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If a positive integer n, divided by 5 has a remainder 2, whi
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07 Apr 2020, 03:44
07 Apr 2020, 03:44
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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
Kudos for the right answer and explanation
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
Kudos for the right answer and explanation
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If a positive integer n, divided by 5 has a remainder 2, whi
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07 Apr 2020, 05:10
07 Apr 2020, 05:10
1
Carcass 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
Kudos for the right answer and explanation
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
Kudos for the right answer and explanation
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.
Cheers,
Brent
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Re: If a positive integer n, divided by 5 has a remainder 2, whi
[#permalink]
07 Apr 2020, 05:43
07 Apr 2020, 05:43
Carcass 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
Kudos for the right answer and explanation
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
Kudos for the right answer and explanation
let n/5 = q remainder 2
therefore,
n = 5q + 2
case 1: n is odd
when q is 1,2,3
n=7,12,17 (not valid)
case2: cannot be a prime
when q is 1,2,3
n+1= 8,13,18 (not valid)
case3: has remainder 2
when q is 1,2,3
(n+2)/7 has remainders = 2,0,5 (not valid)
hence ans is A
