For which of the following would modular division be useful?
下列哪项对于模除有用？

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BlackTom AI · Accepted Answer

The question asks for situations in which modular division would be useful, and provides several candidate scenarios to evaluate.
Option 1: testing whether numbers are even or odd. Modular division is directly related to parity, as a number is even if it is divisible by 2 (i.e., modulo 2 equals 0). This is a classic use of modular arithmetic, so this option is plausible.
Option 2: money calculations using dollars and cents. While currency computations often involve base-10 arithmetic, modular division itself is not a typical go-to tool for everyday money calculations; however, modular concepts can appear in algorithms (like hash functions or rounding strategies) that involve remainders. This option remains potentially relevant in broader algorithmic contexts, though less immediately about standard money math itself.
Option 3: All choices are correct. If each of the other options can be argued to involve a modular or remainder concept in some useful way, then this would be the correct umbrella answer. Here, parity checks are a clear modular use, and while everyday currency math isn’t a standard direct application of modular division, modular ideas can underpin more complex monetary computations in programming contexts.
Option 4: identifying the digits of an integer. Modular arithmetic is used to extract digits via division and remainder operations, such as getting the least significant digit (n mod 10) or successive digits when combined with division by powers of 10. This is another direct application of modular division concepts.
Option 5: time calculations using days and weeks. Similar to the money example, modular arithmetic can be employed to compute cycles and remainders when converting time units (for instance, determining how many days remain after allocating complete weeks). This is a standard area where modular reasoning helps.
In summary, each of the nontrivial options (parity, digit extraction, and time unit cycling) aligns with modular arithmetic ideas, and even money-related calculations can involve modular thinking in algorithmic contexts. Therefore, the option stating that all choices are correct correctly captures the broad applicability of modular division across these scenarios.

(862646) AP CS A Unit 1 Exam 第一单元考试

For which of the following would modular division be useful? 下列哪项对于模除有用？

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