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# The positive integer 4 can NOT be written as the sum of two

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Manager
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The positive integer 4 can NOT be written as the sum of two [#permalink]  17 Jun 2010, 07:59
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>My understanding of the use of the word "Can" in this instance implies possibility, regardless of degree. Am I right?

I think you are interpreting the question wrong. The question is not asking if it is possible that a positive n exists, that can be written as the sum of two different positive prime numbers. It is asking if a specific n can be. Since you don't know the value of n, see if you can find conflicting answers.

For statement 1:
The positive integer 4 can NOT be written as the sum of two different positive prime numbers.

The positive integer 5 CAN be written as the sum of two different positive prime numbers (3+2).

NS, BCE.

For statement 2:
The positive integer 1 can NOT be written as the sum of two different positive prime numbers.

The positive integer 5 CAN be written as the sum of two different positive prime numbers (3+2).

NS, CE.

Both statements:
The positive integer 11 can NOT be written as the sum of two different positive prime numbers.

The positive integer 5 CAN be written as the sum of two different positive prime numbers (3+2).

NS, E.
[Reveal] Spoiler: OA
Manager
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Re: DS question OG 10 [#permalink]  19 Jun 2010, 11:00
I think since they are asking if it is possible to write a number as a sum of 2 different prime numbers ...5 and 13 both satisfies the conditions so answer should be D

any thoughts ?
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Re: DS question OG 10 [#permalink]  19 Jun 2010, 11:50
Expert's post
virupaksh2010 wrote:
I think since they are asking if it is possible to write a number as a sum of 2 different prime numbers ...5 and 13 both satisfies the conditions so answer should be D

any thoughts ?

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

The point here is that $$n$$ is some particular number.

Two statements cannot narrow the possible values of $$n$$ so that we can arrive to one answer: YES or NO. Which means statement(s) are insufficient.

For example:
If $$n=5=odd>3$$, then the answer would be - YES, $$5=2+3=prime+prime$$ but if $$n=11=odd>3$$, then the answer would be - NO.

Hope it's clear.
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QR DS 90 Integer [#permalink]  22 Feb 2011, 09:12
Can the positive integer n be written as the sum of two diiferent positive prime numbers?
(1) n is greater than 3
(2) n is odd.
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Re: QR DS 90 Integer [#permalink]  22 Feb 2011, 09:17
Expert's post
Merging similar topics.
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Re: DS question OG 10 [#permalink]  05 Jul 2011, 17:42
Bunuel wrote:
virupaksh2010 wrote:
I think since they are asking if it is possible to write a number as a sum of 2 different prime numbers ...5 and 13 both satisfies the conditions so answer should be D

any thoughts ?

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

The point here is that $$n$$ is some particular number.

Two statements cannot narrow the possible values of $$n$$ so that we can arrive to one answer: YES or NO. Which means statement(s) are insufficient.

For example:
If $$n=5=odd>3$$, then the answer would be - YES, $$5=2+3=prime+prime$$ but if $$n=11=odd>3$$, then the answer would be - NO.

Hope it's clear.

Sorry for the necrobump, but I just wanted something cleared up in my head. While I understand Bunuel's line of reasoning as to why the answer is (E), I don't think that explanation satisfies the question posed by the OP. The question, as I understand it, is about the semantics of the language of the question. In fact, the solution posted by Bunuel proves that 'n' CAN be written as the sum of two primes in the case where 'n' > 3 AND where 'n' is odd.

My question is if I run into this in the GMAT, can I always expect a statement to be Insufficient if I can answer both 'Yes' AND 'No' or do I have to watch out for subtleties in the language?

Given that the OA is (E), my inclination is that this is just a poorly worded question, however I just wanted a little input so I can put this behind me and move on.

Thanks!!
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Re: DS question OG 10 [#permalink]  06 Jul 2011, 22:27
Expert's post
dsg wrote:
Bunuel wrote:
virupaksh2010 wrote:
I think since they are asking if it is possible to write a number as a sum of 2 different prime numbers ...5 and 13 both satisfies the conditions so answer should be D

any thoughts ?

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

The point here is that $$n$$ is some particular number.

Two statements cannot narrow the possible values of $$n$$ so that we can arrive to one answer: YES or NO. Which means statement(s) are insufficient.

For example:
If $$n=5=odd>3$$, then the answer would be - YES, $$5=2+3=prime+prime$$ but if $$n=11=odd>3$$, then the answer would be - NO.

Hope it's clear.

Sorry for the necrobump, but I just wanted something cleared up in my head. While I understand Bunuel's line of reasoning as to why the answer is (E), I don't think that explanation satisfies the question posed by the OP. The question, as I understand it, is about the semantics of the language of the question. In fact, the solution posted by Bunuel proves that 'n' CAN be written as the sum of two primes in the case where 'n' > 3 AND where 'n' is odd.

My question is if I run into this in the GMAT, can I always expect a statement to be Insufficient if I can answer both 'Yes' AND 'No' or do I have to watch out for subtleties in the language?

Given that the OA is (E), my inclination is that this is just a poorly worded question, however I just wanted a little input so I can put this behind me and move on.

Thanks!!

In Data Sufficiency questions, if you can answer the question with a 'Yes' in one case and a 'No' in another case, it means the data is not sufficient.
What Bunuel is explaining here is absolutely to the point.
Forget this question for a moment. Look at this one:
Q: Can 5 be written as the sum of two different positive prime numbers?
A: Yes, it can. (2+3)
Q: Can 6 be written as the sum of two different positive prime numbers?
A: No, it cannot.
Q: Can 7 be written as the sum of two different positive prime numbers?
A: Yes, it can. (2+5)
Q: Can n be written as the sum of two different positive prime numbers?
A: I do not know yet since I don't know the value of n. Give me some data that will help me decide.

Here is some data: Stmnt 1: n is greater than 3.
There are many numbers greater than 3. Some can be written as the sum of two diff primes, some cannot. Not enough information.
Ok then. Stmnt 2: n is odd.
5 and 7 can be written as sum of prime. 11 cannot be. I still don't know.
Just knowing that n is odd and greater than 3 does not help me decide whether I can write n as sum of two different primes. I need to know the actual value of n. So both statements together are not sufficient.

And actually, it is not a poorly worded question. It is quite clear and concise. There could be similar questions in the actual test. I understand your confusion but practice some more to get used to the GMAT wording.
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Director
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Re: DS question OG 10 [#permalink]  08 Jul 2011, 20:04
1. Not sufficient

n>3

n=4, cannot be expressed as sum of two different prime numbers.
n=5 can be expressed as sum of two different prime numbers.

2. Not sufficient

n=1 cannot be expressed as sum of two different prime numbers.
n=5 can be expressed as sum of two different prime numbers.

together , Not sufficient.

n>3 and odd
n=5 can be expressed as sum of two different prime numbers
n=11 cannot be expressed as sum of two different prime numbers.

Re: DS question OG 10   [#permalink] 08 Jul 2011, 20:04
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# The positive integer 4 can NOT be written as the sum of two

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