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# Math Strategies for Firefighter Exam Study Guide (page 2)

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Updated on Jun 23, 2011

### Backdoor Approaches for Answering Questions That Puzzle You

Remember those word problems you dreaded in high school? Many of them are actually easier to solve by backdoor approaches. The two techniques that follow are terrific ways to solve multiple-choice word problems that you don't know how to solve with a straightforward approach. The first technique, nice numbers, is useful when there are unknowns (like x) in the text of the word problem, making the problem too abstract for you. The second technique, working backward, presents a quick way to substitute numeric answer choices back into the problem to see which one works.

### Nice Numbers

1. When a question contains unknowns, like x, plug nice numbers in for the unknowns. A nice number is easy to calculate with and makes sense in the problem, such as 5, 10, 25, or even 1 or 2.
2. Read the question with the nice numbers in place. Then solve it.
3. If the answer choices are all numbers, the choice that matches your answer is the right one.
4. If the answer choices contain unknowns, substitute the same nice numbers into all the answer choices. The choice that matches your answer is the right one. If more than one answer matches, do the problem again with different nice numbers. You will only have to check the answer choices that have already matched.
Example: Judi went shopping with p dollars in her pocket. If the price of shirts was s shirts for d dollars, what is the maximum number of shirts Judi could buy with the money in her pocket?
1. psd

To solve this problem, let's try these nice numbers: p = \$100, s = 2; d = \$25. Now reread it with the numbers in place:

Judi went shopping with \$100 in her pocket. If the price of shirts was 2 shirts for \$25, what is the maximum number of shirts Judi could buy with the money in her pocket?

Since 2 shirts cost \$25, that means that 4 shirts cost \$50, and 8 shirts cost \$100. So your answer is 8. Let's substitute the nice numbers into all 4 answers:

1. 100 × 2 × 25 = 5000