GMAT Quant Chapter 5: Inequalities & Absolute Values Flashcards

1
Q

When we divide or multiply an inequality by a negative sign, what happens?

A

The inequality sign flips

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

What must we do before adding two separate inequalities?

A

Both inequality signs must be facing the same direction

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

We never perform an operation to an inequality if we don’t know what?

A

The sign of the unknown.

Never multiply or divide an inequality unless the sign of the variable is known

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What is a compound inequality?

A

A 3 part inequality where an unknown is defined in both directions

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

When manipulating a compound inequality, how do we maintain the original inequality?

A

Apply the operation to every individual part of the compound inequality.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

What happens when we divide a compound inequality by a negative number?

A

We must reverse both of the inequality signs.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Which method of solving algebraic equations can we use to solve inequalities and in what order must we perform the operation?

A

Substitution.

isolate a variable in a separate equation and substitute the result into the inequality.

We cannot isolate a variable in an inequality and substitute that into an equation.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Which part of a compound inequality must we substitute an unknown variable equation into?

A

It does not matter as long as all manipulations afterwards are applied to all parts of the compound inequality

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

How should we solve when we are given lots of independent inequalities?

e.g. a > x x < y y < c

A

Draw a number line and visually see how they relate to each other.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

How do we solve inequalities with squared variables?

A

Solve them like an equation but realise that the root of the squared number produces absolute values so we will often get two solutions.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

What are the two solutions when x^2 > B and B > 0

A

X > Root B
or
X < - Root B

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

What are the two solutions when x^2 < B, and B > 0?

A
  • Root B < x < Root B
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

How should we find the minimum and maximum values when we are given two compound inequalities?

A

evaluate the limits of the 4 inequalities given the smallest will be the minimum and the largest will be the maximum

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

How many times do we need to solve an equation that has absolute value bars?

A

Solve the equation twice. Once the absolute value bars are positive and once when they are negative.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

How do we solve an equation that absolute value bars only around part of the expression?

A

Isolate the absolute value bars and put everything else together on the other side.

Then solve the absolute value bars twice.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What do we know if two absolute values are equal?

A

The expressions within the absolute value bars are either equal or opposite.

17
Q

what do we know about | a + b | ?

A

| a + b | < or = |a| + |b|

a + b | < = |a| + |b|

18
Q

What do we know when | a + b | = |a| + |b|?

A

I. One or both quantities is 0
II. Both quantities are of the same sign

19
Q

What do we know about| a - b| ?

A

|a - b| > or = |a| - |b|

20
Q

What do we know when |a - b| = |a| - |b|?

A

Either of the following two things is true:
I. The second quantity is 0
II. Both quantities have the same sign & |a| > or = |b|

21
Q

How should we mentally rephrase inequalities that contain absolute values?

A

We are looking for all values of x that are greater or lesser than a certain number away from 0

22
Q

If |x| > b, does that mean x > b?

A

Not necessarily.
x > b
or
x < b

23
Q

Solving which type of inequalities is similar to solving equations that have absolute values?

A

When we have to square root x^2 because the solution can be either positive or negative.

24
Q

What is a fundamental truth about absolute values?
How can this fundamental truth stop us from being caught out?

A

Absolute values are non-negative.

If an absolute value of an expression is set equal to a negative number, there will be no solution to that equation

25
Q

What must you EVERY SINGLE TIME after solving absolute value equations with multiple solutions?

A

Check that all of the solutions satisfy the original equation. Often times they don’t and if you don’t remove that incorrect solution you will get the question wrong.

26
Q

When we take the square root of a binomial ( |a+b|) how many solutions are we likely to get?

A
  1. one negative and one positive.
27
Q

What equation trap frequently occurs in absolute value and inequality problems?

A

Assuming that the value of a variable cannot be 0.

If the variable can be 0 then we cannot multiply or divide both sides of the equation because it will ruin the solution.