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# Can the positive integer n be written as the sum of two

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Can the positive integer n be written as the sum of two [#permalink]

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17 Jun 2008, 08:14
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Can the positive integer n be written as the sum of two different positive prime numbers?

(1) n is greater than 3
(2) n is odd

I am confused with the term "the positive integer" ? Does this mean "any positive integer" "some positive integer n" or
"all positive integer n"

This question is from OG-quant-Green(DS-86)
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17 Jun 2008, 09:00
I think its E.

You can write 5 as sum of 3 and 2, but you cant do it with 7
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17 Jun 2008, 09:08
pmenon wrote:
I think its E.

You can write 5 as sum of 3 and 2, but you cant do it with 7

7 can be written as 5 + 2 (both primes)
but yes E is still the answer (consider 27)

back to the original question of what "the positive int" means. I think it means any positive integer.

1) is obviously insuff

2) still insufficient (consider 5 and 27 as above)

1)2) still insufficient
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17 Jun 2008, 15:06
why cant we have we 5*5+2=27..
isnt 27 really the sum of 2 different prime integers..

where does it say that the number of integers has to be 2??

I think C makes sense..
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17 Jun 2008, 15:07
pmenon wrote:
I think its E.

You can write 5 as sum of 3 and 2, but you cant do it with 7

why cant be we write 7=5+2?
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17 Jun 2008, 23:37
fresinha12 wrote:
pmenon wrote:
I think its E.

You can write 5 as sum of 3 and 2, but you cant do it with 7

why cant be we write 7=5+2?

7 is also equal or a sum of 1 and 6 (1+6), & 3 and 4 (3+4).

Quote:
Can the positive integer n be written as the sum of two different positive prime numbers?
(1) n is greater than 3
(2) n is odd

is it a correct question?

the question is not asking for n to be a prime integer rather it is asking whether "can n be a sum of two +ve prime integers"? the question for me is ambigious cuz any odd integer > 3 can be written as sum of two prime or non prime integers. since its a yes/no question, the answer is yes/no, both.

lets say n is 5, which is equal to 2+3. so yes. n=5 is also equal to 1+4, so no...
lets say n is 7, which is equal to 2+5 or 3+4. again yes or no.

so there is no integer that is a sum of only two +ve prime integers.
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18 Jun 2008, 01:14
fresinha12 wrote:
why cant we have we 5*5+2=27..
isnt 27 really the sum of 2 different prime integers..

where does it say that the number of integers has to be 2??

I think C makes sense..

what about 8 after combining 1,2

6+3 but 6 is even
5+4 but 4 is even
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18 Jun 2008, 01:25
GMAT TIGER wrote:
is it a correct question?

the question is not asking for n to be a prime integer rather it is asking whether "can n be a sum of two +ve prime integers"? the question for me is ambigious cuz any odd integer > 3 can be written as sum of two prime or non prime integers. since its a yes/no question, the answer is yes/no, both.

lets say n is 5, which is equal to 2+3. so yes. n=5 is also equal to 1+4, so no...
lets say n is 7, which is equal to 2+5 or 3+4. again yes or no.

so there is no integer that is a sum of only two +ve prime integers.

It doesn't say "only", it says "can be written".

And it it the case for 5 : "it can be written as the sum of two different positive prime numbers" (5=2+3)

It is the case for 7 too : "it can be written as the sum of two different positive prime numbers" (7=5+2)

But it is not the case for 27 as buffdady said (no : if we write 27=25+2 it doesn't work since 25 is not a prime number)

It works for 7 but not for 27: (1) and (2) are insufficient.
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18 Jun 2008, 06:27
I disagree and actually agree with Tiger..the wording is weird..Look, I can write 25 as a sum of 1 prime integer..which is 5..and i can add 5*5+2=27..here i have 2 different prime integers..5 and 2..

Oski wrote:
GMAT TIGER wrote:
is it a correct question?

the question is not asking for n to be a prime integer rather it is asking whether "can n be a sum of two +ve prime integers"? the question for me is ambigious cuz any odd integer > 3 can be written as sum of two prime or non prime integers. since its a yes/no question, the answer is yes/no, both.

lets say n is 5, which is equal to 2+3. so yes. n=5 is also equal to 1+4, so no...
lets say n is 7, which is equal to 2+5 or 3+4. again yes or no.

so there is no integer that is a sum of only two +ve prime integers.

It doesn't say "only", it says "can be written".

And it it the case for 5 : "it can be written as the sum of two different positive prime numbers" (5=2+3)

It is the case for 7 too : "it can be written as the sum of two different positive prime numbers" (7=5+2)

But it is not the case for 27 as buffdady said (no : if we write 27=25+2 it doesn't work since 25 is not a prime number)

It works for 7 but not for 27: (1) and (2) are insufficient.
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18 Jun 2008, 06:35
fresinha12 wrote:
I disagree and actually agree with Tiger..the wording is weird..Look, I can write 25 as a sum of 1 prime integer..which is 5..and i can add 5*5+2=27..here i have 2 different prime integers..5 and 2..

Nop.

Wording is okay : "Can the positive integer n be written as the sum of two different positive prime numbers?"

"Sum of 2 numbers" means that you can sum... two numbers. In your case it's 5*5 and 2.

But 5*5 (=25) is not prime.
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18 Jun 2008, 22:53
fresinha12 wrote:
why cant we have we 5*5+2=27..
isnt 27 really the sum of 2 different prime integers..

where does it say that the number of integers has to be 2??

I think C makes sense..

hi,
n be written as the sum of two different positive prime numbers
means n=p1+p2 where p1,p2 are prime

i have seen this question in other forums

check 11

10+1 both are not prime
9+2 both are not prime
8+3 both are not prime
7+4 both are not prime
6+5 both are not prime
5+6 both are not prime
it again repeats

but when u take the number as 7

5+2 both are prime

so two different results

its E
Re: positive integer n?   [#permalink] 18 Jun 2008, 22:53
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