GMAT - Operations with Rational Numbers, Simplifying Algebraic Expressions, Properties of Numbers, Geometry, Volumes & Surface Area, Simultaneous equations, Probability, Inequalities, fractions, first-degree equations

1/9

0.11111

1/8

0.125

1/6

0.166666

5/6

0.8333333

Even × Even

Even

Even × Odd

Even

Odd ± Odd

Even

Solve the simultaneous equations 3x + 4y = 200 (1) 2x + 3y = 144 (2)

(1) x 2: 6x + 8y = 400 (3) (2) x 3: 6x + 9y = 432 (4) (4) - (3): y = 32 Subst. into (2): 2x + 96 = 144 2x = 48 x = 24

Solve the simultaneous equations 5x + 2y = 11 (1) 4x - 3y = 18 (2)

(1) x 3: 15x + 6y = 33 (3) (2) x 2: 8x - 6y = 36 (4) (3) + (4): 23x = 69 x = 3 Subst. into (1): 15 + 2y = 11 2y = -4 y = -2

(Area of sector OABC)/(Area of circle O)

(Arc ABC)/Circum. =

n/360

(Area of sector OABC)/(Area of circle O) =

Formula for sum of interior angles of a polygon

(N-2) x 180

X^2 + 2xy + y^2

(X+y)(x+y) = (x+y)^2

x^2 - y^2

(X+y)(x-y)

X^2 - 2xy +y^2

(X-y)(x-y) = (x-y)^2

Solve the simultaneous equations 3x + 5y = 19 4x - 2y = -18

(eqtn 1) x 2: 6x + 10y = 38 (eqtn 3) (eqtn 2) x 5: 20x - 10y = -90 (eqtn 4) (3) + (4) : 26x = -52 (÷ 26): x = -2 Subst. into (1): -6 +5y = 19 5y = 25 y = 5

Golden Rule for simultaneous equations:

*If coefficients of variable are same number and SAME SIGNS, then SUBTRACT them. *If coefficients of variable are same number and DIFFERENT SIGNS, then ADD them.

Properties of evenly spaced sets

-average and median are equal to each other -mean and median of set are equal to average of first and last terms

Consecutive integers and divisibility

-every number is divisible by all factors of its factors -for any set of consecutive integers w/ an odd number of items, the sum of all integers is always a multiple of the number of items

In order to calculate the cumulative probability of one event AND another, you... In order to calculate the cumulative probability of one event OR another, you...

1) Multiply the probabilities 2) Add the probabilities

10^3

1000

How Many Edges on a Cube?

12

Isosceles Triangle

2 equal sides, 2 equal angles

Circumference

2 x Pi x r

4!

24

Equilateral Triangle

3 equal sides, 3 equal angles

Sum of interior angles of a polygon

3 sides = 180 degrees 4 sides = 360 degrees 5 sides = 540 degrees 6 sides = 720 degrees

1 : √3 : 2

30-60-90 Side Ratio?

1 : 1 : √2

45-45-90 Side Ratio?

How many Faces on a Cube?

6

4^3

64

How Many Vertices (corners) on a Cube?

8

Interest formula

=P(1+(r/n))^(nt) P=principal R=rate N=number of times/year T=number of years

(b1 + b2)/2 * h

A =

bh

A =

Surface Area of a Cylinder

A = 2πr² + 2πrh

πr^2

A=

60° each; all 3 equal

Angle degree?

(1/2) * b * h

Area=

Sum of consecutive integers (inclusive, evenly spaced)

Average x # of terms

Squaring inequalities

Both sides known to be -: flip Both sides known to be +: no change One side +, one side -: can't square Signs are unclear: can't square

2πr or πd

C=

Area of sector

Central angle/360 x pi x r^2

Even ± Even

Even

Parabolas

F(x) = ax^2 +bx + c + value for a --> curve opens up - value for a --> curve opens down Large |a| --> narrow curve Small |a| --> wide curve

A __ is a positive integer that divides evenly into an integer. For example, 1, 2, 4, and 8 are all the __ (also called divisors) of 8. A __ of an integer is smaller than or equal to that integer.

Factor

A way not to confuse factors and multiples is...

Fewer factors, more multiples

A __ of an integer is formed by multiplying that integer by any integer, so 8, 16, 24 and 32 are some of the __ of 8.

Multiple

Combination formula (without repetition)

N!/k! X (n-k)!

Odd Number of negative signs

Negative

If you are Squaring an Inequality; & both sides are Positive: Do you flip the inequality sign?

No: Do NOT Flip the Inequality when you Square

Dividend

Number being divided (8/5, 8=dividend)

Quotient

Number of times divisor goes into dividend COMPLETELY -always an integer (8/5, quotient = 1)

Divisor

Number that is dividing (8/5, 5=divisor)

Even ± Odd

Odd

Odd × Odd

Odd

What is the probability equation for P(A) and P(B) if they are independent?

P(A and B) = P(A) * P(B)

What is the probability of dependent events P(A) and P(B) occurring together?

P(A and B) = P(A) * P_a_(B) ...which is the conditional probability of B

What is the probability of event P(A) or P(B) occurring?

P(A or B) = P(A) + P(B) - P(A and B)

What is the equation describing the probability of complimentary events?

P(A) + P(!A) = 1 P(A) = 1 - P(!A)

What equation defines the probability of event A?

P(A) = (# of outcomes when A occurs) / (# of total possible outcomes)

Even Number of negative signs

Positive

A __ number is any positive integer with exactly two different factors: 1 and itself. In other words, a __ number has on factors other than 1 and itself. 1 is not a prime number!

Prime

x^2 + y^2 = z^2

Pythagorean theorem for right triangles

3:4:5 5:12:13 7:24:25 8:15:17

Pythagorean triple #1

Dividend=

Quotient x divisor +remainder

(y2 - y1) / (x2 - x1)

Slope of a Line =

Formula for Surface Area of a rectangular solid?

Suface Area = 2hw + 2hd + 2wd

Greater than the 3rd side

Sum of any 2 sides is >, <, =?

Triangle inequality law

Sum of any two sides of a triangle must be greater than the 3rd side -if given 2 sides of a triangle, length of 3rd must lie between the difference and sum of 2 given sides

Formula for Surface Area of a Cube?

Surface Area = 6s²

Combining terms with the same base (exponents)

Terms are being multiplied: add exponents (z^2 x z ^3 = z^5) Terms are being divided: subtract exponents (x^15/x^8 = x^7)

An integer is divisible by 3 if

The sum of the integers digits is divisible by 3

360

Total °?

What are complimentary events? What is P(A or B) in this case?

Two events are complimentary if one or the other must occur P(A or B) = 1

What are dependent events? Are individual probabilities affected by what has occurred previously?

Two events are dependent if the occurrence of one event affects the probability of the other YES

What are independent events? Are individual probabilities affected by what has occurred previously?

Two events are independent if the occurrence of one does not affect the occurrence of the other NO

What are mutually exclusive events? What is P(A and B) if events are mutually exclusive?

Two events that can never occur together P(A and B) = 0

Formula for Volume of a Cube?

V = length x width x height

Formula for Cylinder Volume is...

V= πr²h

Remainder

What is leftover if dividend is not divisible by divisor (8/5, remainder =3)

If you are Squaring an Inequality; & both sides are Negative: Do you flip the inequality sign?

Yes: Flip the Inequality when you Square

360°

a+b+c=

y + z

a=

x + z

b=

x + y

c=

2r

d=

State the factor foundation rule

if a is a factor of b, and b is a factor of c, then a is a factor of c.

(Arc ABC/Circum.)

n/360 =

b

y-Intercept =

When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the ___ root. That is: √9=3 NOT +3 or -3

positive

Two numbers are reciprocals of each other if and only if...

their product is 1.

On the GMAT x² = 9 has __ possible solutions.

two

180°

x+y+z=

-b/m

x-intercept =

Sqrt(2)

~1.4

Sqrt(3)

~1.7

Sqrt(5)

~2.25