Algebra

Question 1

To solve normally need as many equations as there are variables.

What are the exceptions?

Answer 1

When there are defined constraints
ie x is a positive integer ; y is a prime #

When there are inequalities
ie x < 5

Question 2

x x

a * b

Answer 2

a+b

x

Question 3

a b

x

Answer 3

ab

x

Question 4

a b

x / x

Answer 4

a-b

x

Question 5

-a

x

Answer 5

1
____
a
x

Question 6

1
_____
-a
x

Answer 6

a

x

Question 7

All positive numbers have how many square roots?

Answer 7

Two one positive and one negative
2
ie x = 16 means x = 4 or -4

Question 8

For GMAT √x equals what?

Answer 8

Only the positive square root

ie √16 = 4 only

Question 9

√x expressed as an exponent

Answer 9

1/2

x

Question 10

a

√x expressed as an exponent

Answer 10

1/a

x

Question 11

a

√xⁿ expressed as an exponent

Answer 11

n/a

x

Question 12

√a/b expressed as a fraction

Answer 12

√a / √b

Question 13

√a*b expressed as a fraction

Answer 13

√a * √b

Question 14

Can you multiply or divide an inequality by a negative

Answer 14

Yes, but you must flip the direction of the sign

ex. 2 > 1
- 2 < -1

Question 15

Express
2 < x+2 < 4
as two inequalities

Answer 15

It means

x+2 > 2 AND x+2 < 4

Question 16

Find the range of possible values for y

y < x+2 AND y > (x-1)/2

Answer 16

(x-1)/2 < y < x+2

Question 17

Can you add two inequalities together?

Answer 17

Yes - if the signs are going in the same direction

Question 18

What is |x|

Answer 18

x or -x

ex. |x+5| =10
means x = 5 OR x = -15

Question 19

Quadratics
Recognizing when you are dealing with quadratics and factoring them is a key GMAT skill
Factor:
x² = 81

Answer 19

(x+9)(x-9)=0

Question 20

Quadratics

x² + (a+b)x + ab = 0

Answer 20

(x+a)(x+b) = 0

ex. x² + 2x - 8 = 0
(a+b) = 2
(a*b) = -8
(x+4)(x-2)=0

Question 21

When should you factor?

Answer 21

● When you see addition or subtraction of roots, exponents, or factorials

● When you can remove a variable

● When you can change a mix of variables

Question 22

Exponents

Which exponents have a units digit that repeats every time

Answer 22

0
1
5
6

Question 23

Exponents

Which exponents have a units digit that repeats every 2 times

Answer 23

4

9

Question 24

Exponents

Which exponents have a units digit that repeats every 4 times

Answer 24

2
3
7
8

Question 25

Factoring
Remember to factor out smallest root
Factor: 2¯³ + 2¯² + 2¯⁵

Answer 25

2¯⁵ ( 2² + 2³ + 1)

Question 26

Identify the range of values for the expression

|x| < y

Answer 26

-y < x < y

Question 27

Identify the range of values for the expression

|x| > y

Answer 27

x < -y or x > y

Question 28

What are the properties of 0

Answer 28

● It is even
● It is neither positive or negative - it is non-negative
● It is a multiple of every number
● It is a factor of no number

Question 29

What numbers when squared become smaller?

Answer 29

All numbers between 0 & 1