What the ASVAB is actually testing
Number properties questions check conceptual knowledge, not calculation skill. The test asks about odd/even behavior, prime numbers, absolute value, factors, and multiples — things you either know or you don't. The good news is these rules are short, fixed, and completely learnable in an afternoon.
Absolute value: always non-negative
Absolute value is the distance from zero on a number line. Distance is never negative. So |−7| = 7 and |7| = 7. The expression inside can be negative; the result never is.
When absolute value appears in an equation — like |2x − 6| = 10 — there are always two cases: the inside equals the positive value, or the inside equals the negative of the right side. Solve both and check both.
Prime numbers: know the list
The ASVAB tests primes up to about 50. Memorize: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47. Two key facts: 2 is the only even prime. 1 is not prime (by definition).
To test an unfamiliar number, check divisibility by all primes up to its square root. For 51: √51 ≈ 7.1, so test 2, 3, 5, 7. It's divisible by 3 → not prime.
GCF vs. LCM: which direction are you going?
GCF (Greatest Common Factor) is used when you want to reduce or split — the biggest number that divides evenly into both. LCM (Least Common Multiple) is used when you need a common denominator or want the smallest number both divide into.
A quick way to remember: GCF shrinks, LCM grows.
Sign behavior with multiple negatives
Count the negative signs. Even number of negatives → positive result. Odd number → negative result. This applies to both multiplication and division chains.
Connection to other topics
Number properties underlie fraction work (GCF helps simplify, LCM gives common denominators), exponent rules (sign behavior matters when bases are negative), and polynomial operations. Strong number property knowledge speeds up everything else on the MK section.