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GMAT > Number Properties > Flashcards

Number Properties Flashcards

1
Q

What would you do if you needed to know the remainder when 12 * 13 * 17 is divided by 5?

A

Remember that remainders can be multiplied. Hence, multiply the remainders and if the multiple is more than 5, then further divide the multiple by 5.

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2
Q

What would you do if you needed to know the remainder when 12 + 13 + 17 is divided by 5?

A

Remember that remainders can be added. Hence, add the remainders and if the sum is more than 5, divide the sum by 5.

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3
Q

A number is divisible by 2 when _______?

A

The ones digit is even. 0,2,4,6, or 8.

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4
Q

A number is divisible by 3 when _______?

A

The sum of all the digits is divisible by 3.

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5
Q

A number is divisible by 4 when _______?

A

The the last two digits of the number is divisible by 4 OR the number is a multiple of 100 (all multiples of 100 are divisible by 4). e.g. 100/4 = 25.

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6
Q

A number is divisible by 5 when _______?

A

The last (ones) digit is a 0 or 5.

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7
Q

A number is divisible by 6 when _______?

A

The number is an even number whose digits sum to a multiple of 3.

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8
Q

A number is divisible by 7 when _______?

A

Remember to do the divisions for this.

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9
Q

A number is divisible by 8 when _______?

A

The number is even and the last 3 digits are divisible by 8 OR the number is a multiple of 1,000.

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10
Q

A number is divisible by 9 when _______?

A

The sum of all the digits is divisible by 9.

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11
Q

A number is divisible by 10 when _______?

A

If the ones digit is zero, the number is divisible by 10.

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12
Q

A number is divisible by 11 when _______?

A

A number is divisible by 11 if the sum of the odd numbered place digits MINUS the sum of the even-numbered place digits is divisible by 11.

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13
Q

A number is divisible by 12 when _______?

A

A number is divisible by 12 if it is divisible by both 3 and 4.

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14
Q

Is 0 an integer? Y/N?

A

Yes.

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15
Q

Is 0 a whole number? Y/N?

A

Yes

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16
Q

There is only ONE number equal to its opposite (negative). What number is that?

A

Zero.

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17
Q

When an Even number is divisible by an Odd number, what is the result?

A

The result is an Even number.

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18
Q

When an Odd number is divisible by an Odd number, what is the result?

A

The result is an Odd number.

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19
Q

When an even number is divisible by an even number, what is crucial to remember?

A

It is crucial to remember that quotient can be either even or odd.

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20
Q

Is there a rule for Odd numbers divided by Even numbers?

A

No, because an odd number cannot be divisible by an even number.

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21
Q

When an non-zero base is raised to an even exponent, what is always true about the result?

A

The result will always be positive.

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22
Q

When a non-zero base is raised to an odd exponent, what is true about the result?

A

If the original base is positive then the result will be positive, and if the original base is negative, then the result will be negative.

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23
Q

There is only one number that is both an even and a prime number. What number is that?

A

The number 2.

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23
Q

There is only one number that is both an even and a prime number. What number is that?

A

The number 2.

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24
Q

Recall the first 25 Prime Numbers.

A

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 83, 89, 97.

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25
Q

Recall the process to find the total number of positive integer factors of a number.

A

1: Find the prime factorization of the number. At the end of the process, make all exponents visible, including the exponent of 1.

2: Add 1 to the value of each exponent, and then multiply these results. The product will be the total number of factors of that number.

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26
Q

If some number x, has y unique prime factors, then how many prime factors would x^n have?

A

The same number, y, of unique prime factors.

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27
Q

If two positive integer x and y share no prime factors, what is the Lowest Common Multiple of x and y?

A

The LCM is x*y. Otherwise, the LCM is some number less than xy.

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28
Q

What is the Greatest Common Factor of a set of positive integers with no prime factors in common?

A

The GCF is 1.

29
Q

x and y are positive integers. We know the LCM and GCF of both x and y. What else can we determine?

A

LCM(x,y) * GCF(x,y) = x * y.

30
Q

If positive integer y divides evenly into positive integer x, what is the LCM of x and y?

A

x.

31
Q

If positive integer y divides evenly into positive integer x, what is the GCF of x and y?

A

y.

32
Q

If two process that occur at different rates will collide, what mathematical process can you use to determine when they will collide?

A

LCM.

33
Q

For any set of positive integers, the LCM will always be greater than or equal to___________?

A

The largest number in the set.

34
Q

For any set of positive integers, the GCF will always be less than or equal to___________?

A

The smallest number in the set.

35
Q

z is divisible by both x and y; based on LCM, z must also be divisible by?

A

The LCM of x and y.

36
Q

The product of any n consecutive integers will always be divisible by?

A

n!, and all the factors of n!

37
Q

Consecutive integers are sometimes disguised as algebraic expressions.

A

n^2 - n; n^2 +n; n^3 - n; n^5 - 5n^3 + 4n

38
Q

If n is odd, then (n+1) and (n-1) are?

A

Even.

39
Q

The product of n even consecutive integers is divisible by?

A

2^n * n!

40
Q

When the division of 2 integers results in a decimal, the actual remainder must be a multiple of the most reduced remainder. For e.g., if the remainder is 0.48, which is reduced to 12/25, what is a multiple of the actual remainder?

A

12.

41
Q

A remainder must be a non-negative integer that is less than?

A

The divisor.

42
Q

How do you determine the number of trailing zeros of a number?

A

The number of trailing zeros is the number of (5 * 2) pairs of prime factorization of that number.

43
Q

If a factorial is >= 5!, what is the units digit?

A

0.

44
Q

If x is an integer, where x IS NOT a perfect power of 10, then how many leading zeros will 1/x have?

A

K - 1 leading zeros.

45
Q

If x is an integer, where x IS a perfect power of 10, then how many leading zeros will 1/x have?

A

K - 2 leading zeros.

46
Q

What if we wanted to know the largest number of some prime number that divides into y!, what should we do?

A

For prime number x, we successively divide y by x^1, X^2, X^3, until we obtain a quotient of zero, then we add the quotients.

47
Q

What if we wanted to know the largest number of some number that divides into y!, where the number is not a prime number, what should we do?

A

We first break the non-prime number into prime factors, for e.g. 6^n = 2^n * 3^n and then apply the shortcut rule, based on the highest prime factor obtained.

48
Q

If all the prime factors of a number has even exponents, how do we describe the number?

A

The number is a perfect square.

49
Q

cube root(0) = ?; cube root(1) = ?; cube root(8) = ?; cube root(27) = ?; cube root(64) = ?; cube root(125) = ?; cube root(216) = ?; cube root(343) = ?; cube root(512) = ?.

A

cube root(0) = 0; cube root(1) = 1; cube root(8) = 2; cube root(27) = 3; cube root(64) = 4; cube root(125) = 5; cube root(216) = 6; cube root(343) = 7; cube root(512) = 8.

50
Q

If all the prime factors of a number have exponents that are divisible by 3, how do we describt that number?

A

The number is a perfect cube.

51
Q

How do you know if the decimal equivalent of a fraction will terminate?

A

The decimal equivalent of a fraction will terminate if and only if the denominator of the reduced fraction has a prime factorization that contains only 2s or 5s or both.

52
Q

How do you know that the decimal equivalent of a fraction will not terminate?

A

If the prime factorization of the reduced fraction’s denominator contains anything other than 2s or 5s, the decimal equivalent will not terminate.

53
Q

What is the consecutive powers pattern of 2?

A

2-4-8-6

54
Q

What is the consecutive powers pattern of 3?

A

3-9-7-1

55
Q

What is the consecutive powers pattern of 4?

A

4-6

56
Q

What is the consecutive powers pattern of 5?

A

Only 5.

57
Q

What is the consecutive powers pattern of 6?

A

Only 6.

58
Q

What is the consecutive powers pattern of 7?

A

7-9-3-1

59
Q

What is the consecutive powers pattern of 8?

A

8-4-2-6

60
Q

What is the consecutive powers pattern of 9?

A

9-1

61
Q

When a whole number is divided by 10, what will be the remainder?

A

The remainder will be the units digit of the dividend.

62
Q

When a whole number is divided by 100, what will be the remainder?

A

The remainder will be the last two digits of the dividend.

63
Q

When integers with the same units digit are divided by 5, is the result constant? Y/N?

A

Yes.

64
Q

The numbers in an evenly spaces set share a common difference, what is it and why does it exist?

A

It exists because the numbers increase by the same amount, which is the common difference.

65
Q

Recall 3 ways in which consecutive integers usually show up on the GMAT?

A
  1. A set of consecutive integers (even and/or odd).
  2. A set of consecutive multiples of a given number.
  3. A set of consecutive numbers with a given remainder, when divided by some integer.

E.g. A set of numbers with remainder 2 when divided by 6: {14,20,26,32}

66
Q

Can two Consecutive integers share the same prime numbers? Y/N

What is the GCF of 2 consecutive integers?

A

No.

The GCF of two consecutive integers is 1.

66
Q

Can two Consecutive integers share the same prime numbers? Y/N

What is the GCF of 2 consecutive integers?

A

No.

The GCF of two consecutive integers is 1.

67
Q

How can you determine a remainder when a very large number is divided by another number?

A

Since division produces a remainder pattern that will repeat infinitely, the remainder pattern for e.g. when 2 is raised to consecutive integers and divided by a certain integer, say 7, will provide a pattern of repeating remainders.

68
Q

How can you identify the square of a prime number, by using the number’s factors?

A

Only integers with EXACTLY 3 factors are the squares of Prime Numbers: the square itself, the base (prime number), AND 1.

GMAT (5 decks)

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