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19: What is the sum of 10% of x and 20% of 2x?

　　(a) 10% of x

　　(b) 20% of x

　　(c) 30% of x

　　(d) 50% of x

　　(e) 100% of x

Answer:

10% of x is .1x.

20% of 2x = .2·2x = .4x.

The sum of 10% of x and 20% of 2x is .1·x + .4·x = .5·x. In conclusion the sum is 50% of x.

20: What are the solutions of the equation 5x(x + 1)·5x = 1?

　　(a) x1 = 0 and x2 = 2

　　(b) x1 = 0 and x2 = 1

　　(c) x1 = 2 and x2 = -2

　　(d) x1 = 0 and x2 = -2

　　(e) x1 = 1 and x2 = -2

Answer:

The left side of the equation: 5x·(x + 1)·5x = 5x2 + 2x.

The right side of the equation: 1 = 50.

5x2 + 2x = 50

x2 + 2x = 0, x·(x + 2) = 0, and x1 = 0 and x2 = -2

21: Out of all of the houses characterized in the table below, what is the percentage of new ranches?

Houses Old New Total Ranch 23 ? 30 Colonial ? 40 ? Total 23 ? ?

　　(a) 10%

　　(b) 12%

　　(c) 15%

　　(d) 25%

　　(e) 8%

Answer: The number of new ranches will be 30 - 23 = 7. We need to find the total number of houses.

The number of old colonials will be 23 - 23 = 0, and the total number of colonials will be 40 + 0 = 40.

The total number of houses will be the total number of ranches + the total number of colonials, 30 + 50 = 70. We can rewrite the table: Houses Old New Total Ranch 23 7 30 Colonial 0 40 40 Total 23 47 70

The percentage of new ranches will be (7  70)·100 = 10%

延伸阅读：

SAT数学专项练习题（六）

SAT数学专项练习题（七）

SAT数学专项练习题（八）

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