Inequalities

If 0 < a < b < c, which of the following statements must be true?

What is the smallest integer n for which 25^n > 5^12 ?

If x^2 − 2 < 0, which of the following specifies all the possible values of x?

If 1 < x < y < z, which of the following has the greatest value?

If m and p are positive integers and m 2 + p 2 < 100 , what is the greatest possible value of mp ?

How many of the integers that satisfy the inequality (x + 2) (x + 3) (x − 2) ≥ 0 are less than 5?

If a = − 0.3 , which of the following is true?

Which of the following describes all values of x for which 1 − x 2 ≥ 0 ?

If x + 5 > 2 and x - 3 < 7, the value of x must be between which of the following pairs of numbers?

How many integers n are there such that 1< 5n +5 < 25?

If 0 ≤ x ≤ 4 and y < 12 , which of the following CANNOT be the value of xy?

If 0 < x < 1, which of the following inequalities must be true ? I. x 5 < x 3 II. x 4 + x 5 < x 3 + x 2 III. x 4 − x 5 < x 2 − x 3

If it is true that x > -2 and x < 7, which of the following must be true?

If d > 0 and 0 < 1 - c/d < 1, which of the following must be true? I. c > 0 II. c/d < 1 III. c^2 + d^2 > 1

If Mel saved more than $10 by purchasing a sweater at a 15 percent discount, what is the smallest amount the original price of the sweater could be, to the nearest dollar?

If u > t, r> q, s > t, and t > r, which of the following must be true? I. u > s II. s > q III. u > r

If x < 0 , which of the following is NOT necessarily true?

If x > 0 and x 2 = 161 , what is the best whole number approximation of x ?

All the T-shirts a clothing store stocks are plain—and they are all in one of exactly four colors: blue, green, red, and yellow. On any day, the store sells about twice as many blue T-shirts as it does green T-shirts. Last week, did the store sell more blue T-shirts than red T-shirts? (1) Last week, the store sold fewer blue T-shirts than red T-shirts and green T-shirts combined. (2) Last week, the store sold more blue T-shirts than half the total number of red T-shirts and yellow T-shirts combined.

If x and y are positive numbers, is x + 1 y + 1 > x y x + 1 y + 1 > x y ? (1) x > 1 (2) x < y