Tip #31 to Get a Top SAT Math Score

Example Problems

Easy

1. For a fund raiser, the meditation club is selling tee-shirts with a choice of two slogans, "See clearly" or "Non-attachment." Each shirt is available in small, medium, or large. How many different types of shirts are available?
2. Five actors are being cast to fill five roles. If each actor plays only one role, how many different arrangements of actors in the five roles are possible?
   1. 5
   2. 10
   3. 60
   4. 120
   5. 240
3. At the build-your-own-burrito bar, you can choose chicken, beef, or shrimp. You can include no vegetable, spinach, or sautÉed zucchini; and you can top it with mild, medium, hot, or killer salsa. How many different burritos can be ordered?
   1. 8
   2. 18
   3. 24
   4. 36
   5. 48

Medium

4. The four digits 1, 2, 3, and 4 are used to form a number in which no digit is used more than once. How many such numbers are possible?
   1. 8
   2. 16
   3. 18
   4. 21
   5. 24
5. How many different three-digit positive integers have only prime numbers as digits?
   
6. Kyle will write 3 different symbols shown above on a banner. How many such arrangements are possible?

Answers

1. 6   Draw a blank for each option. Then write in the number of possibilities that can fill each option. There are 2 slogan options and 3 size options, so 2 × 3 = 6. Notice that this question is simple enough to do without the strategy, you could just picture shirts in piles, like at Old Navy, with two different slogans available in S, M, and L, making 6 piles.
2. D   Draw a blank for each role that needs to be filled by an actor. Then write in the number of actors who can fill the role. Remember that each actor can play only one role, so once someone is assigned, that actor can't be used again. Then multiply. 5 × 4 × 3 × 2 × 1 = 120
3. D   Draw a blank for each spot at the burrito bar. Then write in the number of possibilities that can fill each slot. There are 3 options for meat, 3 options for vegetables, and 4 options for salsas, so 3 × 3 × 4 = 36
4. E   Draw a blank for each digit of the four-digit number. Fill in the number of possible digits that can go in each blank. No digit can be used more than once. So, 4 × 3 × 2 × 4 = 24.
5. 64   Draw a blank for each digit of the three-digit number. Fill in the number of possible digits that can go in each blank. There are 4 prime numbers that can fill each blank: 2, 3, 5, and 7. Remember that 1 is not prime, but 2 is. Notice that the question does not say that a digit can be used only once. So, 4 × 4 × 4 = 64.
6. 60   Draw a blank for each spot on the banner. Fill in the number of possible symbols that can go in each spot. Notice that the three symbols must be different. So, 5 × 4 × 3 = 60.

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