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k is a positive integer. Is k prime?

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k is a positive integer. Is k prime? [#permalink]

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k is a positive integer. Is k prime?

(1) At least one number in the set {1, k, k + 7} is prime.
(2) k is odd.
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Apr 2013, 03:57, edited 1 time in total.
RENAMED THE TOPIC.
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Re: k is a positive integer. Is k prime? [#permalink]

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k is a positive integer. Is k prime?

Notice that we are told that k is a positive integer.

(1) At least one number in the set {1, k, k + 7} is prime. Clearly insufficient.
(2) k is odd. Clearly insufficient.

(1)+(2) The set is {1, k=odd, k+7=even>2}. Since at least on number in this set is a prime, then it must be k. Sufficient.

Answer: C.
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Re: k is a positive integer. Is k prime? [#permalink]

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New post 30 Apr 2013, 04:36
Bunuel wrote:
k is a positive integer. Is k prime?

Notice that we are told that k is a positive integer.

(1) At least one number in the set {1, k, k + 7} is prime. Clearly insufficient.
(2) k is odd. Clearly insufficient.

(1)+(2) The set is {1, k=odd, k+7=even>2}. Since at least on number in this set is a prime, then it must be k. Sufficient.

Answer: C.


you made it look so simple...thanks a ton Bunuel.
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Re: k is a positive integer. Is k prime? [#permalink]

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New post 14 Jan 2014, 07:38
Bunuel wrote:
k is a positive integer. Is k prime?

Notice that we are told that k is a positive integer.

(1) At least one number in the set {1, k, k + 7} is prime. Clearly insufficient.
(2) k is odd. Clearly insufficient.

(1)+(2) The set is {1, k=odd, k+7=even>2}. Since at least on number in this set is a prime, then it must be k. Sufficient.

Answer: C.


I thought it was A because I thought that in a set, the numbers are organized by size. So I assumed that k is prime because any prime + 7 = no prime. But obviously a set is not sorted. I get the rest of the reasoning. Am I right assuming that sets don't need to be sorted? Please verify!

Thanks!
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Re: k is a positive integer. Is k prime? [#permalink]

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New post 14 Jan 2014, 07:57
unceldolan wrote:
Bunuel wrote:
k is a positive integer. Is k prime?

Notice that we are told that k is a positive integer.

(1) At least one number in the set {1, k, k + 7} is prime. Clearly insufficient.
(2) k is odd. Clearly insufficient.

(1)+(2) The set is {1, k=odd, k+7=even>2}. Since at least on number in this set is a prime, then it must be k. Sufficient.

Answer: C.


I thought it was A because I thought that in a set, the numbers are organized by size. So I assumed that k is prime because any prime + 7 = no prime. But obviously a set is not sorted. I get the rest of the reasoning. Am I right assuming that sets don't need to be sorted? Please verify!

Thanks!


A set is not necessarily ordered but this has nothing to do with the first statement.

The question asks whether k is a prime number. (1) says that at least one number in the set {1, k, k + 7} is prime. Sure k can be prime but k can as well be for example 4, so not a prime and in this case k+7=11 is a prime.

Hope it's clear.
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Re: k is a positive integer. Is k prime? [#permalink]

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Re: k is a positive integer. Is k prime? [#permalink]

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New post 29 Jul 2015, 22:01
Hi All,

This question can be solved by TESTing VALUES.

We're told that K is a POSITIVE INTEGER. We're asked if K is PRIME. This is a YES/NO question.

Fact 1: At least one number in the set {1, K, K + 7} is prime.

IF....
K = 2, the set is {1, 2, 9} and has at least 1 prime number
The answer to the question is YES.

IF...
K = 4, the set is {1, 4, 11} and has at least 1 prime number
The answer to the question is NO.
Fact 1 is INSUFFICIENT

(2) K is ODD.

IF....
K = 1, then the answer to the question is NO.
K = 3, then the answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, we know...
At least one number in the set {1, K, K + 7} is prime.
K is ODD

IF...
K = 3, the set is {1, 3, 10} and has at least 1 prime number
The answer to the question is YES.

From the above example, if K is an ODD PRIME, then the answer is ALWAYS YES. We now have to look for possibilities when K is NOT prime....

IF...
K = 9, the set is {1, 9, 16} BUT this does NOT have any primes, so K CANNOT BE 9...

From this example, we can see that if K = an ODD NON-PRIME, then (K+7) will be EVEN (thus, NOT prime). Thus, there are no possible values of K that are odd AND non-prime that will 'fit' these Facts. By extension, that means that K MUST be an ODD PRIME and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

Final Answer:
[Reveal] Spoiler:
C


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Re: k is a positive integer. Is k prime?   [#permalink] 29 Jul 2015, 22:01
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