Inequalities

Inequalities are where careless algebra habits go to die: flip the sign when multiplying by a negative, test boundary values, and never square both sides without thinking about signs. This topic set drills pure inequality manipulation plus the GMAT favorites — absolute value inequalities, compound ranges, and inequality logic inside word problems. The test cases that matter are almost always the same five: a big positive, a fraction between 0 and 1, zero, a fraction between −1 and 0, and a big negative.

Comparisons, sign analysis, |x|.·Show:20 30 50

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Sub 505 (Easy)

Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

Sub 505 (Easy)

Which of the following is equivalent to the pair of inequalities x + 6 > 10 and x - 3 <= 5 ?

Sub 505 (Easy)

If p/q < 1, and p and q are positive integers, which of the following must be greater than 1 ?

Sub 505 (Easy)

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

Sub 505 (Easy)

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

Sub 505 (Easy)

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

Sub 505 (Easy)

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

555-605 (Medium)

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

705-805 (Hard)

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

555-605 (Medium)

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

505-555 (Easy)

Which of the following describes all values of x for which 1 â x 2 â¥ 0 ?

Sub 505 (Easy)

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

505-555 (Easy)

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

Sub 505 (Easy)

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

555-605 (Medium)

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 â x 5 < x 2 â x 3

555-605 (Medium)

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

705-805 (Hard)

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

505-555 (Easy)

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?

Sub 505 (Easy)

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

505-555 (Easy)

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

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