Comment. Inequalities quiz
Comment. This quiz is designed to test your ability to handle inequalities
Comment. involving real numbers and absolute values, etc.
Comment. In all of these questions, all variables are real numbers.
Shuffle Questions.
Question. If |a-10| < 2 and |b-10| <= 3, then the best we can say about |a-b| is that
Answer. 1 < |a-b| < 5.
Correct Answer. |a-b| < 5.
Answer. |a-b| >= -1.
Answer. |a-b| <= 5.
Answer. |a-b| < 25.
Answer. |a-b| = 1.
Answer. |a-b| = -1.
Question. If |a| < 4, and |b| > 9, then the best we can say about |a-b| is that
Answer. |a-b| < -5.
Correct Answer. |a-b| > 5.
Answer. 5 < |a-b| < 13.
Answer. -5 < |a-b| < 5.
Answer. No conclusion regarding |a-b| can be drawn.
Answer. |a-b| < 5.
Answer. |a-b| > 13.
Question. If |a-10| < 3, and b <= a, then the best that can be said about b is that
Correct Answer. b < 13.
Answer. b <= 13.
Answer. b <= 10.
Answer. b <= 7.
Answer. b < 7.
Answer. No conclusion about b can be drawn.
Answer. 7 <= b <= 13.
Question. If a > 10, b > 15, and a < c < b, the best that can be said about c is that
Correct Answer. c > 10.
Answer. c > 15.
Answer. 10 < c < 15.
Answer. c < 10.
Answer. c < 15.
Answer. No conclusion about c can be drawn.
Answer. Either c < 10 or c > 15.
Question. If |a-10| <= 3, and |b-a| < 5, the best that can be said about b is that
Correct Answer. 2 < b < 18.
Answer. 5 < b < 15.
Answer. b < 18.
Answer. b <= 18.
Answer. |b| <= 8.
Answer. 2 <= b <= 18.
Answer. No conclusion about b can be drawn.
Question. If |a-10| > 6, and |b-a| < 1, then the best that can be said about b is that
Correct Answer. Either b > 15 or b < 5.
Answer. 3 < b < 17.
Answer. Either b <= 3 or b >= 17.
Answer. No conclusion about b can be drawn.
Answer. |b| < 7.
Answer. |b| > 7.
Answer. 5 < b < 15.
Question. If -2 < a < 4, and 1 > b > -5, then the best that can be said about ab is that
Correct Answer. -20 < ab < 10.
Answer. -20 < ab < 4.
Answer. -2 > ab > -20.
Answer. 4 < ab < 10
Answer. Either ab < 10, or ab > -20.
Answer. No conclusion about ab can be drawn.
Answer. Either ab > -2, or ab < -20.
Question. Suppose we know that |a-L| <= c, and |b-L| <= d. Which of the following statements will be enough to imply that |a-b| < e?
Correct Answer. c+d < e.
Answer. Either d < c+e or c < d+e.
Answer. c+d <= e.
Answer. |c-d| < e.
Answer. |c-d| <= e.
Answer. c=d=e.
Question. Suppose that we know that |a| < 3. Which of the following statements is enough to imply that |b| < 5?
Answer. |a+b| < 8.
Answer. 2 < |a-b| < 8.
Correct Answer. |a-b| <= 2.
Answer. 3 < |a-b| < 5.
Answer. a-b < 2.
Answer. a+b < 2.
Answer. None of the other statements will imply |b| < 5.
Question. Suppose that we know that |b| < 5. Which of the following statements is enough to imply that |a| < 3?
Answer. |a+b| < 8.
Answer. 2 < |a-b| < 8.
Answer. |a-b| <= 2.
Answer. 3 < |a-b| < 5.
Answer. a-b < 2.
Answer. a+b < 2.
Correct Answer. None of the other statements will imply |a| < 3.
Question. Suppose that we know that 3 <= a < 7 and 1 < b <= 4. What is the best we can say about a-b?
Correct Answer. -1 <= a-b < 6.
Answer. -1 < a-b < 6.
Answer. 2 < a-b < 3.
Answer. 2 <= a-b <= 3.
Answer. 2 <= a-b < 6.
Answer. -1 < a-b <= 3.
Answer. No conclusion about a-b can be drawn.
Question. Suppose we know that -1 < a <= 2. What is the best we can say about a^2 (the square of a)?
Correct Answer. 0 <= a^2 <= 4.
Answer. 1 <= a^2 <= 4.
Answer. -1 <= a^2 <= 4.
Answer. 1 < a^2 <= 4.
Answer. 0 < a^2 <= 4.
Answer. 0 <= a^2 < 4.
Answer. 1 < a^2 < 4.
Question. Suppose we know that 4 <= a^2 < 9. What is the best we can say about a?
Correct Answer. Either -3 < a <= -2, or 2 <= a < 3.
Answer. 2 <= a < 3.
Answer. |a| < 3.
Answer. |a| > 2.
Answer. 0 <= a < 3.
Answer. Either -3 <= a < -2, or 2 <= a < 3.
Answer. Either a >= 2, or a <= -2.
Question. If we know that a < b and c <= d, then we can deduce that
Correct Answer. a-d < b-c.
Answer. a-c < b-d.
Answer. a-c <= b-d.
Answer. c-a < d-b.
Answer. c-a <= d-b.
Answer. b-c < a-d.
Answer. b-c <= a-d.