ARArithmetic Reasoning

Percent & Markup

Percent problems on the ASVAB always come down to one equation — part = percent × whole — and knowing which of the three you're solving for.

Formula Reference

  • Percent of a number: part = (percent ÷ 100) × whole
  • What percent: percent = (part ÷ whole) × 100
  • Find the original: whole = part ÷ (percent ÷ 100)
  • Percent increase/decrease: % change = (new − old) ÷ old × 100
  • Markup: new price = original × (1 + rate). Example: $40 × 1.25 = $50
  • Discount: sale price = original × (1 − rate). Example: $80 × 0.80 = $64

What the ASVAB is actually testing

Percent questions on AR come in two flavors: straight percentage calculations (what is X% of Y?) and percent change problems (something went up or down — by what percent?). The test also pairs percent with real-world situations like pay, cost, and discounts — common military finance scenarios.

The math is simple. The errors come from setup, not computation.

The three percent question types

Type 1 — Find the part: "What is 30% of 80?" Convert the percent to a decimal (0.30) and multiply: 0.30 × 80 = 24.

Type 2 — Find the percent: "24 is what percent of 80?" Divide part by whole, then multiply by 100: (24 ÷ 80) × 100 = 30%.

Type 3 — Find the whole: "30% of what number is 24?" Divide the part by the decimal: 24 ÷ 0.30 = 80.

Before you calculate, identify which type you have. The numbers in the problem tell you what's given and what's missing.

Percent change vs. markup/discount

Percent change is always measured from the original (old) value, not the new one. A price that goes from $40 to $50 increased by $10 — but that's a 10/40 = 25% increase, not a 25% of the new price.

For markup and discount, the shortcut is the multiplier: 25% markup = multiply by 1.25. 20% discount = multiply by 0.80. This saves time over calculating the dollar change separately and adding/subtracting.

The most common trap

Applying percent change to the wrong base. "A price increased by 10%, then decreased by 10%" does NOT return to the original. If you start at $100, a 10% increase gives $110, and a 10% decrease of $110 gives $99 — not $100. The ASVAB doesn't usually test that specific trap, but it does test whether you anchor the calculation to the right starting number.

Connection to other topics

Percent connects directly to fractions/decimals (they're all the same idea in different notation) and to ratio problems (part-to-whole ratios are just percents in disguise). Strong percent skills also help on MK geometry when formulas require computing areas as fractions of totals.

Common Pitfalls

  • Confusing percent change with absolute change (a $20 increase on $80 is 25%, not 20%)
  • Applying discount to the wrong base — discounts apply to the original price, not a previous discounted price (unless the problem says otherwise)
  • Forgetting to convert percent to decimal before multiplying (35% must become 0.35)
  • Mixing up 'what is 30% of 60' with '30 is 60% of what number' — these use different setups

Worked Examples

Q1: A soldier's pay is $3,200/month. He spends 15% on food. How much does he spend on food?

Answer: Part = 0.15 × 3,200 = $480

Q2: A jacket originally costs $120 and is on sale for $90. What is the percent discount?

Answer: % change = (120 − 90) ÷ 120 × 100 = 30 ÷ 120 × 100 = 25%

Q3: After a 20% markup, an item costs $60. What was the original price?

Answer: 60 = original × 1.20 → original = 60 ÷ 1.20 = $50

Q4: A vehicle gets 18 mpg. After a tune-up, mileage improves by 10%. What is the new mpg?

Answer: New mpg = 18 × 1.10 = 19.8 mpg

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