What is the remainder when the positive integer n is divided

Question

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

Bunuel · Accepted Answer

What is the remainder when the positive integer n is divided by 3?

(1) The remainder when n is divided by 2 is 1 -->  n=2k+1 , just tells us that  n  is odd. Not sufficient.

(2) The remainder when n + 1 is divided by 3 is 2 -->  n+1=3q+2  -->  n=3q+1 , hence  n  divided by 3 yields remainder of 1. Sufficient.

Answer: B.

shaselai · Answer

Lets take another approach if you couldnt derive what bunnel did.

1. remainder n/2 =1 
lets try some numbers:
n=3 remainder =1 n/3 remainder =0
n=5 remainder = 1 5/3 remainder =2
So NO FOOD

2. 
n=4 n+1 =5 5/3 =2 4/3 =1
n=7 n+1=8 8/3=2 7/3 =1

Notice how the trend is every 3 for n. so it is working correctly

B

TGC · Answer

n=3A+r

What is r?

(1).

n=2B+1 => N is odd but odd numbers also can give different remainders when divided by 3 .
INSUFFICIENT

(2).

n+1 = 3C +2
n= 3C +1

REM=1

Hence (B) it is !!

Kinshook · Answer

Asked: What is the remainder when the positive integer n is divided by 3?

(1) The remainder when n is divided by 2 is 1. 
n = 2k + 1
If n=1; The remainder when the positive integer n is divided by 3 = 1
If n=3: The remainder when the positive integer n is divided by 3 = 0
If n=5; The remainder when the positive integer n is divided by 3 = 2
The remainder when the positive integer n is divided by 3 = {0,1, 2}
NOT SUFFICIENT

(2) The remainder when n + 1 is divided by 3 is 2
n + 1 = 3k + 2
n = 3k + 1
The remainder when the positive integer n is divided by 3 = 1
SUFFICIENT

IMO B

MHIKER · Answer

(1) n=2q+1;1, 3, 5, 7.. When divided 3 there are different remainders; Insufficient.

(2) n+1=3q+2

Or, n=3q+1; Sufficient.

The answer is B

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What is the remainder when the positive integer n is divided

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What is the remainder when the positive integer n is divided

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