| Problem |
Solution |
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1) The largest number in a set of five integers is 92. The range of the set is 57 and the median is 80. What is the smallest possible value of the mean of the set? |
1. If the largest number is 92 and the range is 57, then the lowest number is
92 - 57 = 35
2. For 80 to be the mean, there must be one number lower than it and one equal or higher.
3. Find the lowest number for the number lower than 80 = 35
4. Find the lowest number that lets 80 remain the median = 80
5. The mean is (35 + 35 + 80 + 80 + 92)/5 = 64.4
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2) You are playing a lottery game. A number is pulled at random from a box containing the numbers 1 to 1000, both inclusive. You win if a number containing exactly two 5s is drawn. What is
your probability of winning?
(Express as a percentage) |
1. There are 3 types of numbers that you can win with:
(remember, the X in the following number
representations cannot be a 5):
1. Numbers that start with 5 and end with 5: (5X5) = 9
2. Numbers whose first 2 digits are 5: (55X) = 9
3. Numbers whose second and 3rd digits are 5
and do not start with a 5. (X55) = 9
2. Count these up and add = 9 + 9 + 9 = 27 numbers
3. Divide by 1000 = 27/1000 = 2.7%
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3) After six math tests, Julian's average was 82. After the final exam, which was worth two tests, his average rose to 85. What was Julian's grade on the final exam? |
Let S6 = the sum of the first 6 tests = 82 X 6 = 492
Let F = the score of the final exam.
1. Then (S6 + 2F)/8 = 85.
2. Solve this for F =
(492 + 2F)/8 = 85
492 + 2F = 680
2F = 680 - 492 = 188
F = 94
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Here is the table of the sum of 2 dice.