Prime Factorization
What is the greatest prime factor of 42 ?
42 = 6 • 7 = 2 • 3 • 7
So the greatest prime factor of 42 is 7
2 / ? = 6 / 9
3
On a number line, points A-D (from left to right) represent the numbers 0.4, 1/2, 0.45, and 3/5, though not necessarily in that order. Which letter represents 3/5 ?
D
On a coordinate plane, point A is at (4, 6). Point B is 5 units right and 2 units down from point A. If point B is at (m, n), what is m + n?
m + n = 13
How many positive integers less than or equal to 20 are divisible by 2 or 5?
12
What is the greatest prime factor of 1700 ?
1700 = 100 • 17 = 20 • 5 • 17 = 4 • 5 • 5 • 17
= 2 • 2 • 5 • 5 • 17
So the greatest prime factor of 1700 is 17
3 / ? = 5 / 30
18
On a number line, points A-D (from left to right) represent the numbers 3/8, 0.35, 2/5, and 0.38, though not necessarily in that order. Which letter represents 3/8 ?
B
On a coordinate plane, point A is at (2, −3). Point B is 6 units left and 4 units up from point A. Point C is a reflection over the y-axis of point B. If point C is at (m, n), what is m + n?
m + n = 5
How many positive integers less than 50 are divisible by 3 or 4?
24
What is the sum of the distinct prime factors of 1001 ?
1001 = 7 • 11 • 13
7 + 11 + 13 = 31
Solve for x:
(x + 1) / 3 = (x + 5) / 5
x = 5
On a number line, points A-D (from left to right) represent the numbers 3.05, 3.1, 13/4, and √10, though not necessarily in that order. Which letter represents √10 ?
C
On a coordinate plane, point A is at (−5, 8). Point B is 12 units right and 11 units down from point A. Point C is a reflection over the x-axis of point B, and point D is a reflection over the y-axis of point C. If point D is at (m, n), what is m + n?
m + n = -4
How many positive integers less than 100 are not divisible by 3 or 5?
53
How many factors does 720 have?
720 = 24 • 32 • 5
5 ways to use 2 as a factor.
3 ways to use 3.
2 ways to use 5.
5 • 3 • 2 = 30 total factors
On a map, 3/4 inch represents 15 miles. Two cities are 4.5 inches apart on the map. How many miles apart are the cities?
90 miles
On a number line, points A-D (from left to right) represent the numbers √3, 1.7, 3/2, and 7/5, though not necessarily in that order. Which letter represents √3 ?
D
On a coordinate plane, rectangle ABCD has A(−3, −4) and B(9, −4). The perimeter of ABCD is 38 units, and points C and D are above side AB. If point C is at (m, n), what is m + n?
m + n = 12
How many positive integers less than 100 are not divisible by 2, 5, or 7?
87
What is the smallest integer that 504 must be multiplied by so that the product is a perfect square?
504 = 23 • 32 • 7
So you need another 2 and another 7 (so 14)
504 • 14 = 7056 = 842
The ratio of a to b is 3:5, and the ratio of b to c is 10:7 If a + c = 52, what is the value of b?
b = 40
On a number line, points A-D (from left to right) represent the numbers −√20, −9/2, −4.4, and −4.6, though not necessarily in that order. Which letter represents −√20 ?
C
On a coordinate plane, point A is at (−2, 9). Point P is 4 units left and 5 units down from point A. Point Q is a reflection over the x-axis of point P, and point R is a reflection over the y-axis of point Q. What is the area, in square units, of triangle PQR?
48 square units
How many positive integers less than or equal to 210 are not divisible by 2, 3, 5, or 7?
48