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What is the remainder when x is divided by 6?

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Bunuel
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What is the remainder when x is divided by 6? [#permalink] New post   18 Mar 2020, 01:21
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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
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B
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Re: What is the remainder when x is divided by 6? [#permalink] New post   18 Mar 2020, 02:12
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What is the remainder when x is divided by 6?

(1) x is divisible by 1,005,879
We need to find out whether 1,005,879 is divisible by 6? - No, it leaves the remainder of 3.
So, remainder of 3, let's check if 2*1,005,879 is divisible by 6? - Yes, it leaves the remainder of 0.

Two different possibilities. Insufficient.

(2) x is divisible by 1,234,890
We need to find out whether 1,234,890 is divisible by 6? - Yes, so clearly it is divisible with a Remainder 0.
So, the multiples of 1,234,890 will be divisbile by 6 and leaves the remainder 0.

One possibility. Sufficient.

'B' is the Winner
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Re: What is the remainder when x is divided by 6? [#permalink] New post   18 Mar 2020, 02:26
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What is the remainder when x is divided by 6?

(1) x is divisible by 1,005,879
--> x = 1,005,879*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
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Re: What is the remainder when x is divided by 6? [#permalink] New post   18 Mar 2020, 02:37
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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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Re: What is the remainder when x is divided by 6? [#permalink] New post   18 Mar 2020, 07:38
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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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Re: What is the remainder when x is divided by 6? [#permalink] New post   18 Mar 2020, 10:19
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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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Re: What is the remainder when x is divided by 6? [#permalink] New post   18 Mar 2020, 10:50
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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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Re: What is the remainder when x is divided by 6? [#permalink] New post   18 Mar 2020, 10:50
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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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Re: What is the remainder when x is divided by 6? [#permalink] New post   07 Nov 2022, 04:19
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Re: What is the remainder when x is divided by 6? [#permalink]
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