when positive integer n is divided by 3, the remainder is 1. when n is divided by 5, the remainder is 4. what is the smallest positive integer p, such that ( n + p ) is a multiple of 11?  Options:
A) 1
B) 2
C) 5
D) 7
E) 20
<gadget id="calculator">4 % 5</gadget>
<output>4</output>

<gadget id="calculator">11 - 4</gadget>
<output>7</output>

<result>D</result>
when positive integer n is divided by 3, the remainder is 1. when n is divided by 5, the remainder is 4. what is the smallest positive integer p, such that ( n + p ) is a multiple of 11?
subtract(11, reminder(4, 5))
when positive integer n is divided by 3 , the remainder is 1 i . e . , n = 3 x + 1 values of n can be one of { 1 , 4 , 7 , 10 , 13 , 16 , 19 , 22 . . . . . . . . . . . . . . 49 , 52 , 59 . . . . . . . . . . . . . . . . . . } similarly , when n is divided by 5 , the remainder is 5 . . i . e . , n = 5 y + 4 values of n can be one of { 4 , 9 , 14 , 19 , . . . } combining both the sets we get n = { 4,19 , 52 , . . . . . . . . . . . } what is the smallest positive integer p , such that ( n + p ) is a multiple of 11 or 11 x in case of n = 4 p = 7 so for min value of p , we take min value of n . d is the answer .