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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

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19 Mar 2014, 20:27

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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]

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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
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My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

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]

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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

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My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

Unfortunately, that logic is NOT correct (and it was lucky that you ended up with the correct answer). Here's a simple example that proves the logic is NOT correct.

17 has one prime factor: 17

Using the logic you described... 17 = 10+7 10 has prime factors of 2 and 5 and 7 has one prime factor: 7

However, these prime factors (re: 2, 5 and 7) are NOT the same prime factors of 17 (re: 17) and the NUMBER of prime factors is also different.

Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

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01 May 2016, 11:40

EMPOWERgmatRichC wrote:

Hi colorblind,

Unfortunately, that logic is NOT correct (and it was lucky that you ended up with the correct answer). Here's a simple example that proves the logic is NOT correct.

17 has one prime factor: 17

Using the logic you described... 17 = 10+7 10 has prime factors of 2 and 5 and 7 has one prime factor: 7

However, these prime factors (re: 2, 5 and 7) are NOT the same prime factors of 17 (re: 17) and the NUMBER of prime factors is also different.

GMAT assassins aren't born, they're made, Rich

Rich,

Thanks for clarifying with an example.
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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

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02 May 2016, 06:22

Walkabout wrote:

How many prime numbers between 1 and 100 are factors of 7,150 ?

(A) One (B) Two (C) Three (D) Four (E) Five

We start by prime factoring 7,150.

7,150 = 715 x 10 = 143 x 5 x 10

At this point we must be careful. They WANT you to think that 143 is prime. Using our divisibility rules, however, we can determine that 143 is divisible by 11. A number is divisible by 11 if the sum of the odd-numbered place digits minus the sum of the even-numbered place digits is divisible by 11. We can test 143 to prove this:

1 + 3 – 4 = 4 – 4 = 0

Since zero is divisible by 11, we know that 143 is divisible by 11. We can now finish the prime factorization.

143 x 5 x 10 = 11 x 13 x 5 x 5 x 2

11 x 13 x 5^2 x 2

Thus we can see that there are 4 different prime factors in 7,150.

Answer is D.
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Jeffrey Miller Jeffrey Miller Head of GMAT Instruction

Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

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03 Dec 2016, 20:08

Great Question. So many nice takeaways. When i saw the first line i rushed to write the prime factors between 1-100 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101

But wait. It would be a HUGE task to check for each of these numbers. And GMAT would never ask us that. noted i prime factored 7150 and saw that it has only four prime factors which are all in the range (1,100) Hence E

Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

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09 Jan 2017, 19:19

NoHalfMeasures wrote:

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

Hi. Actually there is a formulae. In oder to check to check whether a given number is prime or not => We just need to check the divisibility with all the primes less than or equal to the square root of that number. Question in case is 143 \(√143\) = 11.something So we need to check the divisibility with primes less than or equal to 11.somthing => 2,3,5,7,11

Another example => Say 211 Here \(√211\) = 14.something Hence we need to check the divisibility with all the primes less than or equal to 14.something => 2,3,5,7,11,13 211 is actually a prime number as every divisibly test fails.

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