SOLUTION STRATEGIES
1. Apply a general rule or formula to answer the question.
In Example 2, you can apply a property from geometry that says that
when two chords intersect inside a circle, the segments formed have
lengths such that the product of the segment lengths is the same for each
chord.
2. Apply basic properties of numbers.
In Example 4, you can use the definition of a prime number so that you
do not include 1, but do include 2.
3. Eliminate as many answers as possible so that you can select from
a smaller set of answer choices.
In Example 3, you can eliminate some of the answers by noting that since
each can of mixed nuts is at least 30% peanuts, the mixture of the two cans
will be least 30% peanuts. Thus, before doing any computation, you could
eliminate answers A, B, and C. Therefore, if you need to guess, you only
have two answer choices left and have increased your odds of guessing
correctly.
4. Substitute answers into the given question to see which one produces
the correct result.
In Example 1, you are given
b/(a + b)= 7/12, and you want the value of a/b. You can divide the numerator and denominator of b
a + b by b to get 1/((a/b)+ 1)
Now you can substitute the answer choices into the expression to see which answer produces a value of 7/12. Answer A produces 12/17 , so it is wrong. Answer B produces 7/12 , so it is correct. Since this type of question has only one correct answer, you know the correct answer is B. You do not have to test the rest of the answer choices.
This strategy cannot be employed on the majority of questions, but
you can use it when you can see a way to quickly test the answer choices.
5. Break down the situation into individual steps.
In Example 5, you have an everyday situation of mixing paint. Break the problem down into steps. First, find the total amount of paint the formula makes. Then set up a proportion to find the increased amount of red paint. Taking word problems one step at a time makes them more manageable.
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