Number Properties

Question 1

An integer is divisible by 3 if…

Answer 1

The sum of digits is divisible by 3

Question 2

An integer is divisible by 4 if…

Answer 2

Integer is divisible by 2 twice or if last 2 digits is divisible by 4

Question 3

An integer is divisible by 6 if…

Answer 3

The integer is divisible by both 2 and 3

Question 4

An integer is divisible by 8 if…

Answer 4

The integer is divisible by 2 three times or if last 3 digits are divisible by 8

Question 5

An integer is divisible by 9 if…

Answer 5

The sum of digits is divisible by 9

Question 6

__ factors, __ multiples

Answer 6

Fewer factors, more multiples

Question 7

If you add or subtract multiples of N, what does that mean for the result of that equation?

Answer 7

The result of adding and subtracting a multiple of N is a multiple of N

Question 8

What is the factor foundation rule?

Answer 8

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

Question 9

The remainder is (larger/smaller) than the divisor?

Answer 9

Smaller

Question 10

Dividend = __ x __ + ___

Answer 10

Dividend = Quotient x Divisor + Remainder

Question 11

Even +/- Even =

Answer 11

Even

Question 12

Odd +/- Odd =

Answer 12

Even

Question 13

Even +/- Odd =

Answer 13

Odd

Question 14

Even x Even =

Answer 14

Even

Question 15

Even x Odd =

Answer 15

Even

Question 16

Odd x Odd =

Answer 16

Odd

Question 17

The sum of any two prime numbers is (odd / even)?

Answer 17

Even, unless one of the primes is 2, then the sum of 2 primes is odd

Question 18

What are the steps for testing cases?

Answer 18

1) What possible cases are allowed?
2) Choose numbers that work for the statement.
3) Try to prove the statement is insufficient.

Question 19

What is considered “insufficient” for DS questions?

Answer 19

When there are 2+ answers, or situations where the answer could be either yes or no

Question 20

For PS problems, what does “must be” or “could be” mean?

Answer 20

Consider how to disprove the other 4 answers.

Question 21

What are the categories to consider when picking numbers to test?

Answer 21

1) Even or odd
2) Fractions between 0 and -1
3) Fractions between 0 and 1
4) Primes

Question 22

What types of numbers do you pick when testing for absolute values?

Answer 22

Negatives

Question 23

What types of numbers do you use when testing for exponents?

Answer 23

0 or 1

Question 24

What do you test for fractions?

Answer 24

Numbers between 0 and 1

Question 25

OR means __ and AND means __

Answer 25

OR means add, AND means multiply

Question 26

"How many" is a __ problem.

Answer 26

Combinatorics

Question 27

A factorial is...

Answer 27

...the number of ways to arrange n distinct objects if no restrictions are stated.

Question 28

If making different decisions, determine the concepts separately and __ the results.

Answer 28

Determine the ideas separately and multiply the results.

Question 29

"At most" means that you have __ decisions.

Answer 29

You have multiple decisions and it is an OR decision

Question 30

In probability, numerators and denominators are related but must be calculated (together/separately).

Answer 30

Separately

Question 31

Equation for probability adding to 1

Answer 31

P(A) + P(not A) = 1

Question 32

In probability, "at least" / "at most" means that you calculate the probability in what way?

Answer 32

Calculate the probability that something doesn't happen, based on what the problem specifies.

Question 33

What makes a number prime?

Answer 33

It has only 2 factors.

Question 34

If you add/subtract a multiple of N with a non-multiple of N...

Answer 34

The result is a non-multiple of N.

Question 35

If you add 2 non-multiples of N, the result...

Answer 35

...the result could either be a multiple or not.

Question 36

What is the Greatest Common Factor?

Answer 36

It is the largest divisor of 2+ integers, and it smaller than or equal to the starting integers.

Question 37

What is the Least Common Multiple?

Answer 37

It is the smallest multiple of 2+ integers, and the multiple will be larger than or equal to the starting integers.

Question 38

If a prime factor appears to the Nth power, there are __ possibilities for occurrences of that prime factor.

Answer 38

There are N+1 possibilities.

Question 39

If a number has a prime factorization of (a)(b)(c), all raised to different exponents (x, y, and z)...

Answer 39

...then the number has (x+1)(y+1)(z+1) different factors.

Question 40

All perfect squares have (odd/even) number of total factors.

Answer 40

Odd.

Question 41

The prime factorization of a perfect square has only (odd/even) powers of primes.

Answer 41

Even. Numbers with odd powers of primes are not perfect squares.

Question 42

N! is a multiple of all integers from...

Answer 42

All integers from 1 to N. Eg. 10! + 7 is a multiple of 7.

Question 43

What is the glue method for combinatorics problems?

Answer 43

Where items or people must be next to each other, pretend all the items are "glued" together as a larger item. Find the total possibilities then subtract the circumstances where it can't work.

Question 44

What is the domino effect rule?

Answer 44

The rule states that you should multiply probabilities of events in a sequence, taking earlier events into account.

Question 45

How do you calculate a problem with a symmetrical situation, with multiple equivalent cases?

Answer 45

Calculate the probability of one case and multiply by the number of possible cases to find the probability of any of the cases.