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

Question

(1) when n+6 is divided by 3, the remainder is 1.

(2) when n^2 is divided by 3, the remainder is 1.

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lacktutor · Answer

( Statement1 ): when  n+6  is divided by  3 , the remainder is  1 .
 n+6 = 3*k +1  
 n+ 3*2 = 3*k +1 
-->  n = 3(k-2) +1 
The remainder will be  1 .
 Sufficient

( Statement2 ): when  n^2  is divided by  3 , the remainder is  1 .
if  n^{2} = 4^{2} , then  16= 3*5 +1 
-->  4= 3*1+1  (remainder is  1 )

if  n^{2} = 5^{2} , then  25= 5*5 +1 
-->  5= 3*1+2  (remainder is  2 )
 Insufficient

Answer (A).

GMATWhizTeam · Answer

Solution 
 Step 1: Analyse Question Stem 
 • n is a positive integer. 
We need to find the remainder when n is divided by 3.
 Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
 Statement 1:  When n+6 is divided by 3, the remainder is 1.
 • n + 6 = 3Q + 1
• n = 3Q +1-6
• n = 3(Q-2)+1
 o When n is divided by 3, the remainder is 1  
Hence, statement 1 is sufficient, we can eliminate answer options A and D.
 Statement 2:  When  n^2  is divided by 3, then the remainder is 1.
 • Whenever the square of a positive integer is divided by 3, then the remainder is either 0 or 1.
 o n is either be of the form 3q + 1 or 3q + 2, where p is a positive integer.
  If n = 3q+1, then remainder is 1
 If n =3q+2, then the remainder is 2.  
• We are not getting a unique answer. 
Hence, statement 2 is not sufficient, the correct answer is  Option A

the27s · Answer

(A)

Condition (1): Since n+6 gives reminder 1 when divided by 3, n=3m+1. When divided by 3, this always gives reminder 1.

Condition (2): n^2= 3m+1 for all m.
n=√3m+1 should be a perfect square, but not all squares can be expressed in this form. Hence, inadequate information to make a conclusion on 'n'.

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Archit3110 · Answer

the value of +ve integer n is to be determined
#1
when n+6 is divided by 3, the remainder is 1.
here n can be 1,4,7,10.. so on
we see that we get remainder 1 for all values of n ; sufficient
#2
when n^2 is divided by 3, the remainder is 1.
n=5,7,11 
insufficient as remainder are 2,1 
OPTION A ; sufficient

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

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