When n is divided by 13, the remainder is 2 and the quotient is k. Whe

Question

When positive integer n is divided by 13, the remainder is 2 and the quotient is k. When n is divided by 17, the remainder is 2. What is the remainder when k is divided by 17?

(A) 0
(B) 2
(C) 4
(D) 13
(E) 15

gvij2017 · Accepted Answer

n= 13k+2 
n= 17x+2 
then 13k= 17x 
k must be multiple of 17 because 13 and 17 both are prime. 
Reminder when dividing k by 17 is 0. 
A is answer

GMATBusters · Answer

As per the Question, 
n = 13k+2 = 17m+2
Hence, 13k = 17m
k/17 = m/13
Since k and m are integers, k must be multiple of 17 and m must be multiple of 13.

So, the remainder when k is divided by 17 = 0.

Answer = A

gracie · Answer

if least value of n=2,
then k=0
0/17 leaves remainder of 0
A

GMATWhizTeam · Answer

Solution 
 • When n is divided by 13, remainder is 2 and quotient is k, so
 o  n = 13k + 2 …………Eq.(i)  
• Also, when n is divided by 17, the remainder is 2. So, we can write,
 o  n = 17m +2 ……….Eq.(ii) 
o Here, m is a positive integer.  
• From Eq.(i) and Eq.(ii), we can observe that when n is divided by 13 and 17, remainder is 2.
 o This means,  n – 2  should be L.C.M of 13 and 17.
o Since, 13 and 17 are prime numbers, so L.C.M. of (13, 17)   = 13*17  
  or,  n - 2 = 13*17 
 Hence,  n = 13*17 +2 
 Comparing the above equation with Eq. (i) we get,  k = 17 
 Thus, reminder of  \frac{k}{17} =  remainder of  \frac{17}{17} = 0    
Thus, the correct answer is  Option A.

ScottTargetTestPrep · Answer

We can create the equations:

n/13 = k + 2/13

n = 13k + 2

and

n/17 = Q + 2/17

n = 17Q + 2

Setting the equations equal, we have:

13k + 2 = 17Q + 2

13k = 17Q

13k/17 = Q

Since Q is an integer and 13 is not divisible by 17, then k must be divisible by 17, and hence the remainder is 0 when k is divided by 17 .

Answer: A

hiranmay · Answer

When positive integer n is divided by 13, the remainder is 2 and the quotient is k. When n is divided by 17, the remainder is 2. What is the remainder when k is divided by 17?

(A) 0 --> correct
(B) 2
(C) 4
(D) 13
(E) 15

solution:
n = 13k+2, 0<=k, k =integer --(i)
n = 17l+2, 0<=l, l =integer --(ii)
so, combining (i) & (ii)=> n = 13*17d+2, 0<=d, d =integer ---(iii)
comparing (i) & (iii)=> k =17d = 17d+0
so, the remainder when k is divided by 17 is 0

bumpbot · Answer

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When n is divided by 13, the remainder is 2 and the quotient is k. Whe

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