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If Z is an integer, is Z prime?

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If Z is an integer, is Z prime?  [#permalink]

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New post 12 May 2011, 03:49
2
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A
B
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If Z is an integer, is Z prime?

(1) 15! < Z
(2) 17! + 2 <= Z <= 17! + 17

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Re: Is Z prime?  [#permalink]

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New post 15 May 2011, 19:54
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@ akhileshgupta05:
Satment 1 is not sufficient

For statement 2 possible values of z are

17! + 2 is Divisible by 2 . Hence not prime
17! + 3 is Divisible by 3 . Hence not prime
17! + 4 is Divisible by 4 . Hence not prime
17! + 5 is Divisible by 5 . Hence not prime
17! + 6 is Divisible by 6 . Hence not prime
17! + 7 is Divisible by 7 . Hence not prime
17! + 8 is Divisible by 8 . Hence not prime
17! + 9 is Divisible by 9 . Hence not prime
17! + 10 is Divisible by 10 . Hence not prime
17! + 11 is Divisible by 11 . Hence not prime
17! + 12 is Divisible by 12 . Hence not prime
17! + 13 is Divisible by 13 . Hence not prime
17! + 14 is Divisible by 14 . Hence not prime
17! + 15 is Divisible by 15 . Hence not prime
17! + 16 is Divisible by 16 . Hence not prime
17! + 17 is Divisible by 17 . Hence not prime


In any case z cannot not be prime hence answer is B
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Re: Is Z prime?  [#permalink]

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New post 12 May 2011, 04:14
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The answer is B:

17! + 2 <= Z <= 17! + 17 means that z is like 17! + 2, 17! + 3 etc. So you can factor out a common integer from the expressions that will divide 17! + n (2 <= n <=17), e.g. 2 divides 17! + 2 because 17! also includes 2.

So z is not a prime.

(1) is not sufficient because there are primes and non-primes above 15!

Please ask if you have any more queries.
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Re: Is Z prime?  [#permalink]

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Re: Is Z prime?  [#permalink]

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New post 12 May 2011, 07:45
a z can be 15! + 1 thereby giving co-prime numbers or 15!+17

b z = 17! + 2 = 2[(1*3*4*17) +1] similarly 3,4 till 17 can be factored out.

Thus B.
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Re: Is Z prime?  [#permalink]

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New post 12 May 2011, 19:16
1. Not sufficient.

z>15!

z may or may not be prime

2. Sufficient.

z cannot be prime as all the numbers in that range will atleast another factor other than 1 and the number.

Answer is B.
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Re: Is Z prime?  [#permalink]

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New post 15 May 2011, 07:44
I did not understand the explanation.

Could someone please elaborate a little more ?
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Re: Is Z prime?  [#permalink]

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New post 15 May 2011, 19:59
hussi9 wrote:
@ akhileshgupta05:
Satment 1 is not sufficient

For statement 2 possible values of z are

17! + 2 is Divisible by 2 . Hence not prime
17! + 3 is Divisible by 3 . Hence not prime
17! + 4 is Divisible by 4 . Hence not prime
17! + 5 is Divisible by 5 . Hence not prime
17! + 6 is Divisible by 6 . Hence not prime
17! + 7 is Divisible by 7 . Hence not prime
17! + 8 is Divisible by 8 . Hence not prime
17! + 9 is Divisible by 9 . Hence not prime
17! + 10 is Divisible by 10 . Hence not prime
17! + 11 is Divisible by 11 . Hence not prime
17! + 12 is Divisible by 12 . Hence not prime
17! + 13 is Divisible by 13 . Hence not prime
17! + 14 is Divisible by 14 . Hence not prime
17! + 15 is Divisible by 15 . Hence not prime
17! + 16 is Divisible by 16 . Hence not prime
17! + 17 is Divisible by 17 . Hence not prime


In any case z cannot not be prime hence answer is B


Oh yes! thats correct if it would have been 17! + 1 instead of 17!+2 it would be insufficient. But rest all values are not prime. Thank you for the explanation.

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Re: Is Z prime?  [#permalink]

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New post 15 May 2011, 20:04
akhileshgupta05 wrote:

Oh yes! thats correct if it would have been 17! + 1 instead of 17!+2 it would be insufficient. But rest all values are not prime. Thank you for the explanation.

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How did u figured out that 17!+1 is a prime number ?
I dont think thats safe to assume unless you really did calculated


Cause

17!+1 will be insufficient only if 17!+1 is a prime number.
I believe It is not practice to figure that out manually hence it is not included in the range.

May be you can solve and let us know ;)
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Re: Is Z prime?  [#permalink]

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New post 15 May 2011, 21:11
Very simple, if one thinks logically. thank you Fluke for the trick here.
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Re: Is Z prime?  [#permalink]

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New post 03 Nov 2011, 12:21
Tricky one. Thanks.
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Re: Is Z prime?  [#permalink]

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New post 03 Nov 2011, 17:41
InspiredAnimal wrote:
If Z is an integer, is Z prime?

1) 15!<Z

2) 17! + 2 <= Z <= 17! + 17

I don't understand the official explanation, can anyone help out here?


2 is sufficient because if z is an integer, then z can only be 17!+k, and 2<=k<=17
but 17! has all the factors from 2 to 17, so z=k(17!/k+1), and is not a prime
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Re: If Z is an integer, is Z prime?  [#permalink]

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New post 28 Oct 2018, 04:24
hussi9 wrote:
@ akhileshgupta05:
Satment 1 is not sufficient

For statement 2 possible values of z are

17! + 2 is Divisible by 2 . Hence not prime
17! + 3 is Divisible by 3 . Hence not prime
17! + 4 is Divisible by 4 . Hence not prime
17! + 5 is Divisible by 5 . Hence not prime
17! + 6 is Divisible by 6 . Hence not prime
17! + 7 is Divisible by 7 . Hence not prime
17! + 8 is Divisible by 8 . Hence not prime
17! + 9 is Divisible by 9 . Hence not prime
17! + 10 is Divisible by 10 . Hence not prime
17! + 11 is Divisible by 11 . Hence not prime
17! + 12 is Divisible by 12 . Hence not prime
17! + 13 is Divisible by 13 . Hence not prime
17! + 14 is Divisible by 14 . Hence not prime
17! + 15 is Divisible by 15 . Hence not prime
17! + 16 is Divisible by 16 . Hence not prime
17! + 17 is Divisible by 17 . Hence not prime


In any case z cannot not be prime hence answer is B


But how do you know all of the above? Did you calculate it or is this a known fact?
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Re: If Z is an integer, is Z prime?  [#permalink]

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New post 28 Oct 2018, 05:31
barbz91 wrote:
hussi9 wrote:
@ akhileshgupta05:
Satment 1 is not sufficient

For statement 2 possible values of z are

17! + 2 is Divisible by 2 . Hence not prime
17! + 3 is Divisible by 3 . Hence not prime
17! + 4 is Divisible by 4 . Hence not prime
17! + 5 is Divisible by 5 . Hence not prime
17! + 6 is Divisible by 6 . Hence not prime
17! + 7 is Divisible by 7 . Hence not prime
17! + 8 is Divisible by 8 . Hence not prime
17! + 9 is Divisible by 9 . Hence not prime
17! + 10 is Divisible by 10 . Hence not prime
17! + 11 is Divisible by 11 . Hence not prime
17! + 12 is Divisible by 12 . Hence not prime
17! + 13 is Divisible by 13 . Hence not prime
17! + 14 is Divisible by 14 . Hence not prime
17! + 15 is Divisible by 15 . Hence not prime
17! + 16 is Divisible by 16 . Hence not prime
17! + 17 is Divisible by 17 . Hence not prime


In any case z cannot not be prime hence answer is B


But how do you know all of the above? Did you calculate it or is this a known fact?


They didn't: it's just logic.
I'll try to explain it this way:
17! Already includes the product of all the numbers from 1 to 17, hence, by adding n | 2<n<17 to a number which already is a multiple of the number you are adding, will give you as a result a number which is still divisible by the n you are adding. Thus, B is sufficient

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Re: If Z is an integer, is Z prime? &nbs [#permalink] 28 Oct 2018, 05:31
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