Warming Up
Level 1
Double Double
Triple's Alley
What's your bet?
100
There are 30 students in Mrs. Taylor’s kindergarten class. If there are twice as many students with blond hair as with blue eyes, 6 students with blond hair and blue eyes, and 3 students with neither blond hair nor blue eyes, how many students have blue eyes?
11
1.3.3
100
At the Gooddog Obedience School, dogs can learn to do three tricks: sit, stay, and roll over. Of the dogs at the school:
50 dogs can sit 17 dogs can sit and stay
29 dogs can stay 12 dogs can stay and roll over
34 dogs can roll over 18 dogs can sit and roll over
9 dogs can do all three 9 dogs can do none
How many dogs are in the school?
84 dogs
1.3.4
200
How many multiples of 3 are between 62 and 215?
51
1.4
200
How many numbers are in the list
64
1.2.2
200
At Brown High School, there are 12 players on the basketball team. All of the players are taking at least one foreign language class. The school offers only Spanish and French as its foreign language classes. 8 of the players are taking Spanish and 5 of the players are taking both languages. How many players are taking French?
9
1.7
200
Every student in my school is in either French class or Spanish class, or both. Let 
be the number of students in French class, 
be the number of students in Spanish class, and 
be the number of students that are in both classes. Find an expression in terms of , , and for how many students there are in my school.
(x-z)+(y-z)+z=x+y-z
1.3.5
300
There are 20 cars in my building’s parking lot. All of the cars are red or white. 12 of them are red, 15 of them are 4-door, and 4 of them are 2-door and white. How many of the cars are 4-door and red?
11
1.3.1
300
There are 27 cats at the pound. 14 of them are short-haired. 11 of them are kittens. 5 of them are long-haired adult cats (not kittens). How many of them are short-haired kittens?
x=3
1.8
300
At the Gooddog Obedience School, dogs can learn to do three tricks: sit, stay, and roll over. Of the dogs at the school:
50 dogs can sit 17 dogs can sit and stay
29 dogs can stay 12 dogs can stay and roll over
34 dogs can roll over 18 dogs can sit and roll over
9 dogs can do all three 9 dogs can do none
How many dogs are in the school?
84 dogs
1.3.4a
400
How many numbers are in the list 
19
400
How many numbers are in the list 
58
1.2.1
400
How many perfect squares are between 50 and 250?
8
1.2.7
400
How many sets of four consecutive positive integers are there such that the product of the four integers is less than 
?
16
1.2.9
Since 
, we check the value of 
. Also 
, so 
is the largest product of four consecutive positive integers which is less than . So there are 
sets.
500
Going back to the 12-person basketball team from Problem 1.7, all 12 players are taking at least one of biology or chemistry. If 7 players are taking biology and 2 players are taking both sciences, how many players are taking chemistry?
7
1.3.2
500
How many odd perfect squares are between 5 and 211?
6
1.2.8