Question

\( k \) is a digit in the decimal \( 1.3k5 \), and \( 1.3k5 \) is less than \( 1.33 \).
Quantity A: \( k \)
Quantity B: \( 1 \).

• A. Quantity A is greater.
• B. Quantity B is greater.
• C. The two quantities are equal.
• D. The relationship cannot be determined from the information given.
• E.

Hint:

When comparing digits in inequalities, always check all possible digit values (0–9). Sometimes multiple cases lead to indeterminate relationships.

Answer 1

The Correct Option is D

Step 1: Understanding the condition.
We know that \( k \) is a digit (0 to 9) in the number \( 1.3k5 \), and it is given that \( 1.3k5<1.33 \).
Step 2: Establishing the range.
The number can be expressed as \( 1.3k5 = 1.305, 1.315, 1.325, \dots \) depending on the value of \( k \).
Since \( 1.3k5<1.33 \), possible values are: \[ 1.305, \, 1.315, \, 1.325 \] which correspond to \( k = 0, 1, 2 \).
Step 3: Comparing with 1.
Thus, \( k \) could be 0, 1, or 2. This means sometimes \( k = 1 \) (equal to Quantity B), sometimes \( k>1 \) (2 is greater than 1), and sometimes \( k<1 \) (0 is less than 1).
Step 4: Conclusion.
Since all cases (greater, less, equal) are possible, no definite relationship can be determined. Therefore, the correct answer is: \[ \boxed{\text{(D) The relationship cannot be determined.}} \]