If n is an integer, what is the remainder when 3+8n is divided by 6?

Question

If  n  is an integer, what is the remainder when  3+8n  is divided by 6? 
1)  n  is a multiple of 2
2)  n  is a multiple of 3

SHoylandBPrep · Answer

Stat (1) 
You can plug in for n and calculate the remainder:

If n = 2, then
→ 3 + 8n = 19
→ The remainder of 19 ÷ 6 is 1.

If n = 4, then
→ 3 + 8n = 35
→ The remainder of 35 ÷ 6 is 5.

Insufficient

Stat (2) 
You can prove that this is sufficient. If n is a multiple of 3, then 8n is a multiple of 6 because its prime factorization will have a 2 from 8 and a 3 from n. Therefore,

→ 3 + 8n = 3 + (multiple of 6)

so the remainder when you divide 3 + 8n by 6 has to be 3.
 Sufficient

(b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Mona2019 · Answer

B IMO is sufficient 
As when n is a multiple of 3, 8*3m = 6*4m will always be divisible by 6, so the remainder will always be 3.

In option 1, the remainder varies with different multiples of 2

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TestPrepUnlimited · Answer

Instead of finding the remainder of (8n + 3) / 6, we can ask for the remainder of (8n / 6). Knowing the remainder of (8n / 6) is enough to determine the remainder of (8n + 3) / 6.

Then (8n / 6) = (4n / 3) = (3n + n) / 3. We know 3n is a multiple of 3, thus the remainder of (4n / 3) is determined by (n / 3).  So we want to know the remainder of n divided by 3.

Statement 1:

Doesn't tell us anything about n/3, insufficient.

Statement 2:

The remainder of n/3 has to be 0 thus this is sufficient.

(With this statement, the remainder of 8n / 6 would also be 0, and the remainder of (8n + 3)/6 would be 3.)

Ans: B

chetan2u · Answer

3+8n=3+6n+2n

As 6n is divisible by 6 and we are looking for divisiblity by 6, we now have to look for divisiblity of 3+2n.
3+2n will always be ODD and so would surely leave a odd remainder when divided by 6. Possible remainders are 1,3 and 5, and we will surely have a pattern or cyclicity of these three numbers here.

n=1....3+2n=5.....R=5
n=2....3+2n=7.....R=1
n=3....3+2n=9.....R=3
and so on
So cyclicity is 5,1,3,5,1,3.....

1) n is a multiple of 2
Remainder can be 1,5,3 when n is 2,4,6.
Insufficient

2) n is a multiple of 3
Remainder is always 3.
Sufficient

B

Archit3110 · Answer

#1
3+8n
Where n can be 2,4,6 we get different value.of remainder when divided by 6 insufficient
#2
N is multiple of 3
3+8n
Always give remainder of 3 when divided by 6 sufficient
Option B

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PRAJESH0133 · Answer

(3+8n) mod 6
=(3 mod 6 + 8n mod 6) mod 6
=( 3 mod 6 + 4n mod 3) mod 6
Only value of n mod 3 is required.

Hence, statement 2 is sufficient. B

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If n is an integer, what is the remainder when 3+8n is divided by 6?

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If n is an integer, what is the remainder when 3+8n is divided by 6?

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