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Remainder If n is a positive integer greater than 16, is n a prime number? includes the answer to the question developed step by step.



Domingo 12 de octubre de 2014, por hurtado claudio

If n is a positive integer greater than 16, is n a prime number?

(1) n is odd

(2) The remainder when n is divided by 3 is 1, and the remainder when n is divided by 7 is 1.


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Mensajes

  • This is a problem of sufficiency of data, which involves rest.

    They indicate that n is greater than 16 and asked if n is Prime?

    With condition 1) N is odd, there are many odd older than 16 who are not prime numbers, example numbers: 21, 25 and more. Eye and there are also many odd greater than 16, that if are prime numbers for example: 17, 19, and more.

    Given the situation that there is both Prime and non-prime numbers, we conclude that the condition 1) is not enough.

    Condition 2) rest 1, is obtained by dividing N by 3, and rest 1 is obtained by dividing N by 7.
    This results in N = 3 K + 1 and N = 7 p + 1, given that N is unique and that 3 and 7 are prime numbers, we can conclude that N to be divided by (7 x 3) 21, also gets rest 1, since N must be divisible simultaneously for 3 and 7 for rest 1.

    So N = 21J + 1, then N may be 22, 43, and other values, given that 22 is even and 43 is prime number, there is ambiguity, then 2) is not enough.

    Let’s see if it is enough 1) and 2).

    1) N = 17, 19, 21, 25,..., 43,..., 85,...

    (2) N = 22, 43, 64, 85...

    There we can see two values that satisfy both conditions 43 and 85, and as 43 is a prime number and 85 it is not a prime number, again produced ambiguity and we conclude that the two conditions together nor we can affirm or deny, initial sentence.

    Conclusion the answer is E.

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