Answer: [A]: "(33/66) is a rational number."
_____
Explanation:
Note: An irrational numbe" would refer to a number that meets both of the following criteria (by definition):
1) non-terminating decimal value; and:
2) non-repeating decimal value; or, "non-repeating sequence" of decimal values.
_____
Otherwise, the number would be a rational number.
Let's examine the given 'answer choices'—as follows:
_________________
Choice [A]: "(33/66) is a rational number."
Note: "33/66" = (33 ÷ 33) / (66 ÷ 33) = 1/2 = 1 ÷ 2 = 0.5 .
→ "0.5" is "terminating" and "non-repeating".
Since the decimal does not meet both criteria for an "irrational number";
"(33/66)" is, in fact, a rational number.
Choice [A]: "(33/66) is a rational number." → is a true statement!
_____
Now, let's consider the other answer choices:
_____
Choice [B]: "(-33/66) is not a rational number."
Note: This is the negative value of Choice: [A]—as explained ^above.
→ "(-33/66)" = -0.5 ; which is a rational number—see explanation ^above.
Choice: [B] "(-33/66) is Not a rational number"—is Incorrect.
_____
Choice [C]: "(66/24) is not a rational number."
Note: "66/24" = (66 ÷ 6) / (24 ÷ 6) = (11 ÷ 4) = 2.75 .
→ "2.75" is "terminating" and "non-repeating".
Since the decimal does not meet both criteria for an "irrational number";
"(66/24)" is, in fact, a rational number.
Choice [C]: "(66/24) is not a rational number"—is Incorrect.
_____
Choice [D]: "(2.45678...) is a rational number."
Note: This given answer choice suggests the decimal value is:
1) not terminating; and
2) non-repeating (no "repeating bars"—and no repetitive decimals or groups of the same decimals repeating);
→ And as such, by definition, is an irrational number.
→ Choice: [D]: "(2.45678...) is a rational number"—is Incorrect.
_____
The correct answer is: [A]: "(33/66) is a rational number."
_____
Hope you find this helpful! Best of luck to you!
_____