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We are to determine if x is divisible by 6.

Statement 1: x is divisible by 1,005,879
Statement 1 basically means that x=1,005,879a, where a is integer.
But since we don't know a, and 1,005,879 is divisible by 3 but not by 6, when a is even, then x is divisible by 6 but when a is odd, x is not divisible by 6. Statement 1 is insufficient.

Statement 2: x is divisible by 1,234,890
Statement 2 means: x=1,234,890b
The sum of the digits 1+2+3+4+8+9=27 is divisible by 3, hence 1,234,890 is divisible by 6.
Therefore x is also divisible by 6. Statement 2 is sufficient.

The answer is B.
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Quote:
What is the remainder when x is divided by 6?

(1) x is divisible by 1,005,879
(2) x is divisible by 1,234,890

a number is divisible by 6 if its an even multiple of 3
a number is divisible by 3 if sum digits is a multiple of 3

(1) insufic

sum of digits 1,005,879 is divisible by 3
so, x is a multiple of 3
if x is an even, then remainder x/6 is 0
if x is an odd, then remainder x/6 is 3

(2) sufic

sum of digits 1,005,879 is divisible by 3
x is an even multiple of 3
remainder is 0

Ans (B)
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What is the remainder when x is divided by 6?

(1) x is divisible by 1,005,879
x = 1,005,879k where k is a positive integer. And 1,005,879 is divisible by 3.
\(\frac{x}{6} = \frac{1,005,879k }{ 6}\)

\(R[\frac{x}{6}] = R[\frac{1,005,879 * 1 }{ 6 }]\) (for k=1)
\(R[\frac{x}{6}]\) = 3

\(R[\frac{x}{6}] = R[\frac{1,005,879 * 2 }{ 6 }]\) (for k=2)
\(R[\frac{x}{6}]\) = 0

INSUFFICIENT.

(2) x is divisible by 1,234,890
\(R[\frac{x}{6}] = R[\frac{1,234,890 * 1 }{ 6 }]\) (for k=1)
\(R[\frac{x}{6}]\) = 0

So, any multiplier of 1,234,890 would be divisible by 6 and remainder would be '0'.

SUFFICIENT.

Answer B.
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What is the remainder when x is divided by 6?

(1) x is divisible by 1,005,879
(2) x is divisible by 1,234,890

1) When x is 1,005,879, then dividing it by 6 will produce 3 as a reminder. When x is 2* 1005879, then it will b divisible by 6. No single answer is possible. Insufficient.

2) Lets say, x =1,234,890,which is divisible by 6. Hence, the remainder in all cases will be 0. Sufficient.

B is the answer.
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What is the remainder when x is divided by 6?

(Statement1): x is divisible by 1,005,879
1005,879 is not divisible by 2.
but it is divisible by 3 (1+0+0+5+8+7+9=30 )
--> if x =2*1,005,879, then x is divisible by 6(remainder will be zero)
--> if x =3*1,005,879, then x is not divisible by 6 (remainder will be 3)
Insufficient

(Statement2): x is divisible by 1,234,890
1,234,890 is EVEN number--> divisible by 2.
1+2+3+4+8+9+0= 27 --> divisible by 3

--> 1,234,890 is divisible by 6 --> x is multiple of 1,234,890
Sufficient

The answer is B.
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