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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]
19 Mar 2014, 20:27
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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]
29 Mar 2015, 18:01
3
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Expert's post
Hi elisabettaportioli,
The speed with which you 'prime-factor' 7150 into its 'pieces' is likely going to be influenced by the 'first' number you factor out.
Looking at 7150, you could easily start with a 2 (because 7150 is even), a 5 (because 7150 ends in a 0) or a 10 (also since it ends in a 0).
I actually started with 50, since 50 divides into 100 twice.....7100 = (71x2) fifties....
So 7150 = 142 fifties + 1 fifty = (50)(143)
The (50) can be quickly broken down into (2)(5)(5)
Now, looking at the 143, we know that NO even numbers will divide in (since even numbers do NOT divide into odd numbers). If you know the 'rule of 3', then you know that 3 does NOT divide in. Since 3 doesn't divide in, 9 won't divide in either. 5 won't divide in for obvious reasons. Thus, we're really left with just a handful of possibilities:
1) 143 might be prime 2) 7, 11 and/or 13 might divide in
It's pretty easy to eliminate 7 as an option (it divides into 14, but not 3). Once you find that 11 divides in, you end up with the 13 by default.
Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]
01 Dec 2015, 05:16
EMPOWERgmatRichC, Bunuel, VeritasPrepKarishma: I stopped at 143 as felt it was a prime number after trying 3, 5, 7 n 9. I didnt go to 11. If i had taken that one extra step I would have gotten it right. But how far one should go? Here it is 11 but on some other questions it could be 17, 19, 23 etc. Is there a neat formula too tell all prime factors of a number? thanks _________________
Please consider giving 'kudos' if you like my post and want to thank
Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]
01 Dec 2015, 20:52
1
This post received KUDOS
Expert's post
Hi MensaNumber,
When you say that you tried 3, 5, 7 and 9, what actual 'work' did you do? I ask because your Quant skills are clearly strong (you have a Q48 to prove it), so I would guess that you would have figured out rather quickly that those single-digit primes wouldn't divide into 143.
Since those smaller primes don't divide in, there can't be that many left to check out (and checking EITHER 11 or 13 would have been enough work to correctly answer the question). At it's core, this is a test of 'thoroughness' - it's true that most people wouldn't think to try dividing 11, but most people can't score Q48+, so you have to decide what 'extra work' (if any) YOU'RE willing to do to be thorough, prove that your answer is correct and pick up those extra points.
Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]
01 Dec 2015, 22:41
Hi empowergmatrichc:
Thanks for you reply. I think I agree - ultimately it comes down to conscientiousness and this one quality determines who will be extraordinary successful and who will be just successful in GMAT/life.
EMPOWERgmatRichC wrote:
Hi MensaNumber,
When you say that you tried 3, 5, 7 and 9, what actual 'work' did you do? I ask because your Quant skills are clearly strong (you have a Q48 to prove it), so I would guess that you would have figured out rather quickly that those single-digit primes wouldn't divide into 143.
Since those smaller primes don't divide in, there can't be that many left to check out (and checking EITHER 11 or 13 would have been enough work to correctly answer the question). At it's core, this is a test of 'thoroughness' - it's true that most people wouldn't think to try dividing 11, but most people can't score Q48+, so you have to decide what 'extra work' (if any) YOU'RE willing to do to be thorough, prove that your answer is correct and pick up those extra points.
GMAT assassins aren't born, they're made, Rich
_________________
Please consider giving 'kudos' if you like my post and want to thank
gmatclubot
Re: How many prime numbers between 1 and 100 are factors of 7,15
[#permalink]
01 Dec 2015, 22:41
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