Arithmetic and Basic Algebra
What this domain tests
The Arithmetic and Basic Algebra domain of the OAT Quantitative Reasoning test covers order of operations, signed numbers, factors and multiples, exponents, roots, absolute value, and the linear relationships that later algebra depends on. Items reward clean computation and recognition of structure rather than long brute force.
Core rules
- Work inside grouping symbols first, then exponents and roots, then multiplication and division left to right, then addition and subtraction left to right.
- A negative base in parentheses is raised with the exponent: (-2)^3 = -8, but -2^2 = -4.
- For exponents with the same base: x^a x^b = x^(a+b), x^a/x^b = x^(a-b), and (x^a)^b = x^(ab).
- The GCD is the largest factor shared by two integers; the LCM is the smallest positive multiple shared. For 12 and 18, GCD = 6 and LCM = 36.
- Absolute value is distance from zero, so |-7| = 7 and |x| = 5 gives x = 5 or x = -5.
Worked example
Evaluate 3(4 - 7)^2 - 8 / 2 + |-5|. Parentheses: 4 - 7 = -3. Square: (-3)^2 = 9. Multiply: 3 x 9 = 27. Divide: 8 / 2 = 4. Absolute value: 5. Then 27 - 4 + 5 = 28. A common wrong answer, 20, comes from treating -3^2 as 9 without parentheses or from subtracting before dividing.
Traps
Subtracting a negative is addition: 6 - (-4) = 10. Multiplication and division have equal priority, so 12 / 3 x 2 = 8, not 2. Do not distribute an exponent over addition: (a + b)^2 is not a^2 + b^2. When a question asks for the LCM, check whether it wants the least common multiple or the greatest common factor.