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Which of the following is not a perfect square [#permalink]
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04 Nov 2009, 00:22
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Which of the following is not a perfect square 1. 100856 2. 325137 3. 945729 4. All of these Hint value of perfect sq has to end in 1,4,5,6,9...so option 2 is definately not a perfect square But how to find the rest...is ther any shortcut or will we have to find the prime factors of all n bring them to standard form
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Re: Which of the following is not a perfect square [#permalink]
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04 Nov 2009, 00:44
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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



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



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



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Re: Which of the following is not a perfect square [#permalink]
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04 Nov 2009, 01:32
Quote: A perfect square will have exactly an even number of each of its factors. A simple point, but worth remembering, Kudos!



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Re: Which of the following is not a perfect square [#permalink]
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04 Nov 2009, 23:57
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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 Oddfactors, and EVEN number of Evenfactors. 5. Perfect square always has even number of powers of prime factors. Hope it helps.
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Re: Which of the following is not a perfect square [#permalink]
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05 Nov 2009, 00:07
Quote: A perfect square will have exactly an even number of each of its factors. yeah, it holds only for prime factors



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Re: Which of the following is not a perfect square [#permalink]
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05 Nov 2009, 00:15
Man, there should be a way to add some posts to favorites, to "memories" or something like that. The only method available is to save permalinks . . .



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Re: Which of the following is not a perfect square [#permalink]
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05 Nov 2009, 22:02
shalva wrote: Quote: A perfect square will have exactly an even number of each of its factors. yeah, it holds only for prime factors Yes you are right. Thanks for the clarification



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



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Re: Which of the following is not a perfect square [#permalink]
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02 Jan 2011, 08:47



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



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Re: Which of the following is not a perfect square [#permalink]
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02 Jan 2011, 09:04
nonameee wrote: 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.
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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.
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Re: Which of the following is not a perfect square [#permalink]
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02 Jan 2011, 09:07
OK. Thanks. I guess I have to study it.



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Re: Which of the following is not a perfect square [#permalink]
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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 Oddfactors, and EVEN number of Evenfactors. 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? Thanks in advance.




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