p is an integer, n is an integer and p/n is an integer. Is p/n=odd?1) ...
Explanation:
We are given that p is an integer, n is an integer and p/n is an integer, and we need to determine whether p/n is odd or not.
Statement 1: p is divisible by 4
If p is divisible by 4, then p can be written as p = 4k, where k is an integer. Substituting this value of p in the equation p/n = m, we get:
4k/n = m
Dividing both sides by 4, we get:
k/(n/4) = m/4
Since k is an integer, (n/4) must also be an integer. Therefore, n must be a multiple of 4. However, we cannot determine whether p/n is odd or not just from this statement.
Statement 2: n is divisible by 4
If n is divisible by 4, then n can be written as n = 4l, where l is an integer. Substituting this value of n in the equation p/n = m, we get:
p/4l = m
Multiplying both sides by 4, we get:
p = 4ml
Since 4ml is divisible by 4, p is also divisible by 4. However, we cannot determine whether p/n is odd or not just from this statement.
Combined Statements
From both statements, we know that p is divisible by 4 and n is divisible by 4. However, this information is still not sufficient to determine whether p/n is odd or not. Therefore, the correct answer is option D - More information is required as the information provided is insufficient to answer the question.