sparkles3144 wrote:Is x an odd integer?
1) x² is an odd integer
2) 2x is an even integer
Here's one solution . . .
Target question: Is x an odd integer?
Statement 1: x² is an odd integer
There are several values of x that meet this condition. Here are two:
Case a:
x = 5 (5² = 25, and 25 is odd). In this case
x is an odd integer
Case b:
x = √3 ((√3)² = 3, and 3 is odd). In this case
x is not an odd integer
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 2x is an even integer
There are several values of x that meet this condition. Here are two:
Case a:
x = 1, in which case
x is an odd integer
Case b:
x = 2, in which case
x is not an odd integer
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that there are 2 possibilities for the value of x
Possibility #1: x is an odd integer
Possibility #2: x is the square root of an odd integer, where x itself is
not an integer
From statement 2, we can be certain that x is an integer. We know this because we cannot multiply a non-integer by 2 and get an even integer as the product.
So, we can rule out Possibility #2, leaving us with Possibility #1, which means
x must be an odd integer.
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer =
C
Cheers,
Brent
