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GMAT > Unit Digit Patterns > Flashcards

Unit Digit Patterns Flashcards

1
Q

0

A

All powers of 0 end in 0

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2
Q

1

A

All powers of 1 end in 1

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3
Q

2

A

4 number pattern: 2-4-8-6

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4
Q

3

A

4 number pattern 3-9-7-1

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5
Q

4

A

2 number pattern 4-6
odd power = 4
even power = 6

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6
Q

5

A

All powers of 5 end in 5

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7
Q

6

A

All powers of 6 end in 6

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8
Q

7

A

4 number pattern 7-9-3-1

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9
Q

8

A

4 number pattern 8-4-2-6

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10
Q

9

A

2 number pattern 9-1
odd power = 9
even power = 1

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11
Q

When is a number divisible by 0?

A

No number is divisible by 0

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12
Q

When is a number divisible by 1?

A

All numbers are divisible by 1

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13
Q

When is a number divisible by 2?

A

A number is divisible by 2 if the ones digit is even.

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14
Q

When is a number divisible by 3?

A

A number is divisible by 3 if the sum of all its digits is divisible by 3.

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15
Q

When is a number divisible by 4?

A

A number is divisible by 4 if the last 2 digits are divisible by 4.

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16
Q

When is a number divisible by 5?

A

A number is divisible by 5 if the last digit ends in either 0 or 5.

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17
Q

When is a number divisible by 6?

A

A number is divisible by 6 if it is an even number whose digits sum to a multiple of 3.

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18
Q

When is a number divisible by 7?

A

Just do the division

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19
Q

When is a number divisible by 8?

A

A number is divisible by 8 if the number is even and the last 3 digits are divisible by 8.

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20
Q

When is a number divisible by 9?

A

A number is divisible by 9 when the sum of all the digits is divisible by 9.

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21
Q

When is a number divisible by 10?

A

If the ones digit is 0, then the number is divisible by 10.

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22
Q

When is a number divisible by 11?

A

A number is divisible by 11 if the sum of the odd number place digits minus the sum of the even numbered place digits is divisible by 11. For example
253 is divisible by 11 because 2+3 - 5 = 0
2915 is divisible by 11 because (9+5) - (2+1) = 11

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23
Q

When is a number divisible by 12?

A

When a number is divisible by both 3 and 4, it is divisible by 12

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24
Q

Odd + odd

A

even

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25
Q

even + even

A

even

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26
Q

even + odd

A

odd

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27
Q

odd - odd

A

even

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28
Q

even - even

A

even

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29
Q

even * even

A

even

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30
Q

even * odd

A

even

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31
Q

odd * odd

A

odd

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32
Q

even / odd

A

even

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33
Q

odd / odd

A

odd

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34
Q

even / even

A

even OR odd

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35
Q

What is the formula for division

A

x / y = Quotient + remainder / y

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36
Q

What are prime numbers less than 100?

A

2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97

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37
Q

How do you find the number of factors for a number?

A
  1. Find the prime factorization for the number
  2. For each factor, take the power + 1 and multiply

i.e. 240 = 2^4 * 3^1 * 5^1
number of factors = (4+1)(1+1)(1+1) = 20 factors

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38
Q

Given x y and x and y’s LCM and GCF

A

the LCM * GCF = xy

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39
Q

What do we know about prime factors of a perfect square

A

Other than 0 and 1, all its prime factors have to have even powers

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40
Q

What do we know about prime factors for a perfect cube

A

Other than 0 and 1, all of its prime factors have to have powers divisible by 3

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41
Q

What are some perfect squares?

A

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

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42
Q

What are some perfect cubes?

A

0, 1, 8, 27, 64, 125, 216, 343, 512, 729, and 1000

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43
Q

What is the GCF of two consecutive integers

A

Two consecutive integers will NEVER share any prime factors. The GCF is always 1.

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44
Q

What is decimal of 1/6

A

0.166667

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45
Q

What is decimal of 1/7

A

0.142857

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46
Q

What is decimal of 1/9

A

0.1111111

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47
Q

What is the condition for determining if a decimal will terminate

A

A decimal will terminate if and only if the denominator of the reduced fraction contains a prime factorization of only 2s or 5s

48
Q

If Z is divisible by X and Y, Z must also be divisible by

A

the LCM of X and Y, and any combination of factors up to the max of the LCM

49
Q

If I square root an expression with a variable i.e. sqrt((x+3)^2) > 169

A

it becomes |x+3| > 13

50
Q

Any fraction with a whole number numerator and nonzero whole number denominator is

A

either a terminating decimal or a repeating decimal.

51
Q

How do you square decimals with 0s

A

Convert to scientific notation and then multiply accordingly, or just note that there will be 2*number of decimal places

52
Q

What is square root of x^2

A

|x| not x!!!

53
Q

What is square root of (x+y)^2

A

|x+y| not (x+y)!!

54
Q

What is square root of 3

A

1.7

55
Q

What is square root of 5

A

2.2

56
Q

What is square root of 6

A

2.4

57
Q

What is square root of 7

A

2.6

58
Q

What is square root of 8

A

2.8

59
Q

What is square root of 2

A

1.4

60
Q

What is the same exponent base adding rule?

A

2^n + 2^n = 2^n+1
3^n + 3^n + 3^n = 3^n+1
so on so forth . . . .

61
Q

What is the area of an equilateral triangle?

A

A = {side^2(root 3)} / 4

62
Q

What is the longest segment of a rectangle

A

The diagonal sqrt(l^2 + w^2)

63
Q

What is the maximum area of a rectangle with fixed perimeter

A

The maximum area of a rectangle is a square

64
Q

What is the area of a hexagon

A

Area = (3 * sqrt(3)) / 2 * s^2

65
Q

Described how inscribed angles in circles work

A

The inscribed angle will always be 1/2 the degree measure of the central angle

66
Q

What does the right triangle inscribed in a circle suggest

A

The hypotenuse of a right triangle will be the circle diameter

67
Q

If two lines are parallel

A

They will never cross each other

68
Q

If an inequality has the < sign

A

you shade below the line

69
Q

If an inequality has the > sign

A

you shade above the line

70
Q

When you reflect a point (x, y) over the origin, it becomes

A

(-x, -y)

71
Q

When you reflect a point (x, y) over the x axis, it becomes

A

(x, -y)

72
Q

When you reflect a point (x, y) over the y axis, it becomes

A

(-x, y)

73
Q

What is the formula for reflection of (x, y) over a point (a, b)

A

(2a - x, 2b - y)

74
Q

How do we know if a graph can be the graph for a function?

A

Use the vertical line test - for any vertical line, there should be no more than one point intersection

75
Q

In order to make any conclusions about terms in a sequence

A

The rule or formula must be known.

76
Q

What is the arithmetic sequence formula

A

a_n = a_1 + (n-1) d where d is the common difference

77
Q

What is the sum of the first n terms of an arithmetic sequence?

A

S_n = n/2 * (a_1 + a_n)

78
Q

What is the geometric sequence formula

A

a_n = a_1 * r^n-1

79
Q

Is 1 a prime number

A

1 is actually NOT a prime number because it does not have 2 unique factors!!

80
Q

Percent means

A

per 100. Dividing a number by 100 is the equivalent of multiplying by 1/100

81
Q

Translate the equations “p percent of q is equal to r”

A

p / 100 * q = r

82
Q

What is the percent less than formula

A

Final Value = (Initial Value) * (1 - Percent Less than / 100)

83
Q

What is the percent grater than formula

A

Final Value = (Initial Value) * (1 + Percent Greater Than / 100)

84
Q

Ho do you represent markup and markdown on price

A

Given a percentage of x, multiply value by (1 + x/100) for mark up, and (1 - x/100) for mark down

85
Q

How do you calculate precent change

A

Percent Change = [(Final Value - Initial Value) / Initial Value] * 100

Final Value = Initial Value * (1 +/- Percent Change / 100)

86
Q

To return a discounted value back up to original value

A

We must increase the cost by some percent greater than the percent from which it was discounted

87
Q

How many elements are in an inclusive set? (For example 50 to 101 inclusive)

A

Elements = Highest - Lowest + 1

101 - 50 + 1 = 52

88
Q

How do you find the number of elements who are multiples of x between y and z

A

(highest # divisible by given number - lowest # divisible by given number) / given number + 1

89
Q

How do you find the number of elements between two numbers (exclusive)?

A

Last - First - 1

90
Q

How do you find the average of the elements in an evenly spaced set?

A

(first + last) / 2

91
Q

How do we calculate the POSITION of median in an odd element set?

A

(number of elements + 1) / 2

92
Q

How do we calculate the POSITION of the median in an even element set?

A

average between n / 2 and n / 2 + 1 terms

93
Q

Does adding or subtracting the same amount from all terms change the standard deviation

A

Adding or subtracting the SAME amount from all terms does NOT change the standard deviation. We can have datasets with the same standard deviation but different averages.

94
Q

Does multiplying or dividing the same amount by all terms change the standard deviation

A

Multiplying or dividing by the same amount will change the standard deviation.

95
Q

How do you calculate standard deviation?

A

sqrt{[sum of (each points distance from mean)^2] / n + 1}

Standard deviation measures the average distance from the mean for a given set of points.

96
Q

What is the basic combination formula

A

nCk = n! / (n - k)! k!

97
Q

Explain the combination box and fill method

A

We have one box each time we have to make a decision and fill those with numbers. Then, we divide by the number of boxes factorial to make it a combination

98
Q

If there are m ways to perform task 1 and n ways to perform task 2, how many ways are there to perform both tasks

A

m x n (assuming the tasks are independent)

99
Q

When we are presented choices with the word “or” in combinatorics

A

We add instead of multiplying because the events are mutually exclusive

100
Q

What does the word “at least” in a combinatorics problem imply?

A

“At least” typically implies the addition of outcomes

101
Q

If x items from a group of y items must be chosen for a subgroup of z items

A

Mentally place those x items into the subgroup. Then y-x remaining items are being chosen for the z-x remaining spots in the subgroup.

102
Q

Two events are collectively exhaustive if

A

together, those events represent all of the possible outcomes of a scenario.

103
Q

If two events A and B are collectively exhaustive AND mutually exclusive

A

Total Number Of Ways Scenario Can Occur = Number of Ways in Which A Can Occur + Number of Ways in Which B Can Occur

104
Q

What is the basic permutation formula

A

nPk = n! / (n-k)!

105
Q

How do you solve a permutation that contains identical items

A

P = N! / (r1!) x (r2!) . . . where r1 and r2 are the respective frequencies of indistinguishable objects

106
Q

What is the circular permutation formula

A

K items can be arranged in a circle in (k-1)! ways

107
Q

What is the anchor method in permutations?

A

The anchor method asks for one to put the people/items in restricted positions in set spots first, then handle other items.

108
Q

You have y items but x of them must be arranged together. How many ways can you arrange

A

(y-x+1)!(x)! Treat all items in a group as one unit.

109
Q

How do you calculate probability of even A or B occurring when A and B are not mutually exclusive?

A

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

110
Q

How do we know the number of leading zeroes in a decimal?

A

Write the decimal as a fraction of 1/x where x is an integer. There will be k-1 leading zeros where k is the number of digits unless x is a perfect power of 10, in which case there are k-2 zeros

111
Q

What is the rate-time-work formula?

A

Rate x Time = Work

Rate = Work / Time

Time = Work / Rate

112
Q

a/b > c/d if

A

ad > bc

113
Q

Any factorial greater than 5!

A

Will have a trailing 0 as its units digit

114
Q

How do you combine two ratios/proportions?

A

Find the LCM of the two values which connect the two ratios, then scale the proportions accordingly

115
Q

If A and B are NOT independent, what’s the probability of A and B occurring?

A

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

116
Q

Given a rectangle with a fixed area, what is the minimum perimeter?

A

Minimum perimeter is given if the rectangle is a square.

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