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How many prime numbers between 1 and 100 are factors of 7,15

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

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

(A) One
(B) Two
(C) Three
(D) Four
(E) Five
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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

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

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

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New post 19 Mar 2014, 22:17
7150 = 715*5 = 13*55*5*2 = 13*11*5*5*2
The only mistake one could do is count 5 twice

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

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New post 12 Sep 2014, 23:31
Bunuel wrote:
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


Make prime factorization of 7,150 --> \(7,150=2*5^2*11*13\). So, 4 prime numbers between 1 and 100 (namely 2, 5, 11, and 13) are factors of 7,150.

Answer: D.



when they didn't mention distinct prime number. why we shouldn't consider 5 twice?
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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

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New post 13 Sep 2014, 07:12
Expert's post
luckyme17187 wrote:
Bunuel wrote:
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


Make prime factorization of 7,150 --> \(7,150=2*5^2*11*13\). So, 4 prime numbers between 1 and 100 (namely 2, 5, 11, and 13) are factors of 7,150.

Answer: D.



when they didn't mention distinct prime number. why we shouldn't consider 5 twice?


The questions asks about the number of primes which are factors of 7,150. Why should we count any prime more than once?
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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

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New post 29 Mar 2015, 15:06
Bunuel
Bunuel wrote:
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


Make prime factorization of 7,150 --> \(7,150=2*5^2*11*13\). So, 4 prime numbers between 1 and 100 (namely 2, 5, 11, and 13) are factors of 7,150.

Answer: D.


Bunuel,

Do you have any fast tricks to understand that 7,150 is divisible by 11 and 13?

The only silly mistake I made was to miss 11 and 13 as prime factors of 7150.

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

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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.

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

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New post 20 Jun 2015, 13:11
I noticed from past Quant problems that GMAT likes to use number 143. So it is better to remember that 143=11*13.
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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

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New post 01 Dec 2015, 06:16
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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How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

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Hi NoHalfMeasures,

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.

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Last edited by EMPOWERgmatRichC on 01 May 2016, 11:26, edited 1 time in total.
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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

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New post 01 Dec 2015, 23:41
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.

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

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New post 01 May 2016, 10:11
EMPOWERgmatRichC, Bunuel, VeritasPrepKarishma:

Here is my method (and I am guessing this is not the right approach, but wanted to confirm):

7150 = 7000 + 150
7000 = 7 * 1000 (so we have 7, 5 & 2)
150 = 3 * 50 (so we have 3, 5 & 2)

combining both we have 2, 3, 5 & 7 as prime numbers.

At the end, I am still getting the same number of prime numbers for 7150, albeit different values (maybe coincidence).

I will be trying this with the next similar questions I come across, till then any help....greatly appreciated.
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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink]

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New post 01 May 2016, 11:30
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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.

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

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New post 01 May 2016, 12:40
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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New post 02 May 2016, 07:22
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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Re: How many prime numbers between 1 and 100 are factors of 7,15   [#permalink] 02 May 2016, 07:22
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