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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] New post 20 Dec 2012, 05:35
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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
[Reveal] Spoiler: OA
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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink] New post 20 Dec 2012, 05:36
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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.
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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink] New post 19 Mar 2014, 20:27
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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink] New post 19 Mar 2014, 21:17
7150 = 715*5 = 13*55*5*2 = 13*11*5*5*2
The only mistake one could do is count 5 twice

Answer - D
Time Taken - 00:46
Difficulty level - 600
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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink] New post 12 Sep 2014, 22:31
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] New post 13 Sep 2014, 06:12
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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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

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Re: How many prime numbers between 1 and 100 are factors of 7,15 [#permalink] New post 29 Mar 2015, 14:06
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] New post 29 Mar 2015, 18:01
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.

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Re: How many prime numbers between 1 and 100 are factors of 7,15   [#permalink] 29 Mar 2015, 18:01
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