Taking A Guess This week I would like to discuss another very basic math strategy for standardized tests such as the ACT and SAT. This strategy is extremely simple to apply and it will often allow you to avoid messy algebraic computations. I call this strategy “Take a Guess.” Sometimes the answer choices themselves cannot be substituted in for the unknown or unknowns in the problem. But that doesn’t mean you can’t guess your own numbers. Try to make as reasonable a guess as possible, but don’t over think it. Keep trying until you zero in on the correct value. Example Let’s see this simple technique in action with an appropriate math problem. Bill has cows, pigs and chickens on his farm. The number of chickens he has is three times the number of pigs, and the number of pigs he has is 2 more than the number of cows. Which of the following could be the total number of these animals? (A) 14 (B) 15 (C) 16 (D) 17 (E) 18 Let’s take a guess and say that Bill has 3 cows. He then has 3 + 2 = 5 pigs, and also 3·5 = 15 chickens. So the total number of animals is 3 + 5 + 15 = 23. This is too big. So let’s guess lower and say that Bill has 1 cow. Then he has 1 + 2 = 3 pigs, and 3·3 = 9 chickens. It follows that the total number of animals is 1 + 3 + 9 = 13, too small. So Bill must have 2 cows, 2 + 2 = 4 pigs, and 3·4 = 12 chickens. Thus, the total we get is 2 + 4 + 12 = 18 animals. So the answer is choice (E). Note: We were pretty unlucky to have to take 3 guesses before getting the answer, but even so, not too much time was used. Let’s see what happens when we try to solve this algebraically: If we let x represent the number of cows, then the number of pigs is x + 2, and the number of chickens is 3(x + 2). Thus, the total number of animals is x + (x + 2) + 3(x + 2) = x + x + 2 + 3x + 6 = 5x + 8. So some possible totals are 13, 18, 23, … which we get by substituting in the numbers 1, 2, 3, … for x. Substituting 2 in for x gives 18 which is answer choice (E). Be warned that many students incorrectly interpret “three times the number of pigs” as 3x + 2. This is incorrect. The number of pigs is x + 2, and so “three times the number of pigs” is 3(x + 2) = 3x + 6. If this confuses you, you can simply avoid this algebra by using the strategy of taking a guess! You can see that taking a guess is a quick and efficient way to solve this particular SAT math problem. If you begin solving this problem algebraically, then you are much more likely to make a computational error, and ultimately you need to take a guess anyway. Want More Practice? More information on this particular strategy, as well as many more problems to practice with, can be found in the Get 800 collection of test prep books. Click on the picture below for more information about these books. For a more difficult SAT math problem where this strategy is useful, take a look at this post: Taking A Guess – A Further Example Of How To Use This Technique Comments comments