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

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Bunuel
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When n is divided by 13, the remainder is 2 and the quotient is k. Whe [#permalink] New post   05 Mar 2020, 13:43
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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
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Re: When n is divided by 13, the remainder is 2 and the quotient is k. Whe [#permalink] New post   05 Mar 2020, 16:43
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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
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Re: When n is divided by 13, the remainder is 2 and the quotient is k. Whe [#permalink] New post   05 Mar 2020, 16:47
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
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Re: When n is divided by 13, the remainder is 2 and the quotient is k. Whe [#permalink] New post   05 Mar 2020, 19:33
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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

Bunuel wrote:
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
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Re: When n is divided by 13, the remainder is 2 and the quotient is k. Whe [#permalink] New post   05 Mar 2020, 21:07
Bunuel wrote:
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


if least value of n=2,
then k=0
0/17 leaves remainder of 0
A
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Re: When n is divided by 13, the remainder is 2 and the quotient is k. Whe [#permalink] New post   05 Mar 2020, 23:49
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Bunuel wrote:
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


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.
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Re: When n is divided by 13, the remainder is 2 and the quotient is k. Whe [#permalink] New post   07 Mar 2020, 07:24
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Bunuel wrote:
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


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
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Re: When n is divided by 13, the remainder is 2 and the quotient is k. Whe [#permalink] New post   07 Mar 2020, 08:41
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
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Re: When n is divided by 13, the remainder is 2 and the quotient is k. Whe [#permalink] New post   11 Jul 2023, 06:21
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Re: When n is divided by 13, the remainder is 2 and the quotient is k. Whe [#permalink]
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