FDP Strategy: Choose Smart Numbers

Question 1

How do Smart Numbers work?

Answer 1

Some algebra problems — that involve unknowns, or variables — can be turned into arithmetic problems instead.

Step 1: Choose numbers to replace the unknowns. How do you know you can choose a random number in the first place? The problem talks about a number but never supplies a real value for that number anywhere in the problem or in the answers. If you were to do this problem algebraically, you would have to assign a variable. Instead, choose a real number.

• If I have to pick for more than one variable, pick different numbers for each one
• If the problem says that x + y = z, then note that once you pick x and y, you HAVE to calculate Z
• Follow any constraints given in the problem.
• Avoid using 0, 1, or numbers that already appear in the problem
• Choose numbers that work easily in the problem. 100 is most used for percent problems. On fractions problems, try the common denominator of any fractions that appear in the problem.

Step 2: Solve the problem using your chosen smart numbers.

Step 3: Find a match in the answers.

1. Pick the matching fraction or percent in the answers, or
2. Plug your smart numbers into the variables in the answer choices and LOOK for the choice that MATCHES your target.

Question 2

Smart numbers with percents

Answer 2

The choose smart numbers technique can be used any time a problem contains only UNSPECIFIED values. The easiest example of such a problem is one that contains variables, percents, fractions, or ratios. It does not provide real numbers for those variables, even in the answer choices.

Question 3

Smart numbers with fractions

Answer 3

When working with fraction problems, choose a common denominator of the fractions given in the problem.

Question 4

Smart numbers with variables in the answers

Answer 4

The same strategy works when there are variables, rather than percents or fractions, in the answers.

Question 5

Dont’s

Answer 5

1. Do not pick 0 or 1
2. Do not pick numbers that appear elsewhere in the problem
3. If you have to choose multiple numbers, choose different numbers, ideally with different properties (e.g., odd and even).