The Prime Suspects
Pattern Recognition
Jammin' Geometry
Algebraic Achievements
Pot Pourri
100
True or False:
"1" is a prime number.
What is "False."
It only has one factor.
"1" is a square number, however.
100
In this "magic-square," five more nubmers can be placed in the boxes so that the sum of each row, column, and diagonal is always the same. This is the value of the X.
What is 20?
100
An acute angle is an angle whose measure is between 0o and 90o. Using the rays in the diagram below, this is the total number of different acute angles that can be formed.
What is 10?
100
One loaf of bread and six rolls cost $1.80. At the same prices, two loaves of bread and four rolls cost $2.40. This is the amount that one loaf of bread costs. 
What is $0.90?
L = cost of loaf of bread; R = cost of roll
2L+4R=240
L+2R=120
L+6R=180
(L-L)+(6R-2R)=(180-120)
4R=60
R=15
L+30=120
L=90
100
Suppose today is Tuesday. This is the day of the week it will be 100 days from now.
What is Thursday?
Every 7 days is Tuesday. 98 is a multiple of 7 so day 98 is a Tuesday. Day 100 is a Thursday.
200
This is the smallest 3-digit prime number.
What is "101"?
200
Arrange the following digits as a six-digit number in which the 1s are separated by one digit, the 2s are separated by two digits, and the 3s are separated by three digits. This is one of the two possible answers.
1, 1, 2, 2, 3, 3
What are 3 1 2 1 3 2 or 2 3 1 2 1 3?
200
The set of stairs shown is constructed by placing layers of cubes on top of each other. This is the total number of cubes contained in the staircase.
What is 48?
(3 groups of 16 cubes)
200
Consecutive numbers are whole numbers that follow in order, such as 7, 8, 9, and 10.
These are the three consecutive numbers such that the sum of the first and third is 118.
What are 58, 59, and 60?
Divide 118 in half = 59.
The numbers on either side of that will combine to make 118.
200
If 24 gallons of water are poured into and empty tank, then 3/4 of the tank is filled. This is the number of gallons that the full tank can hold.
What is 32 gallons?
w = water capacity of the tank
3/4 x w = 24
4/3 x 3/4 x w = 4/3 x 24
w = 32
300
This is the prime factorization of 30.
What is "2 x 3 x 5"?
300
23 means 2 x 2 x 2 or 8.
33 means 3 x 3 x 3 or 27.
N3 means N X N X N.
Suppose N3 = 4,913.
This is the value of N.
What is 17?
103 = 1,000
203 = 8,000
Must be between 10 and 20
Ignore 10s digit: which set of 1s ends in "3"?
1x1x1=1, 2x2x2=8, 3x3x3=27,...,7x7x7=343
300
Each of the boxes in the figure is a square. This is the number of different squares that can be traced using the lines in the figure. 
What is 38?
21 are 1x1
12 are 2x2
5 are 3x3
300
The number of two-dollar bills needed to pay for a pair of shoes is 9 more than the number of five-dollar bills needed to buy the same shoes.
This is the cost of the shoes.
What is $30.00?
n = number of five-dollar bills
5n=2(n+9)
5n=2n+18
3n=18
n=6
6x5=30
300
Suppose five days before the day after tomorrow was Wednesday. This is the day of the week that was yesterday.
What is Friday?
400
This is the number of twin primes below 100.
What is "8"?
3-5, 5-7, 11-13, 17-19, 29-31, 41-43, 59-61, 71-73
400
In the lunchroom, if 4 students sit on each bench, there will be 3 students who do not have a place.
However, if 5 students sit on each bench, there will be 2 empty places.
This is the smallest number of students in the lunchroom.
What is 23?
(multiples of 4) + 3 = 7, 11, 15, 19, 23, 27, 31, ...
(multiples of 5) - 2 = 3, 8, 13, 18, 23, 28,
400
There are two kinds of toy train cars: 6-inch cars and 7-inch cars. Of the following, this is the length of train cars that cannot be made by hooking together either 6-inch cars, 7-inch cars, or a combination of both:
29 inches, 30 inches, 31 inches, 32 inches, 33 inches
What is 29 inches?
lgth 6-in 7-in
30 5 0
31 4 1
32 3 2
33 2 3
400
$1,200 is shared among four siblings so that each gets $100 more than the sibling who is the next youngest.
This is the amount of money the youngest sibling gets.
What is $150?
y = the share of the youngest sibling
y+100 = next sibling
y+200 = next sibling
y+300 = oldest sibling
4y+600 = 1,200
4y = 600
y = 150
400
A train can hold 78 passengers. The train starts our empty and picks up 1 passenger at the first stop, 2 passengers at the second stop, 3 passengers at the third stop, and so forth.
This is the number of stops it will take for the train to be full.
What is 12?
1+2+3+4+5+6+7+8+9+10+11+12=78
500
This is the prime factorization of 72.
What is 2 x 2 x 2 x 3 x 3
or
23 x 32
500
Of three numbers, two are 1/2 and 1/3. This is the third number, so that the average of all three is 1.
What is 2 1/6?
n = the third number
1/2 + 1/3 + n = 3
3/6 + 2/6 + n = 3
5/6 + n = 3
n = 3 - 5/6 = 2 1/6
500
This figure consists of 3 layers of cubes with no gaps. Suppose the exterior of the figure (including the bottom) is painted red and then separated into individual cubes. This is how many of these cubes will have exactly 3 red faces. 
What is 16?
500
Thirteen plums weigh as much as two apples and one pear. Four plums and one apple have the same weight as one pear.
This is the number of plums that have the same weight as one pear.
What is 7 plums?
13pl = 2a + 1pe
4pl + 1a = 1pe
13pl = 2a + 4pl + 1a
13pl = 4pl + 3a
9pl = 3a
3pl = a
4pl + 3pl = 7pl = 1pe
500
A rectangular garden is 14 ft. by 21 ft. and is bordered by a concrete walk 3 ft. wide, as shown. This is the surface area of just the concrete walk.
What is 246 sq ft?
(20 x 27) - (14 x 21) = 246