Confused with Semantics (IS vs CAN?)

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hmgp22: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Tue Oct 09, 2012 11:15 pm

by hmgp22 » Sat Mar 02, 2013 5:04 pm

I think I'm confused with the wording of the question. To me, it seems like the question is asking for the POSSIBILITY of n being written as a sum of 2 distinct positive primes. In both cases, it's clear that the given statements are sufficient to answer that question. If it's asking whether n IS.... then the question is very straightforward.

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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.

OA: E

Source: OG 13 DS 90

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Source: Beat The GMAT — Data Sufficiency | Sat Mar 02, 2013 5:04 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Mar 02, 2013 5:12 pm

hmgp22 wrote:I think I'm confused with the wording of the question. To me, it seems like the question is asking for the POSSIBILITY of n being written as a sum of 2 distinct positive primes. In both cases, it's clear that the given statements are sufficient to answer that question. If it's asking whether n IS.... then the question is very straightforward.

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.

OA: E

Some numbers can be written as the sum of two different positive prime numbers. For example, 5 can be written as the sum of 2 and 3. Similarly, 10 can be written as the sum of 3 and 7.
Some numbers cannot be written as the sum of two different positive prime numbers. For example, 4 cannot be written as the sum of two different positive prime numbers.

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

Statement 1: n is greater than 3.
n can have many possible values. Consider these two cases:
Case a: n = 5, in which case n can be written as the sum of two different positive prime numbers
Case b: n = 11, in which case n cannot be written as the sum of two different positive prime numbers
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: n is odd.
n can have many possible values. Consider these two cases:
Case a: n = 5, in which case n can be written as the sum of two different positive prime numbers
Case b: n = 11, in which case n cannot be written as the sum of two different positive prime numbers
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statements 1 and 2 combined:
n can still have many possible values. Consider these two cases:
Case a: n = 5, in which case n can be written as the sum of two different positive prime numbers
Case b: n = 11, in which case n cannot be written as the sum of two different positive prime numbers
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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hemant_rajput: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 22, 2012 7:13 amFollowed by: 13 members; Thanked: 46 times; GMAT Score:700

by hemant_rajput » Sun Mar 03, 2013 7:51 am

hmgp22 wrote:I think I'm confused with the wording of the question. To me, it seems like the question is asking for the POSSIBILITY of n being written as a sum of 2 distinct positive primes. In both cases, it's clear that the given statements are sufficient to answer that question. If it's asking whether n IS.... then the question is very straightforward.

=========
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.

OA: E

Source: OG 13 DS 90

Whenever we do DS question we don't look for possible solution but we look for definitive solution.

That is the whole reason of DS; Is data is sufficient to provide certainty? I'm inferring that you've already solved the question for certainty of fact in question.

Anyways here is my solution.

rephrasing question: - Is n = Prime1 + prime2

1. n>3

so n is any no. from the set {4,5,6,7,....}

if n is 4 then answer is no.
if n is 5 then answer is yes.
Not Sufficient.

2. n is odd

n = {1,3,5,7,9...}
if n is 3 then answer is no.
if n is 5 then answer is yes.
Not sufficient.

now using both statement.

n = {5,7,9...}
if n is 7 then no.
if n is 5 then yes.

not sufficient.

Answer is E

I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.

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