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Difference between revisions of "2008 iTest Problems"

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==Problem 25==
 
==Problem 25==
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A cube has edges of length 120 cm. The cube gets chopped up into some number of smaller cubes, all of equal size, such that each edge of one of the smaller cubes has an integer length. One of those smaller cubes is then chopped up into some number of even smaller cubes, all of equal size. If the edge length of one of those even smaller cubes is <math>n</math> cm, where <math>n</math> is an integer, find the number of possible values of <math>n</math>.
  
 
[[2008 iTest Problems/Problem 25]]
 
[[2008 iTest Problems/Problem 25]]
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==Problem 26==
 
==Problem 26==
  

Revision as of 09:06, 30 September 2008

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Problem 1

(story eliminated)

When the Kubiks went on vacation to San Diego last year, they spent a day at the San Diego Zoo. Single day passes cost $$33 for adults (Jerry and Hannah), $$22 for children (Michael is still young enough to get the children’s rate), and family memberships (which allow the whole family in at once) cost $$120. How many dollars did the family save by buying a family pass over buying single day passes for every member of the family?

2008 iTest Problems/Problem 1

Problem 2

2008 iTest Problems/Problem 2

Problem 3

2008 iTest Problems/Problem 3

Problem 4

The difference between two prime numbers is 11. Find their sum.

2008 iTest Problems/Problem 4

Problem 5

2008 iTest Problems/Problem 5

Problem 6

Let $L$ be the length of the altitude to the hypotenuse of a right triangle with legs 5 and 12. Find the least integer greater than $L$.

2008 iTest Problems/Problem 6

Problem 7

Find the number of integers $n$ for which $n^2 + 10n < 2008$.

2008 iTest Problems/Problem 7

Problem 8

(story eliminated)

Given the system of equations

$2x + 3y + 3z = 8$,

$3x + 2y + 3z = 808$,

$3x + 3y + 2z = 80808$,

find $x+y+z$.

2008 iTest Problems/Problem 8

Problem 9

(story eliminated)

What is the units digit of $2008^{2008}$?

2008 iTest Problems/Problem 9

Problem 10

2008 iTest Problems/Problem 10

Problem 11

2008 iTest Problems/Problem 11

Problem 12

2008 iTest Problems/Problem 12

Problem 13

2008 iTest Problems/Problem 13

Problem 14

The sum of the two perfect cubes that are closest to 500 is 343+512 = 855. Find the sum of the two perfect cubes that are closest to 2008.

2008 iTest Problems/Problem 14

Problem 15

How many four-digit multiples of 8 are greater than 2008?

2008 iTest Problems/Problem 15

Problem 16

2008 iTest Problems/Problem 16

Problem 17

2008 iTest Problems/Problem 17

Problem 18

Find the number of lattice points that the line $19x+20y = 1909$ passes through in Quadrant I.

2008 iTest Problems/Problem 18

Problem 19

Let $A$ be the set of positive integers that are the product of two consecutive integers. Let $B$ be the set of positive integers that are the product of three consecutive integers. Find the sum of the two smallest elements of $A \cap B$.

2008 iTest Problems/Problem 19

Problem 20

2008 iTest Problems/Problem 20

Problem 21

2008 iTest Problems/Problem 21

Problem 22

2008 iTest Problems/Problem 22

Problem 23

Find the number of positive integers $n$ that are solutions to the simultaneous system of inequalities

$4n-18 < 2008$,
$7n + 17 > 2008$.

2008 iTest Problems/Problem 23

Problem 24

2008 iTest Problems/Problem 24

Problem 25

A cube has edges of length 120 cm. The cube gets chopped up into some number of smaller cubes, all of equal size, such that each edge of one of the smaller cubes has an integer length. One of those smaller cubes is then chopped up into some number of even smaller cubes, all of equal size. If the edge length of one of those even smaller cubes is $n$ cm, where $n$ is an integer, find the number of possible values of $n$.

2008 iTest Problems/Problem 25

Problem 26

2008 iTest Problems/Problem 26

Problem 27

2008 iTest Problems/Problem 27

Problem 28

2008 iTest Problems/Problem 28

Problem 29

2008 iTest Problems/Problem 29

Problem 30

2008 iTest Problems/Problem 30

Problem 31

2008 iTest Problems/Problem 31

Problem 32

2008 iTest Problems/Problem 32

Problem 33

2008 iTest Problems/Problem 33

Problem 34

2008 iTest Problems/Problem 34

Problem 35

2008 iTest Problems/Problem 35

Problem 36

2008 iTest Problems/Problem 36

Problem 37

2008 iTest Problems/Problem 37

Problem 38

2008 iTest Problems/Problem 38

Problem 39

2008 iTest Problems/Problem 39

Problem 40

2008 iTest Problems/Problem 40

Problem 41

2008 iTest Problems/Problem 41

Problem 42

2008 iTest Problems/Problem 42

Problem 43

2008 iTest Problems/Problem 43

Problem 44

2008 iTest Problems/Problem 44

Problem 45

2008 iTest Problems/Problem 45

Problem 46

2008 iTest Problems/Problem 46

Problem 47

2008 iTest Problems/Problem 47

Problem 48

2008 iTest Problems/Problem 48

Problem 49

2008 iTest Problems/Problem 49

Problem 50

2008 iTest Problems/Problem 50

Problem 51

2008 iTest Problems/Problem 51

Problem 52

2008 iTest Problems/Problem 52

Problem 53

2008 iTest Problems/Problem 53

Problem 54

2008 iTest Problems/Problem 54

Problem 55

2008 iTest Problems/Problem 55

Problem 56

2008 iTest Problems/Problem 56

Problem 57

2008 iTest Problems/Problem 57

Problem 58

2008 iTest Problems/Problem 58

Problem 59

2008 iTest Problems/Problem 59

Problem 60

2008 iTest Problems/Problem 60

Problem 61

2008 iTest Problems/Problem 61

Problem 62

2008 iTest Problems/Problem 62

Problem 63

2008 iTest Problems/Problem 63

Problem 64

2008 iTest Problems/Problem 64

Problem 65

2008 iTest Problems/Problem 65

Problem 66

2008 iTest Problems/Problem 66

Problem 67

2008 iTest Problems/Problem 67

Problem 68

2008 iTest Problems/Problem 68

Problem 69

2008 iTest Problems/Problem 69

Problem 70

2008 iTest Problems/Problem 70

Problem 71

2008 iTest Problems/Problem 71

Problem 72

2008 iTest Problems/Problem 72

Problem 73

2008 iTest Problems/Problem 73

Problem 74

2008 iTest Problems/Problem 74

Problem 75

2008 iTest Problems/Problem 75

Problem 76

2008 iTest Problems/Problem 76

Problem 77

2008 iTest Problems/Problem 77

Problem 78

2008 iTest Problems/Problem 78

Problem 79

2008 iTest Problems/Problem 79

Problem 80

2008 iTest Problems/Problem 80

Problem 81

2008 iTest Problems/Problem 81

Problem 82

2008 iTest Problems/Problem 82

Problem 83

2008 iTest Problems/Problem 83

Problem 84

2008 iTest Problems/Problem 84

Problem 85

2008 iTest Problems/Problem 85

Problem 86

2008 iTest Problems/Problem 86

Problem 87

2008 iTest Problems/Problem 87

Problem 88

2008 iTest Problems/Problem 88

Problem 89

2008 iTest Problems/Problem 89

Problem 90

2008 iTest Problems/Problem 90

Problem 91

2008 iTest Problems/Problem 91

Problem 92

2008 iTest Problems/Problem 92

Problem 93

2008 iTest Problems/Problem 93

Problem 94

2008 iTest Problems/Problem 94

Problem 95

2008 iTest Problems/Problem 95

Problem 96

2008 iTest Problems/Problem 96

Problem 97

2008 iTest Problems/Problem 97

Problem 98

2008 iTest Problems/Problem 98

Problem 99

2008 iTest Problems/Problem 99

Problem 100

2008 iTest Problems/Problem 100

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