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PS  Factor (m04q31) [#permalink]
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17 Sep 2008, 14:34
A perfect number is defined as one for which the sum of all the unique factors less the number itself equals to the number. For instance, 6 is a perfect number, because the factors of 6 (apart from 6 itself) are 1, 2 and 3, and \(1 + 2 + 3 = 6\) . Which of the following is also a perfect number? (A) 12 (B) 20 (C) 28 (D) 48 (E) 60 Source: GMAT Club Tests  hardest GMAT questions



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Re: PS  Factor [#permalink]
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17 Sep 2008, 14:46
I just bruteforced it :
A 12: 1,2,3,4,6 ; sum = 16 B 20: 1,2,4,5,10 ; sum = 22 C 28: 1,2,4,7,14 ; sum = 28 Yes
Answer is (C)
Would be interested to know if there's a better way to do this.



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Re: PS  Factor [#permalink]
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17 Sep 2008, 19:09
Thanks guys .. under the presure of time .. I forgot to take into consideration 4 for 12.



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Re: PS  Factor [#permalink]
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17 Sep 2008, 21:40
There is not really a better way to do this other than realizing that the authors know you're going to have to figure out each answer and sum the numbers to determine if the factors (aside from the number itself) total the number. Because of this quasitrial & error, it seems that often the test makers will put the correct answer towards the end. I would start with C, D E, A B. That's the order I would work them in. Maybe here A first because 12 is a small number and there certainly are less numbers to total. 1, 2, 3, 4, & 6. That's clearly over 12. Then move to C or D. In the end, the safest bet is to just work all answers through and be diligent in making sure you rememebr ever factor. Even if you only save 15 seconds by getting done in 1 min 45 seconds on this question, when you do that on 8 questions, you're an entire question "ahead".
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Re: PS  Factor [#permalink]
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17 Sep 2008, 21:52
rao_1857 wrote: A perfect number is defined as one for which the sum of all the unique factors less the number itself equals to the number. For instance, 6 is a perfect number, because the factors of 6 (apart from 6 itself) are 1, 2 and 3, and \(1 + 2 + 3 = 6\) . Which of the following is also a perfect number?
a) 12 b) 20 c) 28 d) 48 e) 60 when there is to be plugin, i would start with C, the middle answer chcoice.
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Re: PS  Factor [#permalink]
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18 Sep 2008, 21:30
GMAT TIGER wrote: rao_1857 wrote: A perfect number is defined as one for which the sum of all the unique factors less the number itself equals to the number. For instance, 6 is a perfect number, because the factors of 6 (apart from 6 itself) are 1, 2 and 3, and \(1 + 2 + 3 = 6\) . Which of the following is also a perfect number?
a) 12 b) 20 c) 28 d) 48 e) 60 when there is to be plugin, i would start with C, the middle answer chcoice. Lets take the "luck" factor away from all this, I would start with B or D, if used B and need a higher number, then use D, if after that you need a lower one C is the answer, in case a higher is needed E is the one ( if D is used first same logic aplies). Like in the case a present choosing C as the first one will be the same if you need a higer number you have to use D or E, in case of a lower use A or B. Now assuming you did not get to the answer here you find that a maximum of two plugins must be done before getting there. The difference comes if you use B and need a lower you know the answer is A and if you start with D and need a higher the answer is E.
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Re: PS  Factor [#permalink]
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19 Sep 2008, 00:40
MRGiacalone wrote: Lets take the "luck" factor away from all this, I would start with B or D, if used B and need a higher number, then use D, if after that you need a lower one C is the answer, in case a higher is needed E is the one ( if D is used first same logic aplies). Like in the case a present choosing C as the first one will be the same if you need a higer number you have to use D or E, in case of a lower use A or B. Now assuming you did not get to the answer here you find that a maximum of two plugins must be done before getting there.
The difference comes if you use B and need a lower you know the answer is A and if you start with D and need a higher the answer is E.
Good technique !! But how is this applicable in this case because we just have to find the number which is perfect from the presented choices? Please elaborate Thanks
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Re: PS  Factor [#permalink]
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19 Sep 2008, 06:30
Or, you can just remember that the only perfect numbers less than a million are: 6 28 496 8128 Your choice. This is unlikely to be a GMAT type problem.
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Re: PS  Factor [#permalink]
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19 Sep 2008, 06:52
MRGiacalone wrote: GMAT TIGER wrote: rao_1857 wrote: A perfect number is defined as one for which the sum of all the unique factors less the number itself equals to the number. For instance, 6 is a perfect number, because the factors of 6 (apart from 6 itself) are 1, 2 and 3, and \(1 + 2 + 3 = 6\) . Which of the following is also a perfect number?
a) 12 b) 20 c) 28 d) 48 e) 60 when there is to be plugin, i would start with C, the middle answer chcoice. Lets take the "luck" factor away from all this, I would start with B or D, if used B and need a higher number, then use D, if after that you need a lower one C is the answer, in case a higher is needed E is the one ( if D is used first same logic aplies). Like in the case a present choosing C as the first one will be the same if you need a higer number you have to use D or E, in case of a lower use A or B. Now assuming you did not get to the answer here you find that a maximum of two plugins must be done before getting there. The difference comes if you use B and need a lower you know the answer is A and if you start with D and need a higher the answer is E. its all chance. either approach needs a max. of 3 attempts but if you start from C, you do not need to do back and forth: first hammer C then D and then finally E. if you start from B and go to D and then C, one may get confused. anybody has shorter approach?
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Re: PS  Factor [#permalink]
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19 Sep 2008, 09:22
I don't think both approaches need a max of 3 attemps, they need a max of 2, remember that on the GMAT time is everything, after plugingin two answers you don't need to plugin a third one just answer it and go to next. In this case is a bit more difficult but try the example below PS: Remainder Theory Posted: Mon Sep 15, 2008 5:33 pm When 10 is divided by the positive integer n, the remainder is n4. Which of the following could be the value of n ? A) 7 B) 9 C) 10 D) 11 E) 13 (original choices have been modified) Get to the right ecuation and try plugingin numbers for n. I'll start with B. 10 = 14, too high, I'll need a lower number, only 7 is left so answer is A and go to next. If I needed a higher number I would choose D, as my second attempt, after that if I need an even higher number E is your answer and, if a lower one is needed, C will be your answer. A max. of two attempts, and, without choosing the right answer as my first plugin by luck, I still have a chance of doing only one attempt.
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Re: PS  Factor [#permalink]
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18 Oct 2010, 06:57
I'm very familiar with the B or D, then adjust depending on whether you need a higher or lower number type approach. This will not work with the perfect number question this threat started with. If you try B) 20, and it doesn't work, then you still don't know if you need a higher or lower number. This question is not the same as an equation question where we will be able to analyze the result of plugging in one number and seeing if it was close or far away from the value given for the equation in the question. The B or D then higher/lower works well for plugging in numbers but this isn't a typical plugging the numbers question. It's a bruteforce question where you just have to figure out which of the 5 possibilities is correct. MRGiacalone wrote: I don't think both approaches need a max of 3 attemps, they need a max of 2, remember that on the GMAT time is everything, after plugingin two answers you don't need to plugin a third one just answer it and go to next. In this case is a bit more difficult but try the example below
PS: Remainder Theory Posted: Mon Sep 15, 2008 5:33 pm When 10 is divided by the positive integer n, the remainder is n4. Which of the following could be the value of n ? A) 7 B) 9 C) 10 D) 11 E) 13 (original choices have been modified)
Get to the right ecuation and try plugingin numbers for n.
I'll start with B. 10 = 14, too high, I'll need a lower number, only 7 is left so answer is A and go to next. If I needed a higher number I would choose D, as my second attempt, after that if I need an even higher number E is your answer and, if a lower one is needed, C will be your answer. A max. of two attempts, and, without choosing the right answer as my first plugin by luck, I still have a chance of doing only one attempt.
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Re: PS  Factor (m04q31) [#permalink]
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18 Oct 2010, 15:07
Worked this out quickly by knowing bases. Base 60 and base 10 are the two common bases we use, base 10 for counting, base 60 for time. Both of these are useful because they have a lot of factors. Base 60 is divisible by 1,2,3,4,6. Base 10 divisible by 1,2,5.
12 => base 60 20 => base 10 28 => base 7 (most likely this, check it first) 48 => base 60 60 => base 60



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Re: PS  Factor (m04q31) [#permalink]
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18 Oct 2010, 16:12
This is a really tough question, and I would guess beyond GMAT level as well. There is no easy way to check for perfect numbers very quickly except knowing that the first four are 6,28,496,8128 ... which no sane person should know by heart anyway (for the record, I took it off wikipedia and don't remember them by heart either !!)
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Re: PS  Factor (m04q31) [#permalink]
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19 Oct 2010, 08:16
From the GMAT Club math book  Finding the Sum of the Factors of an Integer
First make prime factorization of an integer n=a^p*b^q*c^r, where a, b, and c are prime factors of n and p, q, and r are their powers.
The sum of factors of n will be expressed by the formula: \(\frac{(a^{p+1}1)*(b^{q+1}1)*(c^{r+1}1)}{(a1)*(b1)*(c1)}\)
Example: Finding the sum of all factors of 450: 450=2^1*3^2*5^2
The sum of all factors of 450 is \(\frac{(2^{1+1}1)*(3^{2+1}1)*(5^{2+1}1)}{(21)*(31)*(51)}=\frac{3*26*124}{1*2*4}\)=1209Is this technique worth memorizing for the GMAT?



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Re: PS  Factor (m04q31) [#permalink]
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19 Oct 2010, 09:02
Wow, I'm surprised that many of you say it's a difficult question. I'm not as good as many of you but could anyways answer it correctly in a short time. I didn't see it difficult because the stem tells you what the perfect number is. Otherwise I would have had to guess...



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Re: PS  Factor [#permalink]
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21 Oct 2011, 01:47
mmond4 wrote: I just bruteforced it :
A 12: 1,2,3,4,6 ; sum = 16 B 20: 1,2,4,5,10 ; sum = 22 C 28: 1,2,4,7,14 ; sum = 28 Yes
Answer is (C)
Would be interested to know if there's a better way to do this. Such questions requries to factor all the answers. My stratergy for such question is alsways to start with middle number that is C
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Re: PS  Factor (m04q31) [#permalink]
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22 Oct 2012, 05:24
Prepared test takers are always quick in deciding how to approach a question. Typically, one should decide his/her approach not more than 10 seconds after reading the questions. Next step would be stick to your approach with reasonable conviction; however, one should bear in mind that the key to excelling on quant is flexibility, so there is no need not to try another approach if the first does not work. DO's Pick a method and start solving Be flexibletry another if the first is not working Start writing stuff down as soon as you understand what is being asked DONT's Don't stare at a question for too long Don't attempt to solve the whole question in your head Cheers, Der alte Fritz
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Re: PS  Factor (m04q31)
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