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09 Oct 2017, 03:52
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Bookmarks
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
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
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09 Oct 2017, 04:00
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reemel3bd
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.
11 Oct 2017, 14:25
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Bunuel
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..
