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Sequences and Series
Number Theory
Logic
Proportional Reasoning
100
In the following arithmetic sequence, what is the value of m? -2, 4, m, 16, . . .
What is 10
100
On planet Wobble, 1 womp is equal in value to 3 wamps, and 2 wamps are equal in value to 5 wemps. How many womps are equal in value to 15 wemps?
What is 2
100
Jessica reads 30 pages of her book on the first day. The next day, she reads another 36 pages. On the third day, she reads another 42 pages. If she continues to increase the number of pages she reads each day by 6, how many days will it take her to read a book that has 270 pages?
What is 8 days?
100
Currently, 1/4 of the members of a local club are boys, and there are 80 members. If no one withdraws from the club, what is the minimum number of boys that would need to join to make the club 1/3 boys?
What is 10
200
In the patterns of dots with P1, P2, P3 and P4, each successive pattern of dots has one more row and one more column. What is the ratio of the number of dots in P50 to the number of dots in P25? Express your answer as a common fraction.
What is 4
200
Gary chooses a two-digit positive integer, adds it to 200, and squares the result. What is the largest number Gary can get?
What is 89,401
200
If Jordan passed mile marker 138 at 5:08 pm and then passed mile marker 216 at 6:20 pm, what was her average speed in miles per hour?
What is 65
200
Farmer Fred read that his crop needs a fertilizer that is 8% nitrate for optimal yield. He needs to apply 4 pounds of nitrate per acre. If his field has 188 acres, how many pounds of fertilizer will Fred use?
What is 9400 lbs
300
What is the 2011th term of the arithmetic sequence −4, −1, 2, 5, . . . , where each term after the first is 3 more than the preceding term?
What is 6026
300
What number is halfway between 5/8 and 11/16? Express your number as a common fraction.
What is 21/32
300
What is the least natural number that has four distinct prime factors?
What is 210
300
Tamika’s dad bought a Mustang convertible for $12,000 to celebrate his first job in 1978, which paid him $15,000 a year. If Tamika is to use the same fraction of her salary as her dad to buy a Mustang convertible, which now sells for $32,000, what will her first job have to pay?
What is $40,000
400
Each term after the first term, is three less than the square of the preceding term. If the first term of the sequence is 2, what is the 2011th term?
What is -2
400
If a total of twenty million dollars is to be divided evenly among four million people, how much money, in dollars, will each person receive?
What is $5
400
Lashae will plant pansies and violets around the edge of her garden. She must use the same number of each plant, and she must use all of the flowers she buys. If pansies are sold in packages of 6 and violets are sold in packages of 10, what is the least number of packages of violets she could buy, given that she buys at least 1 package?
What is 3
400
Vivian has 45 songs on her MP3-player, 15 of which are alternative rock and the rest of which are rap. Malik has 60 songs on his MP3-player in the same ratio as Vivian’s songs. How many more rap songs does Malik have on his MP3-player than Vivian has on hers?
What is 10 songs
500
What term is the smallest five-digit palindrome in the arithmetic sequence 2, 7, 12, 17, ....?
What is 20,002
500
If u + w = x and w + x = y and x + y = z, what is the integer value of the sum u +w + x + y + z, given u = 8 and z = 10?
What is 26
500
Two red, two yellow and two green faces, all unit squares, are available for building a cube. How many distinct cubes can be built?
What is 6
500
Four friends (Amanda, Barbara, Charles and Dylan) invested $3000, $5000, $7000 and $9000, respectively, in a certain start-up company. Profits will be divided in the same ratio as the investment. If the business made a profit of $72,000 this year, how much of the profit will the largest investor receive?
What is $27,000?