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# divisibility & primes

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Manager
Joined: 08 Sep 2010
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divisibility & primes [#permalink]  17 Jun 2011, 12:07
00:00

Difficulty:

55% (hard)

Question Stats:

67% (01:34) correct 33% (00:41) wrong based on 15 sessions
please explain how (2) is insufficient

the only way for n to be odd is even+odd = odd. the only even prime = 2. so then ten n = even prime + odd prime.??? whys that wrong?
[Reveal] Spoiler: OA

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Math Forum Moderator
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Kudos [?]: 1259 [0], given: 376

Re: divisibility & primes [#permalink]  17 Jun 2011, 12:13
386390 wrote:
please explain how (2) is insufficient

the only way for n to be odd is even+odd = odd. the only even prime = 2. so then ten n = even prime + odd prime.??? whys that wrong?

n=5
n=11

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Kudos [?]: 8 [0], given: 4

Re: divisibility & primes [#permalink]  17 Jun 2011, 12:18
fluke wrote:
n=5
n=11

ahh.....

3+2=5
9+2=11
^ not a prime

I guess I fell in my own trap. whats the key lesson that i can make a note of?
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Posts: 2026
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Kudos [?]: 1259 [1] , given: 376

Re: divisibility & primes [#permalink]  17 Jun 2011, 12:31
1
KUDOS
386390 wrote:
fluke wrote:
n=5
n=11

ahh.....

3+2=5
9+2=11
^ not a prime

I guess I fell in my own trap. whats the key lesson that i can make a note of?

Doubt yourself when using plugging in. It is not good to make statement sufficient.

Here, you knew even 2 must be involved, which is a good thing. You also knew Odd+Even=Odd; Just that you didn't check enough possibilities.

5=2+3
7=2+5
9=2+7

Ah!!! Looks good!!! Sufficient.

Not so good; Whenever you use plugin, such as in this case, try numbers beyond 10 or even 20. Something different.

2+21=23

23 is odd; but cant be represented as two distinct prime.

Also, we knew 2 must be involved. So, just fix it in our sets;
2
2
2
2
....

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Kudos [?]: 8 [1] , given: 4

Re: divisibility & primes [#permalink]  17 Jun 2011, 12:37
1
KUDOS
fluke wrote:

Doubt yourself when using plugging in. It is not good to make statement sufficient.

Here, you knew even 2 must be involved, which is a good thing. You also knew Odd+Even=Odd; Just that you didn't check enough possibilities.

5=2+3
7=2+5
9=2+7

Ah!!! Looks good!!! Sufficient.

Not so good; Whenever you use plugin, such as in this case, try numbers beyond 10 or even 20. Something different.

2+21=23

23 is odd; but cant be represented as two distinct prime.

Also, we knew 2 must be involved. So, just fix it in our sets;
2
2
2
2
....

thank you! great tips! gotta make notes =D
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Re: divisibility & primes [#permalink]  17 Jun 2011, 16:43
1
KUDOS
prime 2 3 5 7 11 13 17.....

n= p1+p2 and is a positive integer. (p1 and p2 are two different prime numbers)

is n = p1+p2?

1. Not sufficient
n>3

4 5
no yes

2. Not sufficient

n is odd

1 3 5

no no yes

together, Not sufficient

5 7 9 11
yes yes yes no

Director
Joined: 01 Feb 2011
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Kudos [?]: 78 [0], given: 42

Re: divisibility & primes [#permalink]  17 Jun 2011, 16:51
Good observation @fluke - in finding that 2 must be involved.

fluke wrote:
386390 wrote:
fluke wrote:
n=5
n=11

ahh.....

3+2=5
9+2=11
^ not a prime

I guess I fell in my own trap. whats the key lesson that i can make a note of?

Doubt yourself when using plugging in. It is not good to make statement sufficient.

Here, you knew even 2 must be involved, which is a good thing. You also knew Odd+Even=Odd; Just that you didn't check enough possibilities.

5=2+3
7=2+5
9=2+7

Ah!!! Looks good!!! Sufficient.

Not so good; Whenever you use plugin, such as in this case, try numbers beyond 10 or even 20. Something different.

2+21=23

23 is odd; but cant be represented as two distinct prime.

Also, we knew 2 must be involved. So, just fix it in our sets;
2
2
2
2
....

Re: divisibility & primes   [#permalink] 17 Jun 2011, 16:51
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