Note: I removed the word "integral" from the question, since "factor" and "divisor" both imply integral values.vinay1983 wrote:How many more positive factors does 2n have than the positive integer n?
1. n is an odd number
2. n is an odd prime number
Target question: How many more positive factors does 2n have than the positive integer n?
Statement 1: n is an odd number
There are several values of n that satisfy this condition. Here are two:
Case a: n = 5, in which case n has 2 positive factors (1,5) and 2n has 4 positive factors (1,2,5,10). So, 2n has 2 more factors than n has
Case b: n = 9, in which case n has 3 positive factors (1,3,9) and 2n has 6 positive factors (1,2,3,6,9,18). So, 2n has 3 more factors than n has
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: n is an odd prime number
Since n is prime, we know that n will have only 2 positive factors (1 and n).
What about 2n?
The factors of 2n will be 1, 2, n and 2n for a total of 4 positive factors
So, 2n must have 2 more factors than n has
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = B
Cheers,
Brent
