] 11 Oct 2017, 20:44
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GMAT Maths Book Question (Perfect Squares P.6)

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