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# When do we stop pluggin in?

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Director
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When do we stop pluggin in? [#permalink]  03 Nov 2012, 07:15
is the positive integer p prime?

1)p=n^2 -n +41

Is (1) sufficient?
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Re: When do we stop pluggin in? [#permalink]  03 Nov 2012, 08:19
Sachin9 wrote:
is the positive integer p prime?

1)p=n^2 -n +41

Is (1) sufficient?

I would say when testing numbers pick random numbers and test with odd and even numbers. I would try 1 2 and 5 usually if you test 3 cases and its you get similar results its usually sufficient

when n=1 then 1 - 1 + 41 = 41 prime
n=2 4-2+41 = 43 prime

25-5+41 = 61 prime

Hence sufficient.
Director
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 547
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Followers: 2

Kudos [?]: 45 [0], given: 562

Re: When do we stop pluggin in? [#permalink]  03 Nov 2012, 08:47
its actually insufficient..
use 41 and you find that p is not prime..

so I was wondering when to stop pluggin in
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : end-of-my-gmat-journey-149328.html#p1197992

Veritas Prep GMAT Instructor
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Re: When do we stop pluggin in? [#permalink]  06 Nov 2012, 03:07
1
KUDOS
Expert's post
Sachin9 wrote:
its actually insufficient..
use 41 and you find that p is not prime..

so I was wondering when to stop pluggin in

You cannot plug in to prove something. You need to think of the logic why something is true or not true.

Here: p=n^2 -n +41

You want to figure out whether p is prime. Put n = 1, p = 41 (prime)
Put n = 2, p = 43 (prime)
You see there is a pattern. p is prime in these cases.

So now think, will p always be prime?
A prime number has only two factors: 1 and itself. If p can be split into two factors other than 1 and itself, it means it is not prime. (it is much harder to prove that p is prime than to prove that p is not prime). Try to look for a case where p may not be prime.

p=n^2 -n +41 = n(n - 1) + 41

Can you split p into two factors (such that one of them is not 1)? You can if you are able to take something common from n(n-1) and 41. When is this possible?
When n = 41, n = 42 etc

41*40 + 41 = p
p = 41^2

42*41 + 41 = p
p = 41*43

82*81 + 41 = p
p = 41*163

In these cases and many more such cases, p is not prime.
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Karishma
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Director Status: Gonna rock this time!!! Joined: 22 Jul 2012 Posts: 547 Location: India GMAT 1: 640 Q43 V34 GMAT 2: 630 Q47 V29 WE: Information Technology (Computer Software) Followers: 2 Kudos [?]: 45 [0], given: 562 Re: When do we stop pluggin in? [#permalink] 06 Nov 2012, 23:29 Can you split p into two factors (such that one of them is not 1)? You can if you are able to take something common from n(n-1) and 41. When is this possible? When n = 41, n = 42 etc 41*40 + 41 = p p = 41^2 42*41 + 41 = p p = 41*43 82*81 + 41 = p p = 41*163 Thanks Karishma, but I didn't understand the above.. specifically 41*40 + 41 = p p = 41^2 and You can if you are able to take something common from n(n-1) and 41 Please help. . _________________ hope is a good thing, maybe the best of things. And no good thing ever dies. Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595 My GMAT Journey : end-of-my-gmat-journey-149328.html#p1197992 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6062 Location: Pune, India Followers: 1601 Kudos [?]: 8966 [1] , given: 195 Re: When do we stop pluggin in? [#permalink] 07 Nov 2012, 03:54 1 This post received KUDOS Expert's post Sachin9 wrote: Can you split p into two factors (such that one of them is not 1)? You can if you are able to take something common from n(n-1) and 41. When is this possible? When n = 41, n = 42 etc 41*40 + 41 = p p = 41^2 42*41 + 41 = p p = 41*43 82*81 + 41 = p p = 41*163 Thanks Karishma, but I didn't understand the above.. specifically 41*40 + 41 = p p = 41^2 and You can if you are able to take something common from n(n-1) and 41 Please help. . A prime number has no factors other than 1 and itself. If I say that x = a*b and a and b are positive non-1 integers, can I say that x is not prime? Sure. x has two factors a and b which are not 1 (and hence not x either). What we are trying to do here is trying to find whether there is a similar pair of factors that p has. p = n(n-1) + 41 p can have two factors if we can express p like this: p = (..)*(...) To do that, we will need to take something common from n(n-1) and 41. Say if n = 41, then we can take something common p = 41*40 + 41 p = (41) *(40 + 1) Notice that p is the product of 2 factors in this case. Neither one of the factors is 1. Hence, p is not prime. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Director
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 547
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Followers: 2

Kudos [?]: 45 [0], given: 562

Re: When do we stop pluggin in? [#permalink]  16 Nov 2012, 06:38
Thanks a lot Karishma, Prime nos seem easy now

Do you have any blogs on veritas website on prime nos?
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : end-of-my-gmat-journey-149328.html#p1197992

Re: When do we stop pluggin in?   [#permalink] 16 Nov 2012, 06:38
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