Armed Services Vocational Aptitude Battery (ASVAB) Arithmetic Reasoning (AR) Flashcards

24 sample cards from the Arithmetic Reasoning (AR) deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. If two people work together, how do you combine their work rates?

   Add their individual rates (jobs per unit time); the time together = 1 divided by the combined rate (e.g., 1/4 + 1/6 = 5/12, so 12/5 hours).

2. What is the simple interest formula?

   I = P x r x t, where P is principal, r is the annual rate (as a decimal), and t is time in years.

3. What is the compound interest formula for the final amount?

   A = P(1 + r/n)^(nt), where n is the number of compounding periods per year, r the annual rate, t the years.

4. How do you compute the total amount owed or accrued with simple interest?

   Total = Principal + Interest = P + (P x r x t) = P(1 + rt).

5. How do you calculate a discount and the sale price?

   Discount = original price x discount rate; Sale price = original price - discount (or original x (1 - rate)).

6. How do you calculate sales tax and the final total?

   Tax = price x tax rate; Total = price + tax (or price x (1 + tax rate)).

7. How do you calculate percent increase or percent decrease?

   Divide the amount of change by the original value, then multiply by 100: (change / original) x 100.

8. In a word problem, what phrases typically signal addition?

   Sum, total, plus, increased by, more than, combined, altogether.

9. In a word problem, what phrases typically signal subtraction?

   Difference, less than, fewer, decreased by, minus, remain, take away.

10. In a word problem, what phrases signal multiplication and division?

    Multiplication: product, times, of, twice, per (for rates). Division: quotient, per, ratio, split equally, out of.

11. In word problems, what word usually translates to an equals sign?

    Is, are, was, were, gives, results in, or yields all indicate equality (=).

12. How does 'less than' differ in order from normal subtraction wording?

    '5 less than x' means x - 5, not 5 - x; the order is reversed compared to how it is read.

13. What are the general steps to solve a multi-step word problem?

    Read carefully, identify what is asked, list known values, translate to an equation, solve step by step, then check the answer against the question.

14. How do you find the average (arithmetic mean) of a set of numbers?

    Add all the values and divide by the count of values.

15. If you know the average and the number of items, how do you find the total sum?

    Multiply the average by the number of items: Sum = Average x Count.

16. How do you find a missing value when given the desired average?

    Multiply the desired average by the total count to get the required sum, then subtract the sum of the known values.

17. What is a weighted average and when is it used?

    An average where values carry different weights; multiply each value by its weight, sum those products, and divide by the total weight (used when groups differ in size).

18. How do you solve a basic mixture problem (e.g., combining solutions)?

    Track the amount of the key ingredient: (amount1 x concentration1) + (amount2 x concentration2) = total amount x final concentration.

19. What is the median of a data set and how do you find it?

    The middle value when numbers are ordered; with an even count, it is the average of the two middle values.

20. What is the mode of a data set?

    The value that appears most frequently; a set can have one mode, multiple modes, or none.

21. How many inches are in a foot, feet in a yard, and inches in a yard?

    12 inches = 1 foot; 3 feet = 1 yard; 36 inches = 1 yard.

22. What are common U.S. measurement conversions for capacity and weight?

    1 gallon = 4 quarts; 1 quart = 2 pints; 1 pint = 2 cups; 1 pound = 16 ounces; 1 ton = 2000 pounds.

23. How do you convert a quantity between units (e.g., feet to inches)?

    Multiply by the conversion factor when going to a smaller unit (more units), and divide when going to a larger unit (fewer units).

24. What is estimation and a common technique for it?

    Finding an approximate answer by rounding numbers to convenient values before computing, used to check reasonableness of results (e.g., 198 x 21 is about 200 x 20 = 4000).

What this deck covers

Arithmetic Reasoning (AR) flashcards FAQ