The sum of the first 100 positive integers is 5,050. What is the sum of the first 200 positive integers?

When 2/9 of the votes on a certain resolution have been counted, 3/4 of those counted are in favor of the resolution. What fraction of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution?

In the figure above, X and Y represent locations in a district of a certain city where the streets form a rectangular grid.In traveling only north or east along the streets from X to Y, how many different paths are possible?

The letters C, I, R, C, L, and E can be used to form 6-letter strings such as CIRCLE or CCIRLE. Using these letters, how many different 6-letter strings can be formed in which the two occurrences of the letter C are separated by at least one other letter?

Pat will walk from intersection X to intersection Y along a route that is confined to the square grid of four streets and three avenues shown in the map above. How many routes from X to Y can Pat take that have the minimum possible length?

The table above shows the average(arithmetic mean) price per dozen eggs sold in a certain store during three successive months. If 2/3 as many dozen were sold in April as in May,and twice as many were sold in June as in April, what was the average price per dozen of the eggs sold over the three-month period?

The map above shows the trails through a wilderness area. If travel is in the direction of the arrows, how many routes along the marked trails are possible from point A to point B?

King School has an enrollment of 900 students. The school day consists of 6 class periods during which each class is taught by one teacher. There are 30 students per class. Each teacher teaches a class during 5 of the 6 class periods and has one class period free. No students have a free class period. How many teachers does the school have?

Ben and Ann are among 7 contestants from which 4 semifinalists are to be selected. Of the different possible selections, how many contain neither Ben nor Ann?

If s is an integer, is 24 a divisor of s?

(1)Each of the numbers 3 and 8 is a divisor of s. 

(2) Each of the numbers 4 and 6 is a divisor of s.