SAT Skills Insight

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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. 1

    Solve the first stage of a problem, and then apply that solution to solve the next stage of the problem

    Example

    If x and y are positive odd integers and square root (x) + square root (y) = 10, what is one possible value of x plus y?

    Reveal Answer

    50 or 58 or 82

  2. 2

    Recognize complexity in problems that appear at first to be routine

    Example

    In an election for senior class president, Alice received 30 votes more than David. If the ratio of the number of votes Alice received to the number of votes David received was 8 to 7, how many votes did David receive?

    Answer Choices
  3. 3

    Develop and apply an effective strategy and keep track of information in solving a nonroutine problem

    Example

    Figure

    In the figure above, l parallell to m and each circle is tangent to the other two circles at the labeled points. If each circle has diameter 8 and is tangent to one of the two lines, what is the distance, h, between l and m?

    Answer Choices
  4. 4

    Identify relevant and irrelevant information when choosing a solution strategy

    Example

    Figure

    In the figure above, the vertices of quadrilateral A B C D lie on the sides of quadrilateral P Q R S. What is the sum of the degree measures of the eight indicated angles?

    Answer Choices
  5. 5

    Solve multistep problems involving properties of integers

    Example

    If n is the square of a positive integer and n is divisible by both 7 and 14, what is the least possible value of n?

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