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# What is the remainder when the positive integer n is divided

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Senior Manager
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What is the remainder when the positive integer n is divided [#permalink]  03 Aug 2005, 05:35
What is the remainder when the positive integer n is divided by 3?

1) The remainder when n is divided by 2 is 1
2.) The remainder when n+1 is divided by 3 is 2

plz why b is sufficient thanks
Manager
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n+1=3k+2

==>n=3k+1 ==> rem is 1
Director
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Stmt 1 is insufficient because n = 2k + 1 means n is odd. However we cannot conclude the remainder when n is divided by 3 simply by knowing n is odd. E.g. if n = 5, 5/3 = 2. if n = 7, 7/3 = 1. So insuff

Stmt 2 says n + 1 = 3k + 2; n = 3k + 1
This tells us the remainder when n is divided by 3 = 1
so sufficient
Senior Manager
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B

1) The remainder when n is divided by 2 is 1

=> we know n is an odd number, but cannot decide what will be remainder
after divided by 3

2.) The remainder when n+1 is divided by 3 is 2

=> from n+1 divided by 3, remainder is 2, we know n has to be: 3K+1, therefore remainder is 1

==========
What is the remainder of -2 divided by 3 ?
Senior Manager
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From conditon 1 n = 2x+1 insufficient

From COnditon 2 n = 3y + 5 , surely not divisible by 3.
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Senior Manager
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qpoo wrote:
B

1) The remainder when n is divided by 2 is 1

=> we know n is an odd number, but cannot decide what will be remainder
after divided by 3

2.) The remainder when n+1 is divided by 3 is 2

=> from n+1 divided by 3, remainder is 2, we know n has to be: 3K+1, therefore remainder is 1

==========
What is the remainder of -2 divided by 3 ?

We get reminder of -2, -2 = (3*0)-2
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Senior Manager
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thanks ranga,

the remainder of -2 divided by 3, can I also say:

We get reminder of 1, -2 = (-1*3)+1 ?

I guess it depends on if we allow remainder to be negative.
Senior Manager
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qpoo wrote:
thanks ranga,

the remainder of -2 divided by 3, can I also say:

We get reminder of 1, -2 = (-1*3)+1 ?

I guess it depends on if we allow remainder to be negative.

Two reminders for one division...You got me there..
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Manager
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The remainder of -2 divided by 3 is 1.

Remainders should be 0<= r <= q-1

for a = bq + r
Intern
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B. 2nd condition is sufficient.
The question specifically asks for positive integer n

Vik
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