Quant Formulas

Question 1

Work / Distance formula

Answer 1

work / distance = (rate x time)

Question 2

Finding Time from Rate

Answer 2

Flip the Rate (8/15 –> 15/8)

Question 3

Multiplication Rule

Answer 3

Choosing from random to find the NUMBER OF ORDERS POSSIBLE

ex: (10)(9)(8)(7)

Question 4

Prime Factorization

Answer 4

n! is divisible by ___ if it is a prime factor?

ex: 990
=11

Question 5

Combining Percentages

Answer 5

1. x + y = ______
2. (%x)X + (%y)Y = (%z)Z

Set up 2 equations and then sub

Question 6

Remainder Problems

Answer 6

(x/y) = ___ + 9

MEANS

(x/y) = q + (9/y)

q is a factor of y

Question 7

Simultaneous Equations

Answer 7

1. a + b + c
2. a + 2b + 3c

you can subtract these problems from each other to help find the answer!

Question 8

Fraction Increase Per Year

Answer 8

Work from the beginning with N

[also works for percentages]

Question 9

Percent Change [Increase or Decrease]

Answer 9

(new - old) / old

Question 10

Products and Multiples

Answer 10

3^k is a product if there is a multiple of 3

Question 11

Difference in perfect squares

Answer 11

simplifying powers!

Question 12

Sum of positive integers formula

Answer 12

[n(n+1)]/2

Evens have an additional number in the middle that you have to add at the end.

Question 13

P(E or F) =

Answer 13

P(E) + P(F) - P(E and F)

Question 14

P(E and F) =

Answer 14

Independent: P(E)P(F)

Dependent: P(A|B)P(B)

Question 15

Permutation

Answer 15

A way to choose elements one by one in a certain order

3! = 6 permutations

Question 16

Combination

Answer 16

Each possible choice of K objects out of N objects.
Combination of N objects taken K at a time.

|n| = n!
|k| k! (n-k)!

Question 17

Important square roots table
1
2
3
4
5
6
7
8
9
10

Answer 17

n^2 ; n^3 ; sqrroot(n)
1 ; 1 ; 1
4 ; 8 ; 1.41
9 ; 81 ; 1.73
16 ; 64 ; 2
25 ; 125 ; 2.24
36 ; 216 ; 2.45
49 ; 343 ; 2.65
64 ; 512 ; 2.83
81 ; 729 ; 3
100 ; 1000 ; 3.16

Question 18

Simple Annual Interest

Answer 18

(principle) x (interest rate) x (time)

Question 19

Compound Interest over “n” periods

Answer 19

(principle) x (interest rate / n)^n

Question 20

Discounts [discounted by n, and then n is discounted by m]

Answer 20

(100 - n) (100 - m)

Question 21

Work Equation

Answer 21

(1/r) + (1/s) = (1/h)

Time it Takes

h = together
r = person 1
s = person 2

Question 22

If time is constant, what is the direct relationship between work and rate?

Answer 22

If work increased, rate increased by same (2x, 3x, 4x, etc.)

Question 23

If rate is constant, what is the direct relationship between work and time?

Answer 23

If work increased, time increased by same (2x, 3x, 4x, etc.)

Question 24

what can rate be considered as in a workers problem?

Answer 24

work = rate (# of workers) x time

Question 25

Ratio Table [for work / rate / time problems!]

Answer 25

ratio values and real values sum to total parts

use reciprocals for indirect relationships (ex: rates and time)

Question 26

Combining times

Answer 26

[time A x time B] / [time A + time B]

Question 27

Directional Rates

[Opposing and Same Directions]

Answer 27

Opposing = sum of rates
[r + p would be 180km away after 1 hour]

Same = difference of the rates

[p makes up 20km / hour

Question 28

Rate Circle

Answer 28

To calculate directional rates [same direction] by plugging in catchup rate into the work and time (finding rate)

p = 2 hours to catch up 40km [20km/ hour]

p = 100 km/hr
r = 80 km/hr w/ 30 minute start

Question 29

Finding # of different subsets

Answer 29

Use the sum of combinations!

Example:
Empty + C(1 5) + C(2 5) + C(3 5) + C(4 5) + C(5 5)

Question 30

Which is a factor of 18! + 1?

a. 15
b. 17
c. 19
d. 33
e. 39

Answer 30

c. 19

18! = 17…13…11…5…3…
5 x 3 = 15
17
11 x 3 = 33
13 x 3 = 39

The only one that is not a prime factor of 18! is 19, so 19 must be a prime factor of 18! + 1

Question 31

How to calculate the amount of money that Brad has over Chuck if Brad earned 150% more money than Chuck?

Answer 31

150%Chuck + Chuck = 2.5 x Chuck

Question 32

Is 0 a positive integer?

Answer 32

NO!

Question 33

When converting a decimal to a percent [like when asked what percent an asset is of a total] what do you have to do?

Answer 33

multiply the decimal x 100!

Question 34

10,000 = 10^?

Answer 34

10^4

Question 35

Can you add Inequalities (greater than or less that equations) in a Simultaneous Equation?

Answer 35

Yes!

Question 36

How many weeks are in a year?

Answer 36

52 weeks

Question 37

How to find what percent of EC from percent increase of salary and FB?

Answer 37

simultaneous equations and then plug.

Find salary = FB ratio
1.03S + 1.055F = 1.035 (S + F)

Plug back into S + F = EC

F + 4F = EC

5F = EC

1/5 = 20%

Question 38

How to figure out how many possibilities of 2 boy and 2 girls if parents want to have 4 kids

Answer 38

2^4 = possibilities possible from 4 kids.

GGBB, GBGB, GBBG, BBGG, BGGB, BGBG = 6 possibilities of 2 and 2

6/16 = 3/8.

Question 39

what does it mean “x is a factor of y”?

Answer 39

y = kx

multiple and factor are reverse

Question 40

what does it mean “x is a multiple of z”?

Answer 40

x = mz

multiple and factor are reverse

Question 41

If n is divided by 9 and there is a remainder of 0, what does the equation look like?

what is n was n even int?

Answer 41

= 9q + 8

=18q + 8 [because n has to be a multiple of 2]