If n is a positive integer is n + 4 divisible by 8?

Question

(1) n + 12 is divisible by 8

(2) n is divisible by 6

pushpitkc · Answer

We need to check if n + 4 divisible by 8, given n is a positive integer
1. (n+12)/8 
n can take values 4,12,20,..... . 
All of these numbers are divisible by 8, whether added by 4 or 12.
Hence, this condition alone is sufficient

2.n is divisible by 6
n can take values 6, when added with 4, isn't divisible by 8 .
n can be 12, when added with 4, is divisible by 8.
Hence, this condition alone is not sufficient

Hence choice A is the solution

Kurtosis · Answer

Question: Is n + 4 divisible by 8? --> Is n + 4 = 8K

St1: n + 12 = 8k
n = 8k - 12
n + 4 = 8k - 8 = 8(k - 1) = 8K
Sufficient

St2: n = 6k
n + 4 = 6k + 4 --> May or may not be divisible by 8
Not Sufficient

Answer: A

pushpitkc · Answer

Thanks for pointing out the error, vyshak. Corrected the solution!

AkshdeepS · Answer

Given x > 0

Is  \frac{(n + 4)}{8}  = Integer?

Values n can have are 4, 12, 24, 36 etc.

Statement 1: \frac{(n+12)}{8}  = Integer

Values n can take are 4, 12, 24, 36 etc (SUFFICIENT)

Statement 2:  \frac{n}{6}  = Integer

Values n can take are 6, 12, 18, 24 etc.

If n = 6, then answer to the question is NO i.e., n+4 is not divisible by 8

If n = 12, then then answer to the question is YES i.e., n+4 is divisible by 8

So NOT SUFFICIENT

So (A)

yezz · Answer

from 1

n = 8p-12 Thus , n+4 = 8p - 8 , i.e. n+4 is divisible by 8 .... suff

from 2

n = 6k , thus n+4 = 6k+4 ... depends on K .. insuff

A

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If n is a positive integer is n + 4 divisible by 8?

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