Skills Needed for the Test(Edit)

• Deciding when to add/subtract/multiply/divide. If you know which of these steps you need to take with which numbers, then you have solved the problem. Most problems will spell it out, giving you clues to:
• subtract if the problem says "difference" or "how much more"
• add if it talks about one number "and" another
• divide if it asks "how many somethings will fit in some other thing?"
• cross-multiply if it talks about the "rate" or telling you to "scale" something (such as, a 20 pound bag is $5, how much does 160 pounds cost?). (Another example: "5 inches on a map represents 10 feet. How many feet is something that is 32 inches on the map?")
• ...more examples to come.
• Cross-multiplication! The ASVAB loves to cross-multiply. So many problems boil down to this. The Wikipedia article on Cross-multiplication is pretty clear. You have to know this.
• Understanding that a number can be: a percentage (25%), a fraction (1/4 or 4/16), a decimal .25, and a ratio (1:4), and not change its meaning at all.
• To convert a decimal (.25) to a fraction, put the original number over 1 (.25/1) then move the decimal place of both to the right, filling in with zeros, until you get rid of the decimal (25/100), then reduce the fraction (see below).
• To convert a fraction to a decimal, do the long division. 1/4 really means "1 divided by 4".
• To convert a percentage to a decimal, just move the decimal two places to the right. You can think of the % as two zeros (reminding you of how many to move) and an arrow telling you which way to move it (/). So, 25% becomes .25 in decimal.
• To convert a decimal to a percentage just do the opposite---move the decimal place two to the right. So, .25 becomes 25% again.
• Ratios are just fractions with a different symbol. 1:4 is 1/4, or spelled out: "one to four" is "one over four".
• Convert units (inches/feet/yards, dozens, etc.). Many of the questions add these twists in to boost the difficulty, and most of the time the answer without the conversion is a choice. For example, if the answer is in feet, and it's looking for "3", then "36" is probably a choice.
• Filter useless facts out. Figure out what information is useful. Some problems have numbers that you don't have to use at all. Just think deep and wide.
• "Mess Questions". Some have many numbers and you do have to use every last one of them. A typical Mess Question involves several conversions of units, many steps, many pieces, and many places to screw up.
• Interest (financial). Usually "simple interest", but a few "complex interest" thrown in here and there, but nothing you need to memorize a formula for.
• Discounts. ASVAB is big on asking, "How much is this after a 25% discount?" and "This was discounted by 3%, how much was it before?" You just need to know: The discounted price is 100% minus the discount (so 75% if the discount is 25%). Multiply the original price by that new percent, and there is the discounted price. Or, to reverse the process, divide by the discounted price. This same trick is useful when asked how many are not in a group; for example, "32% of 550 people are men. How many people in the group are women?" Just subtract 32% from 100% then multiply: 68% (.68) times 550 is 374.
• Price increases. The problem, "How much is a $200 product after a 35% price increase?" can easily be solved by adding 100% and 35% then multiplying: $200 times 1.35 is $270.
• Distributive Property. They want to be sure you know 5 * (10 + 2) is 5*10 + 5*2. I don't think it gets more complicated than that on the test.
• Reducing fractions. Many times your answer will come out to something like 2/12, but that isn't on the list of choices. So you divide the top (the numerator) and the bottom (the denominator) by 2, and get: 1/6. When I'm reducing fractions I usually:
• divide by 10 if both numbers end in zero (that is, you drop a zero from the right of both numerator and denominator),
• divide by 5 if both numbers end in 5
• divide by 2 if the number is even
• try dividing by 3 if the numbers are odd
• try other odd numbers. Once you've divided by everything from 2 to half the number, you can stop.
• start again from the top any time one of the steps works.

Other Advice(Edit)

There are some general tips that will help on any test like this:

• Be sure to double-check the answer for reasonableness. Often you can instantly estimate a range that the answer has to be within. Once you're done with the work make sure the result is in this boundary.
• Work the problem forward and backward. Let's say the problem asks you for 180 minus 13, and you get 167. Then the safe thing to do is try 167 plus 13 and see if it is 180.
• Combine both of the above tricks: Sometimes you can work backwards from the multiple-choice answers. If you pick the best looking one, plug it into the problem, you can find your answer without the heavy work. Sometimes you are close, so you adjust your next guess accordingly.
• Manage your Notes:
• Use clear handwriting---painfully clear. Even if you feel like you are slowing way down, it will save time.
• Clear language with yourself. That is, make sure you can go back and read everything and understand why you wrote it. A good first step is to write the problem number and circle it before you start your work. Also, put a box around the answers. Everything in that region should be just about that one problem. Write down all the units (if something is 6 inches write "6 in", not "6"). Remember that math is already very stripped down and bare, so if you try to do something (like leaving out the "x" symbol in a long multiplication), you are probably making a mess.

Samples(Edit)

A few example questions, from Official-Asvab.com:

1. If the tire of a car rotates at a constant speed of 552 times in one minute, how many times will the tire rotate in half-an-hour?
2. One in every 9 people in a town vote for party A. All others vote for party B. How many people vote for party B in a town of 810?
3. A motorcycle cost $7,250. If it depreciates by 12% per year, how much will it be worth after one year?

More samples can be found:

• KapTest.com (5 of them)
• ASVABPrepInfo.com (5 of them)

Full Notes(Edit)

This is a new project I'm doing. I'm going to catalog every question on the Peterson's test by the skills needed. Then I'll take the most important skills and make Youtube videos for them. I'll make the process public because the information will have some value even at the early stages.

1 take percentage; avoid confusion (negation)

2 cross-multiply

3 cross-multiply (with 1)

4 distributive property

5 avoid confusion

6 make change (long subtraction)

7 cross-multiply (with 1)

8 cross-multiply

9 ignore distractions; reduce fraction; convert units

10 calculate discount

11 cross-multiply

12 calculate discount (compound)

13 "Craig spent exactly one dollar to buy 3-cent stamps and 5-cent stamps. The number of 5-cent stamps that he could NOT have bought is"

14 cross-multiply (with 1)

15 rate arithmetic

16 calculate price increase

17 cross-multiply

18 time arithmetic

19 calculate percentage

20 cross-multiply; convert units

21 rate arithmetic ("A car that averages 21 miles to the gallon starts a trip with a full 10-gallon tank of gas. If the car travels 150 miles, how many more miles can it go before the tank is empty?")

22 "If a man buys lemons at 3 for 30 cents and intends to sell them at 5 for 60 cents, how many lemons does he have to sell in order to make a profit of 50 cents?"

23 calculate percentage

24 unit cost ($)

25 know ounces in quarts; reduce fractions

26 cross-multiply

27 simple interest; avoid confusion

28 "A plumber needs eight pieces of pipe, each 3 feet 2 inches long. If pipe is sold only in sections of 10 feet each, how many sections must he buy?"

29 average two different rates

30 work equation (cross-multiply)