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What is the remainder when the positive integer n is divided by 6?

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What is the remainder when the positive integer n is divided by 6?  [#permalink]

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New post Updated on: 22 Sep 2018, 02:32
1
2
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A
B
C
D
E

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70% (02:04) correct 30% (01:42) wrong based on 43 sessions

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What is the remainder when the positive integer n is divided by 6?

(1) The remainder is 3 when n is divided by 8
(2)The remainder is 8 when n-1 is divided by 9

Originally posted by AbhishekJain08 on 21 Sep 2018, 10:05.
Last edited by Bunuel on 22 Sep 2018, 02:32, edited 2 times in total.
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Re: What is the remainder when the positive integer n is divided by 6?  [#permalink]

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New post 21 Sep 2018, 10:19
2
What is the remainder when the positive integer n is divided by 6?

A) The remainder is 3 when n is divided by 8
so number is 8x+3...
if x =1, n=11 and 11 divided by 6 leaves a remainder of 5
if x =2, n=19 and 19 divided by 6 leaves a remainder of 1
so n is odd and remainder is also odd
Insuff

B)The remainder is 8 when n-1 is divided by 9
so number is n-1=9x+8.....n=9x+9=9(x+1)...
if x =1, n=18 and 18 divided by 6 leaves a remainder of 0
if x =2, n=27 and 27 divided by 6 leaves a remainder of 3
so remainder is either 0 or 3
Insuff

combined
remainder is 0 or 3 but statement I tells us that remainder is odd, so R=3

C

OA is wrong it will not be D but C
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Re: What is the remainder when the positive integer n is divided by 6?  [#permalink]

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New post 21 Sep 2018, 11:11
1
From statement 1
n = 8a+3
Therefore n could be : 3,11,19,27,35,43,51,59,67...
Hence when n is divided by 6 we will have multiple reminders. Hence Not sufficient
From statement 2
n-1=9b+8 or n=9b+9
Therefore n could be : 9,18,27,36,45,54,63,72,81
Similarly we can have different reminders when n is divided by 6. Hence not sufficient
combining both statements , we will find a number common to both statement 1 and 2.
Here N = 27 satisfies both condition and no other does.
So when n is divided by 6 , we will get a unique value as reminder.
Hence answer should be C
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Re: What is the remainder when the positive integer n is divided by 6? &nbs [#permalink] 21 Sep 2018, 11:11
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