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Problems of the Week for April 23 Do 5 of 8 of your choice

Summary: Problems of the Week for April 23
Do 5 of 8 of your choice
1. Of a group of boys and girls at Central Middle School's after-school party, 15
girls left early to play in a volleyball game. The ratio of boys to girls then
remaining was 22 to 7 . Later, 45 boys left for a football game. The ratio of girls to
boys was then 7 to 13 . How many students attended the party?
2. In the equation a * b = 2310 , a and b are both two-digit numbers. What is the
greatest possible value of a + b ?
3. A circular garden is surrounded by a sidewalk with a uniform width of 11 feet.
The total area of the sidewalk equals the total area of the garden. How many feet
are in the diameter of the garden? Round your answer to the nearest whole number.
4. The first five triangular numbers are pictured. The nth trinagluar number is
formed by drawing a row of n dots below the (n-1)th triangular dot pattern. The k-
th triangular number is represented by 136 dots. What is the value of k?
5. How many ways can the letters of the word NUMBER be scrambled so that the
first and the last letters are both vowels? What if the first and last letters are both
6. What is the sum of all positive integer values of n such (n +25)/n is an integer?
7. A number can be written in the form (m+11)(n+22) , where m and n are two-
digit numbers created by using each of the digits in this set {1, 2, 3, 4} exactly


Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara


Collections: Mathematics