kminnesota14 wrote:
If X>1, what is the value of integer X?
(1)There are X unique factors of X
(2)The sum of X and any prime number larger than X is odd
Target question:
What is the value of integer X?
Statement 1: There are X unique factors of X
In other words, the factors of X must range from 1 to X, with every number in between.
In other words, the factors of X are: 1, 2, 3, . . . X-1, and X
We can see that this works when X=2 (factors are 1 and 2}
For any number greater than 2, X will not have factors ranging from 1 to X.
For any number greater than 2, X-1 cannot be a factor of X. In fact, when we divide X by X-1, the remainder will always be 1 (when X>2).
For example, 4 cannot be a factor of 5, 11 cannot be a factor of 12, etc.
Since only 2 satisfies the given condition,
x must equal 2.
So, statement 1 is SUFFICIENT
Statement 2: The sum of X and any prime number larger than X is odd
There are several values of X that satisfy this condition. Here are two cases:
case a:
X = 2. Here, every prime number greater than 2 will be odd, and 2 plus an odd number will always be odd.
case b:
X = 4. Here, every prime number greater than 4 will be odd, and 4 plus an odd number will always be odd.
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer =
A
Cheers,
Brent
