Arithmetic Reasoning
15 questions · 55 minutes · AFQT
What's covered
Word problems. The arithmetic itself is easy; the difficulty is translating English into an equation. This is one of the two math sections that count toward your AFQT, so it deserves disproportionate study time.
Translate the words
'Of' means multiply. 'Is' means equals. 'Per' means divide. 'More than' means add. 'Less than' reverses the order — '5 less than x' is x − 5, not 5 − x.
Rate problems
d = r × t, rearranged as needed. Two objects moving toward each other: add their speeds to get closing speed. Average speed for a round trip is total distance ÷ total time — never the average of the two speeds.
Percent problems
Convert to a decimal and multiply. For increases and decreases, multiply by (1 ± rate): a 30% discount means paying 70%. Successive discounts never add — 25% then 10% off $80 gives $54, not $52.
Ratio and proportion
Find the multiplier. A 2:3 ratio with 10 boys means the multiplier is 5, so 15 girls. For 'parts of a whole,' add the parts first: 3 sand to 5 gravel is 8 total parts, so sand is 3/8.
Work-rate problems
Add rates, never times. One worker at 1/6 job per hour and another at 1/3 gives 1/2 per hour, so half an hour... no — 1/2 job per hour means the whole job takes 2 hours. For fill-and-drain, subtract the drain rate.
Interest
Simple interest is I = P × r × t. Compound interest grows on the new balance each period.
Method
Read the question twice. Write down what's given. Identify what's actually being asked — problems often make you solve for x and then ask for something else. Estimate before computing; it eliminates wrong choices fast.
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