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Re: If a positive integer n, divided by 5 has a remainder 2
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20 Mar 2013, 15:40

2

If a positive integer n,divided by 5 has a remainder 2,which of the following must be true I. n is odd II. n+1 cannot be a prime number III. (n+2)divided by 7 has remainder 2

Some valid values for n: 7, 12, 17, 22, 27, 32... or, in other words: \(n=(i * 5) + 2\) for i=1,2,3...

I. FALSE: we see that n can we odd or even. II. FALSE: (n+1) could be a prime number. Example: n=12 --> (n+1)=13 is prime. Other example: for n=22, (n+1)=23 is prime. III. FALSE: for n=12, (n+2)=14, divided by 7 has remainder zero.

Re: If a positive integer n, divided by 5 has a remainder 2
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13 Nov 2017, 14:12

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chiccufrazer1 wrote:

If a positive integer n, divided by 5 has a remainder 2, which of the following must be true

I. n is odd II. n+1 cannot be a prime number III. (n+2) divided by 7 has remainder 2

A. None B. I only C. I and II only D. II and III only E. I, II and III

-----------------ASIDE---------------------------------- When it comes to remainders, we have a nice rule that says:

If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.

For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc. ------ONTO THE QUESTION!!!------------------------

Positive integer n, divided by 5 has a remainder 2 Some possible values of n: 2, 7, 12, 17, 22, 27, 32, 37, . . . etc

Now let's examine the statements: I. n is odd. This need not be true. Among the possible values of n, we see that n need not be odd So statement 1 is FALSE

II. n+1 cannot be a prime number. Not true. Among the possible values of n, we see that n COULD equal 2 2+1 = 3, and 3 IS a prime number So, n+1 CAN BE a prime number So statement 2 is FALSE

NOTE: Since statements I and II are false, we need not examine statement III, since there are no answer choices that suggest that only statement III is true. So, the correct must be A

Re: If a positive integer n, divided by 5 has a remainder 2, which of the
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12 Mar 2020, 06:33

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Bunuel wrote:

If a positive integer n, divided by 5 has a remainder 2, which of the following must be true?

I n is odd II n + 1 cannot be a prime number III (n + 2) divided by 7 has remainder 2

A. none B. I only C. I and II only D. II and III only E. I, II and III

When it comes to remainders, we have a nice property that says: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

Given: When positive integer n is divided by 5, we get remainder 2 So, the possible values of n are: 2, 7, 12, 17, 22, 27, 32, . . . .

Now let's examine each statement.... I. n is odd If n = 2, then n is NOT odd. So, statement I need not be true. Check the answer choices.... eliminate B, C and E, since they state that statement I is true.

II. n + 1 cannot be a prime number If n = 2, then n+1 = 3, and 3 is prime. Check the remaining answer choices.... eliminate D, since it states that statement I Iis true.

By the process of elimination, the correct answer is A.

ASIDE: Notice that we are able to arrive at the correct answer without having to analyze statement III. We were able to do this because we eliminated incorrect answer choices after analyzing each statement.