SAT Skills Insight
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12/5
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Problem Solving
Skills needed to score in this band
SKILL 1: Solve the first stage of a problem, and then apply that solution to solve the next stage of the problem
SKILL 2: Recognize complexity in problems that appear at first to be routine
SKILL 3: Develop and apply an effective strategy and keep track of information in solving a nonroutine problem
SKILL 4: Identify relevant and irrelevant information when choosing a solution strategy
SKILL 5: Solve multistep problems involving properties of integers

1
Solve the first stage of a problem, and then apply that solution to solve the next stage of the problem
ExampleIf and are positive odd integers and , what is one possible value of ?
Reveal Answer50 or 58 or 82

2
Recognize complexity in problems that appear at first to be routine
ExampleIn an election for senior class president, Alice received votes more than David. If the ratio of the number of votes Alice received to the number of votes David received was to , how many votes did David receive?

3
Develop and apply an effective strategy and keep track of information in solving a nonroutine problem
ExampleIn the figure above, and each circle is tangent to the other two circles at the labeled points. If each circle has diameter and is tangent to one of the two lines, what is the distance, , between and ?

4
Identify relevant and irrelevant information when choosing a solution strategy
ExampleIn the figure above, the vertices of quadrilateral lie on the sides of quadrilateral . What is the sum of the degree measures of the eight indicated angles?

5
Solve multistep problems involving properties of integers
ExampleIf is the square of a positive integer and is divisible by both and , what is the least possible value of ?