When a positive integer n is divided by 13, what is the remainder?

Question

(1) n + 1 is divisible by 13
(2) n + 14 is divisible by 13

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Michael-DOPS · Answer

statement 1 sufficient, as N+1 is dividible by 13. => hence n+1 has a remainder of 1
statement 2 sufficient, as N+14 is dividible by 13. => meaning that once more the remainder is 1.

Correct answer is D

Aryaa03 · Answer

Sol: Option-D

Asked: Remainder R, when a positive integer n is divided by 13 : 
Mathematically, n = 13k + R , R = ?

St-1: 
n + 1 is divisible by 13
(n+1) = 13m + 0
n = 13m - 1
It can be further written as: n = 13m - 13 + 13 - 1 = 13(m-1) + 12 ; 
Remainder is 12 
e.g. n+1 = 12 + 1 = 13 , where n=12 , 12/13 leaves a remainder of 12
For n + 1 = 26 = 25 + 1 , n = 25, 25/13 leaves a remainder of 12
 Statement is sufficient

St-2: 
n + 14 is divisible by 13
(n+14) = 13m + 0
n = 13m - 14
n = 13m - 13 -1 = 13(m-1) - 1 ; 
n = 13(m-1) -13 + 13 -1
n = 13(m-2) + 12
Remainder is 12 
e.g. n+14 = 12 + 14 = 26 , where n=12 , 12/13 leaves a remainder of 12
For n + 1 = 39 = 25 + 14 , n = 25, 25/13 leaves a remainder of 12
 Statement is sufficient

When a positive integer n is divided by 13, what is the remainder?

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