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Arithmetic Foundations Mastery Hub: The Industry Foundation

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Q1Domain Verified
s for "Arithmetic Foundations Mastery Hub: The Industry Foundation" based on the hypothetical course "The Complete Number System & Divisibility Course 2026: From Zero to Expert!": Question: Consider the set of integers $\mathbb{Z}$. If we define a relation $a \sim b$ if and only if $a - b$ is divisible by 3, which of the following statements accurately describes the properties of this relation?
$\sim$ is symmetric and transitive, but not reflexive.
$\sim$ is an equivalence relation, partitioning $\mathbb{Z}$ into exactly two distinct equivalence classes.
$\sim$ is an equivalence relation, partitioning $\mathbb{Z}$ into exactly three distinct equivalence classes.
$\sim$ is reflexive and transitive, but not symmetric.
Q2Domain Verified
Let $S$ be the set of positive integers $n$ such that $n^2 + 1$ is divisible by 5. What is the cardinality of the set $S \cap \{1, 2, 3, \dots, 100\}$?
40
25
50
20
Q3Domain Verified
A retailer marks up an item by 20% and then offers a 15% discount on the marked price. If the original cost of the item was $100, what is the final selling price?
$107.00
$105.00
$109.00
$103.00

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This domain protocol is rigorously covered in our 2026 Elite Framework. Every mock reflects direct alignment with the official assessment criteria to eliminate performance gaps.

This domain protocol is rigorously covered in our 2026 Elite Framework. Every mock reflects direct alignment with the official assessment criteria to eliminate performance gaps.

This domain protocol is rigorously covered in our 2026 Elite Framework. Every mock reflects direct alignment with the official assessment criteria to eliminate performance gaps.

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