x is the repeating decimal .097531, meaning the sequence of digits 0, 9, 7, 5, 3, 1 repeats indefinitely. Quantity A: The 44th digit of x to the right of the decimal point Quantity B: 3

Rationale

The 44th digit of x is equal to 3.

To determine the 44th digit of the repeating decimal 0.097531, we first note that the repeating sequence consists of six digits: 0, 9, 7, 5, 3, 1. By finding the position of the 44th digit within this cycle, we can ascertain its value.

A (Quantity A is greater.) YOUR ANSWER

This choice suggests that the 44th digit is greater than 3. However, since the repeating sequence contains the digits 0, 9, 7, 5, 3, and 1, the maximum possible digit is 9. Checking the 44th position reveals it is actually 3, which contradicts this option.

B (Quantity B is greater.) YOUR ANSWER

This option implies that the 44th digit is less than 3. As established, the 44th digit corresponds to the digit '3' from the repeating sequence. Therefore, this choice is incorrect because 3 is not less than itself.

C (The two quantities are equal.) CORRECT

The 44th digit corresponds to the 44 mod 6, which is 2 (since 44 divided by 6 gives a remainder of 2). The second digit in the repeating sequence (0, 9, 7, 5, 3, 1) is indeed '3'. Hence, Quantity A and Quantity B are equal.

D (The relationship cannot be determined from the information given.) YOUR ANSWER

This option suggests that we lack sufficient information to compare the quantities. However, the periodic nature of the repeating decimal allows us to definitively determine the value of the 44th digit. Therefore, this statement is incorrect.

Conclusion

Upon analyzing the repeating decimal and determining the position of the 44th digit, we find that it equals 3. Thus, the two quantities are indeed equal, confirming that the answer is C. This highlights the importance of understanding repeating decimals and modular arithmetic in determining specific digits within a sequence.

x is the repeating decimal .097531, meaning the sequence of digits 0, 9, 7, 5, 3, 1 repeats indefinitely. Quantity A: The 44th digit of x to the right of the decimal point Quantity B: 3

The 44th digit of x is equal to 3.

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