Difference between revisions of "2008 iTest Problems"
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==Problem 23== | ==Problem 23== | ||
Find the number of positive integers <math>n</math> that are solutions to the simultaneous system of inequalities | Find the number of positive integers <math>n</math> that are solutions to the simultaneous system of inequalities | ||
| − | <center><math>4n | + | <center><math>4n-18 < 2008</math>, |
<math>7n + 17 > 2008</math>.</center> | <math>7n + 17 > 2008</math>.</center> | ||
Revision as of 08:05, 30 September 2008
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Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 Problem 26
- 27 Problem 27
- 28 Problem 28
- 29 Problem 29
- 30 Problem 30
- 31 Problem 31
- 32 Problem 32
- 33 Problem 33
- 34 Problem 34
- 35 Problem 35
- 36 Problem 36
- 37 Problem 37
- 38 Problem 38
- 39 Problem 39
- 40 Problem 40
- 41 Problem 41
- 42 Problem 42
- 43 Problem 43
- 44 Problem 44
- 45 Problem 45
- 46 Problem 46
- 47 Problem 47
- 48 Problem 48
- 49 Problem 49
- 50 Problem 50
- 51 Problem 51
- 52 Problem 52
- 53 Problem 53
- 54 Problem 54
- 55 Problem 55
- 56 Problem 56
- 57 Problem 57
- 58 Problem 58
- 59 Problem 59
- 60 Problem 60
- 61 Problem 61
- 62 Problem 62
- 63 Problem 63
- 64 Problem 64
- 65 Problem 65
- 66 Problem 66
- 67 Problem 67
- 68 Problem 68
- 69 Problem 69
- 70 Problem 70
- 71 Problem 71
- 72 Problem 72
- 73 Problem 73
- 74 Problem 74
- 75 Problem 75
- 76 Problem 76
- 77 Problem 77
- 78 Problem 78
- 79 Problem 79
- 80 Problem 80
- 81 Problem 81
- 82 Problem 82
- 83 Problem 83
- 84 Problem 84
- 85 Problem 85
- 86 Problem 86
- 87 Problem 87
- 88 Problem 88
- 89 Problem 89
- 90 Problem 90
- 91 Problem 91
- 92 Problem 92
- 93 Problem 93
- 94 Problem 94
- 95 Problem 95
- 96 Problem 96
- 97 Problem 97
- 98 Problem 98
- 99 Problem 99
- 100 Problem 100
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?
Problem 2
Problem 3
Problem 4
The difference between two prime numbers is 11. Find their sum.
Problem 5
Problem 6
Let 
be the length of the altitude to the hypotenuse of a right triangle with legs 5 and 12. Find the least integer greater than .
Problem 7
Find the number of integers 
for which 
.
Problem 8
(story eliminated)
Given the system of equations
,
,
,find 
.
Problem 9
(story eliminated)
What is the units digit of 
?
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 
passes through in Quadrant I.
2008 iTest Problems/Problem 18
Problem 19
Let 
be the set of positive integers that are the product of two consecutive integers. Let 
be the set of positive integers that are the product of three consecutive integers. Find the sum of the two smallest elements of 
.
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 that are solutions to the simultaneous system of inequalities
,
.2008 iTest Problems/Problem 23
Problem 24
2008 iTest Problems/Problem 24
Problem 25
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
