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16: If a, b and c are the sides of any triangle, which of the following inequalities is not true?

　　(a) a·b > 0

　　(b) a + b > c

　　(c) a + c/2 >b

　　(d) b + c > a

　　(e) (a + b)·(b + c) > a·c

Answer:

The first answer is true, since the product of 2 positive reals will be positive.

The second and the fourth answers are also true, since the sum of 2 sides of a triangle is always higher than the third side.

The fifth answer is also true because it is just a multiplication of the second and fourth inequalities.

Answer three should be the one that is not true, and we can verify this result with an example: an isosceles triangle with a = 3, b= 3, c= 10 will not satisfy the inequality.

17: If x + 4y = 6 and x - 2y = 3, which of the following statements is not true?

　　(a) y = 1/2

　　(b) x = 4

　　(c) y = 2

　　(d) xy = 2

　　(e) x + y = 9/2

Answer:

In order to find the values of x and y, we multiply the second equation by 2 and add the 2 equations:

　　x + 4y = 6

　　2x - 4y = 3

　　3x = 12 and x = 4, y = (6 - 3)/4 = 1/2.

　　y = 2 is the only equality that is false.

18: While competing in a marathon event, John is behind Mike by 100 yards. John runs (x - 2) yards while Mike runs (x + 10) yards. What is the new distance between them?

　　(a) 112 yards

　　(b) 108 yards

　　(c) 102 yards

　　(d) 110 yards

　　(e) The answer is a function of x

Solution:

We can reference all distances to the point where John was at the time t1, when the distance between them is 100 yards.

After John runs (x - 2) yards, he is (x - 2) yards from the reference.

After Mike runs (x + 10) yards, he is 100 yards + (x + 10) yards = (x + 110) yards from the reference.

The distance between them will be (x + 110) - (x - 2) = 112 yards.

延伸阅读：

SAT语法练习题及解析（十六）

SAT语法练习题及解析（十七）

SAT语法练习题及解析（十八）

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