Percent-based word problems — discounts, markups, interest, and tip-style calculations — are some of the most common items on the Arithmetic Reasoning subtest. The key skills are converting a percent to a decimal and deciding whether to add (markup, tax) or subtract (discount).
How these questions were selected
These 10 questions were curated by the 247SimpleTests Editorial Team from our Arithmetic Reasoning practice bank. Each was selected because it covers a concept that appears frequently on the real exam and that many candidates find difficult on their first attempt. The full practice test has 30 questions — work through all of them once you've reviewed this guide.
The questions
Question 1
A jacket costs $80. It is on sale for 25% off. What is the sale price?
- $20
- $55
- $60 ✓
- $65
▶ Show full explanation
25% of $80 = $20 discount. Sale price = $80 - $20 = $60.
Source: ASVAB AR, DiscountQuestion 2
A soldier uses 3/8 of a fuel can. The can held 16 gallons. How many gallons were used?
- 4
- 5
- 6 ✓
- 8
▶ Show full explanation
3/8 × 16 = 48/8 = 6 gallons.
Source: ASVAB AR, FractionsQuestion 3
An item costs $1,200. With 6% sales tax, what is the total price?
- $1,272 ✓
- $1,268
- $1,206
- $1,260
▶ Show full explanation
Tax = 6% × $1,200 = $72. Total = $1,200 + $72 = $1,272.
Source: ASVAB AR, Sales TaxQuestion 4
A recipe calls for 3/4 cup of flour. If you want to make 2/3 of the recipe, how much flour do you need?
- 1/2 cup ✓
- 5/12 cup
- 1 1/3 cups
- 7/12 cup
▶ Show full explanation
To find a fraction of a fraction, multiply them: 3/4 × 2/3 = (3 × 2)/(4 × 3) = 6/12 = 1/2 cup. The word 'of' between fractions means multiply. Multiply the numerators (3 × 2 = 6) and the denominators (4 × 3 = 12), then reduce 6/12 to 1/2. A useful shortcut is to cancel before multiplying: the 3 in the numerator and the 3 in the denominator cancel, leaving 1/4 × 2/1 = 2/4 = 1/2. Fraction-of-a-quantity problems appear often in arithmetic reasoning, and the reliable method is to multiply and then reduce.
Source: ASVAB AR, Fraction of a QuantityQuestion 5
A jacket originally priced at $80 is discounted 25%. What is the sale price?
- $55
- $60 ✓
- $65
- $20
▶ Show full explanation
A 25% discount means you subtract 25% of the price. First find the discount: 25% of $80 = 0.25 × 80 = $20. Then subtract from the original: $80 − $20 = $60. A faster method is to recognize that after a 25% discount you pay 75% of the original: 0.75 × $80 = $60. Discount problems test whether you can convert a percent to a decimal and decide whether to subtract (discount) or add (markup/tax). The sale price here is $60; the $20 answer is the discount amount, not the final price, so read the question carefully.
Source: ASVAB AR, Discount PricingQuestion 6
How much simple interest is earned on $1,500 invested at 4% annual interest for 3 years?
- $60
- $180 ✓
- $1,680
- $200
▶ Show full explanation
Simple interest uses the formula I = P × r × t, where P is the principal, r is the annual rate as a decimal, and t is the time in years. Here I = $1,500 × 0.04 × 3 = $60 × 3 = $180. The interest earned is $180. Note the question asks only for the interest, not the total balance — the total would be $1,500 + $180 = $1,680, which is offered as a distractor. Memorize I = Prt for simple interest problems, convert the percent to a decimal (4% = 0.04), and multiply through carefully.
Source: ASVAB AR, Simple InterestQuestion 7
Convert the fraction 7/8 to a decimal.
- 0.78
- 0.875 ✓
- 0.87
- 0.7
▶ Show full explanation
To convert a fraction to a decimal, divide the numerator by the denominator: 7 ÷ 8 = 0.875. You can do this by long division, or by recognizing common conversions (1/8 = 0.125, so 7/8 = 7 × 0.125 = 0.875). Fraction-to-decimal conversions appear in arithmetic reasoning when comparing values or computing with money and measurements. Memorizing the eighths (0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875) is especially handy. The exact decimal value of 7/8 is 0.875.
Source: ASVAB AR, Fraction to DecimalQuestion 8
A store marks up an item that costs $40 by 30%. What is the selling price?
- $12
- $52 ✓
- $70
- $48
▶ Show full explanation
A markup is added to the cost. First find the markup: 30% of $40 = 0.30 × 40 = $12. Then add it to the cost: $40 + $12 = $52. Equivalently, a 30% markup means selling at 130% of cost: 1.30 × $40 = $52. Markup problems are the mirror image of discount problems — you add the percentage instead of subtracting it. The $12 distractor is just the markup amount, not the selling price. The item sells for $52.
Source: ASVAB AR, Markup PricingQuestion 9
If 5 workers can complete a job in 8 days, how many days would 10 workers take to complete the same job?
- 2
- 4 ✓
- 6
- 16
▶ Show full explanation
Inverse proportion: 5 workers × 8 days = 10 workers × d days. d = 40 ÷ 10 = 4 days.
Source: ASVAB AR, Inverse ProportionQuestion 10
A soldier scored 72, 85, 91, and 80 on four tests. What is the average (mean) score?
- 81
- 82 ✓
- 83
- 84
▶ Show full explanation
Sum = 72 + 85 + 91 + 80 = 328. Mean = 328 ÷ 4 = 82.
Source: ASVAB AR, AveragesThe percent principle: convert the percent to a decimal, then multiply by the base amount; subtract for a discount and add for a markup or tax. For simple interest use I = P × r × t. Watch whether the question asks for the change amount or the final total — a common trap.
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