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GMAT Concepts > Number Properties > Flashcards

Number Properties Flashcards

1
Q

An integer is divisible by 3 if…

A

The sum of digits is divisible by 3

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2
Q

An integer is divisible by 4 if…

A

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

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3
Q

An integer is divisible by 6 if…

A

The integer is divisible by both 2 and 3

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4
Q

An integer is divisible by 8 if…

A

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

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5
Q

An integer is divisible by 9 if…

A

The sum of digits is divisible by 9

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6
Q

__ factors, __ multiples

A

Fewer factors, more multiples

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7
Q

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

A

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

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8
Q

What is the factor foundation rule?

A

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

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9
Q

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

A

Smaller

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10
Q

Dividend = __ x __ + ___

A

Dividend = Quotient x Divisor + Remainder

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11
Q

Even +/- Even =

A

Even

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12
Q

Odd +/- Odd =

A

Even

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13
Q

Even +/- Odd =

A

Odd

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14
Q

Even x Even =

A

Even

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15
Q

Even x Odd =

A

Even

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16
Q

Odd x Odd =

A

Odd

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17
Q

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

A

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

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18
Q

What are the steps for testing cases?

A

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

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19
Q

What is considered “insufficient” for DS questions?

A

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

20
Q

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

A

Consider how to disprove the other 4 answers.

21
Q

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

A

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

22
Q

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

A

Negatives

23
Q

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

A

0 or 1

24
Q

What do you test for fractions?

A

Numbers between 0 and 1

25
Q

OR means __ and AND means __

A

OR means add, AND means multiply

26
Q

“How many” is a __ problem.

A

Combinatorics

27
Q

A factorial is…

A

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

28
Q

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

A

Determine the ideas separately and multiply the results.

29
Q

“At most” means that you have __ decisions.

A

You have multiple decisions and it is an OR decision

30
Q

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

A

Separately

31
Q

Equation for probability adding to 1

A

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

32
Q

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

A

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

33
Q

What makes a number prime?

A

It has only 2 factors.

34
Q

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

A

The result is a non-multiple of N.

35
Q

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

A

…the result could either be a multiple or not.

36
Q

What is the Greatest Common Factor?

A

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

37
Q

What is the Least Common Multiple?

A

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

38
Q

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

A

There are N+1 possibilities.

39
Q

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

A

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

40
Q

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

A

Odd.

41
Q

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

A

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

42
Q

N! is a multiple of all integers from…

A

All integers from 1 to N.

Eg. 10! + 7 is a multiple of 7.

43
Q

What is the glue method for combinatorics problems?

A

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.

44
Q

What is the domino effect rule?

A

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

45
Q

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

A

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

GMAT Concepts (2 decks)

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