chaitanya.bhansali wrote:if n=4p, where p is a prime number greater than 2, how many DIFFERENT positive EVEN divisors does n have, including n?
A) 2
B) 3
C) 4
D) 6
E) 8
Solution:
This is an interesting question because we are immediately given the option to insert any prime number we wish for p, as long as it's greater than 2. Since this is a problem-solving question, and there can only be one correct answer, we can select any value for p, as long as it is a prime number greater than 2. We want to work with small numbers if possible, so we can select 3 for p. Thus, we have:
n = 4 x 3
n = 12
Next we have to determine all the factors, or divisors, of p. Remember, the term "factor" is synonymous with the term "divisor."
1, 12, 6, 2, 4, 3
From this we see that we have 4 even divisors: 12, 6, 2, and 4.
If you are concerned that trying just one value of p might not substantiate the answer, try another value for p. Let's say p = 5, so
n = 4 x 5
n = 20
The divisors of 20 are: 1, 20, 2, 10, 4, 5. Of these, 4 are even: 20, 2, 10 and 4. As we can see, again we have 4 even divisors.
In fact, no matter what the value of p is, as long as it is a prime number greater than 2, n will always have 4 even divisors.
The answer is
C
