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

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29 Jan 2012, 11:56

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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.

When I am checking the case using both conditions so can i rephrase problem statement as "Can every odd integer which is greater than 3 can be written as sum of two positive integers " OR "Can any odd integer which is greater than 3 can be written as sum of two positive integers"

90. 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.

When I am checking the case using both conditions so can i rephrase problem statement as "Can every odd integer which is greater than 3 can be written as sum of two positive integers " OR "Can any odd integer which is greater than 3 can be written as sum of two positive integers"

Note that n is some particular, fixed number. If we take two statements together the question becomes: can odd integer n, which is greater than 3, be written as the sum of two different prime numbers?

Now, if EVERY odd integer greater than 3 can be written as the sum of two different prime numbers, then taken together statements would be sufficient as we get definite YES answer to the question (because if it can be done for EVERY odd integer greater than 3 then it can be done for some particular n, from this group, too). Also, if NEITHER odd integer greater than 3 can be written as the sum of two different prime numbers, then taken together statements would still be sufficient, though at this time we'd get definite NO answer to the question (because if it cannot be done for ANY odd integer greater than 3 then it can not be done for some particular n, from this group, too).

Next, if we can find two values of odd integer n greater than 3 and one of them can be written as the sum of two different prime numbers and another cannot, then taken together statements would NOT be sufficient.

For this question the answer is E: If n=5=odd>3, then the answer would be YES, 5=2+3=prime+prime; If n=11=odd>3, then the answer would be NO, (11=odd and in order it to be the sum of two different primes one must be 2=even=prime, in this case another number would be 9, since 9 is not a prime, you cannot write 11 as the sum of two different primes).

So, we have two values of odd integer n greater than 3: one of them can be written as the sum of two different prime numbers and another cannot, hence taken together statements are not sufficient.

90. 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.

When I am checking the case using both conditions so can i rephrase problem statement as "Can every odd integer which is greater than 3 can be written as sum of two positive integers " OR "Can any odd integer which is greater than 3 can be written as sum of two positive integers"

Note that n is some particular, fixed number. If we take two statements together the question becomes: can odd integer n, which is greater than 3, be written as the sum of two different prime numbers?

Now, if EVERY odd integer greater than 3 can be written as the sum of two different prime numbers, then taken together statements would be sufficient as we get definite YES answer to the question (because if it can be done for EVERY odd integer greater than 3 then it can be done for some particular n, from this group, too). Also, if NEITHER odd integer greater than 3 can be written as the sum of two different prime numbers, then taken together statements would still be sufficient, though at this time we'd get definite NO answer to the question (because if it cannot be done for ANY odd integer greater than 3 then it can not be done for some particular n, from this group, too).

Next, if we can find two values of odd integer n greater than 3 and one of them can be written as the sum of two different prime numbers and another cannot, then taken together statements would NOT be sufficient.

For this question the answer is E: If n=5=odd>3, then the answer would be YES, 5=2+3=prime+prime; If n=11=odd>3, then the answer would be NO, (11=odd and in order it to be the sum of two different primes one must be 2=even=prime, in this case another number would be 9, since 9 is not a prime, you cannot write 11 as the sum of two different primes).

So, we have two values of odd integer n greater than 3: one of them can be written as the sum of two different prime numbers and another cannot, hence taken together statements are not sufficient.

Answer: E.

Hope it's clear.

solved it correctly but could not find a clear takeaway for this problem _________________

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

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14 Mar 2013, 22:50

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Expert's post

monikaleoster wrote:

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.

Nothing new to add after Bunuel's explanation. But just to point down what I observed for F.S 2;we know that n is odd. Again we have been asked if n is a sum of 2 different primes. Now we know that only odd+even = odd. Thus out of the two given prime numbers, we can have only 2 as the even prime. So now the statement basically states that if we subtract 2 from n, do we end up with a prime greater than 2.

or Is n-2 = a prime greater than 2. Take any odd integer for n. For n=13, we get a YES. For n=17, we get a NO. Insufficient. _________________

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

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16 Mar 2013, 14:08

vinaymimani wrote:

monikaleoster wrote:

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.

Nothing new to add after Bunuel's explanation. But just to point down what I observed for F.S 2;we know that n is odd. Again we have been asked if n is a sum of 2 different primes. Now we know that only odd+even = odd. Thus out of the two given prime numbers, we can have only 2 as the even prime. So now the statement basically states that if we subtract 2 from n, do we end up with a prime greater than 2.

or Is n-2 = a prime greater than 2. Take any odd integer for n. For n=13, we get a YES. For n=17, we get a NO. Insufficient.

Good explanation!

I almost read n to be one of the numbers and did a mental calculation to arrive at C. But, now i am clear! _________________

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

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02 Sep 2015, 02:07

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

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16 Mar 2016, 12:11

Hi Guys, I am not a native speaker and I am confused by the question - should I read it as "Is the positive integer n represents the sum of two different positive prime numbers?"

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

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16 Mar 2016, 12:15

Expert's post

AlexIV wrote:

Hi Guys, I am not a native speaker and I am confused by the question - should I read it as "Is the positive integer n represents the sum of two different positive prime numbers?"

Thanks!

No. It means is it possible to write positive integer n as the sum of two different positive prime numbers. _________________

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