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Math Strategies for Armed Services Vocational Aptitude Battery (ASVAB) Study Guide (page 2)

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Updated on Jun 23, 2011

Working Backward

You can frequently solve a word problem by plugging the answer choices back into the text of the problem to see which one fits all the facts stated in the problem. The process is faster than you think because you will probably only have to substitute one or two answers to find the right one.

This approach works only when:

• All of the answer choices are numbers.
• You are asked to find a simple number, not a sum, product, difference, or ratio.

Here's what to do:

1. Look at all the answer choices and begin with the one in the middle of the range. For example, if the answers are 14, 8, 2, 20, and 25, begin by plugging 14 into the problem.
2. If your choice doesn't work, eliminate it. Determine if you need a larger or smaller answer.
3. Plug in one of the remaining choices.
4. If none of the answers works, you may have made a careless error. Begin again or look for your mistake.
5. Example: Juan ate of the jellybeans. Maria then ate of the remaining jellybeans, which left 10 jellybeans. How many jellybeans were there to begin with?

1. 60
2. 90
3. 120
4. 140

Starting with the middle answer, let's assume there were 90 jellybeans to begin with:

Since Juan ate of the jellybeans, that means he ate 30 ( × 90 = 30), leaving 60 of them (90 – 30 = 60). Maria then ate of the 60 jellybeans, or 45 of them ( × 60 = 45). That leaves 15 jellybeans (60 – 45 = 15).

The problem states that there were 10 jellybeans left, and we wound up with 15 of them. That indicates that we started with too big a number. Thus, 90, 120, and 140 are all incorrect! With only two choices left, let's use common sense to decide which one to try. The next lower answer is only a little smaller than 90 and may not be small enough. So, let's try 60:

Since Juan ate of the jellybeans, that means he ate 20 ( × 60 = 20), leaving 40 of them (60 – 20 = 40). Maria then ate of the 40 jellybeans, or 30 of them ( × 40 = 30). That leaves 10 jellybeans (40 – 30 = 10).

Because this result of 10 jellybeans remaining agrees with the problem, the right answer is a.

Math Glossary

Denominator     The bottom number in a fraction. Example: 2 is the denominator in

Difference     Subtract. The difference of two numbers means subtract one number from the other.

Divisible by     A number is divisible by a second number if that second number divides evenly into the original number. Example: 10 is divisible by 5 (10 ÷ 5 = 2, with no remainder). However, 10 is not divisible by 3. (See Multiple of .)

Even Integer     Integers that are divisible by 2, like…–4, –2, 0, 2, 4.…(See Integer.)

Integer     Numbers along the number line, like…–3, –2, –1, 0, 1, 2, 3.…Integers include the whole numbers and their opposites. (See Whole Number.)

Multiple of     A number is a multiple of a second number if that second number can be multiplied by an integer to get the original number. Example: 10 is a multiple of 5 (10 = 5 × 2); however, 10 is not a multiple of 3. (See Divisible by.)

Negative Number     A number that is less than zero, like…–1, –18.6, – .…

Numerator     The top part of a fraction. Example: 1 is the numerator of .

Odd Integer     Integers that aren't divisible by 2, like…–5, –3, –1, 1, 3.…

Positive Number     A number that is greater than zero, like…2, 42, , 4.63.

Prime Number     Integers that are divisible only by 1 and themselves, like…2, 3, 5, 7, 11.… All prime numbers are odd, except for number 2. The number 1 is not considered prime.

Product     Multiply. The product of two numbers means the numbers are multiplied together.

Quotient     The answer you get when you divide. Example: 10 divided by 5 is 2; the quotient is 2.

Real Number     All the numbers you can think of, like… 17, –5, , –23.6, 3.4329, 0.… Real numbers include the integers, fractions, and decimals. (See Integer.)

Remainder    The number left over after division. Example: 11 divided by 2 is 5, with a remainder of 1.

Sum     Add. The sum of 2 numbers means the numbers are added together.

Whole Number     Numbers you can count on your fingers, like…1, 2, 3.…All whole numbers are positive.