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

All

Start Practice

Sub 505 (Easy)

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

505-555 (Easy)

1 < x < y < z

, which of the following has the greatest value?

505-555 (Easy)

S = 1 + \frac{1}{2 ^{2}} + \frac{1}{3 ^{2}} + \frac{1}{4 ^{2}} + \frac{1}{5 ^{2}} + \frac{1}{6 ^{2}} + \frac{1}{7 ^{2}} + \frac{1}{8 ^{2}} + \frac{1}{9 ^{2}} + \frac{1}{1 0 ^{2}},

which of the following is true?

505-555 (Easy)

0 < a < b < c

, which of the following statements must be true? I.

2 a > b + c

II.

c - a > b - a

III.

\frac{c}{a} < \frac{b}{a}

505-555 (Easy)

x^{2} - 2 < 0

, which of the following specifies all the possible values of

x

505-555 (Easy)

r

and

s

are positive integers and

r - s = 6

, which of the following has the greatest value?

605-655 (Medium)

[x]

denotes the least integer greater than or equal to

x

and

[\frac{x}{2}] = 0

, which of the following could be the value of

x

605-655 (Medium)

Mark and Ann together were allocated

n

boxes of cookies to sell for a club project. Mark sold 10 boxes less than

n

and Ann sold 2 boxes less than

n

. If Mark and Ann have each sold at least one box of cookies, but together they have sold less than

n

boxes, what is the value of

n

605-655 (Medium)

M

is the sum of the reciprocals of the consecutive integers from 201 to 300, inclusive. Which of the following is true?

605-655 (Medium)

x

and

y

are positive numbers such that

x + y = 1

, which of the following could be the value of

100 x + 200 y

? I. 80 II. 140 III. 199

605-655 (Medium)

For which of the following values of

x

1 - 2 - x

not defined as a real number?

605-655 (Medium)

Which of the following inequalities has a solution set that, when graphed on a number line, is a single line segment of finite length?

655-705 (Hard)

What is the smallest integer

n

for which

2 5^{n} > 5^{12}

655-705 (Hard)

Which of the following is equivalent to the pair of inequalities

x + 6 > 10

and

x - 3 \leq 5

655-705 (Hard)

\frac{p}{q} < 1

, and

p

and

q

are positive integers, which of the following must be greater than 1?

655-705 (Hard)

How many of the integers that satisfy the inequality

\frac{( x + 2 ) ( x + 3 )}{x - 2} \geq 0

are less than

5

← PreviousPage 2 of 2Next →