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Re: What is the remainder when x is divided by 6?
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18 Mar 2020, 02:26
What is the remainder when x is divided by 6?
(1) x is divisible by 1,005,879
--> x = 1,005,879*p, where p = 0, 1, 2, 3, . . . . . .
1,005,879 is divisible by 3(Sum of all digits = 1 + 5 + 8 + 7 + 9 = 30, is divisible by 3)
--> 1,005,879 is an odd multiple of 3 = 3(2n + 1), for some positive integer 'n'
--> x = 3(2n + 1)p
Case 1: If p = 0, x = 0: Remainder when x is divided by 6 = 0
Case 2: If p = 1, x = 6n + 3: Remainder when x is divided by 6 = 3
--> No Definite Value --> Insufficient
(2) x is divisible by 1,234,890
--> x = 1,234,890*q, where q = 0, 1, 2, 3, . . . . . .
1,234,890 is divisible by 3(Sum of all digits = 1 + 2 + 3 + 4 + 8 + 9 = 27, is divisible by 3)
--> 1,234,890 is an even multiple of 3 = 3(2m), for some positive integer 'm'
--> x = 3(2m)q = 6mq
So, x is always a multiple of 6
--> Remainder when x is divided by 6 = 0 always --> Sufficient
Option B