692 MCGRAW-HILL’S SAT
4.A Remember the “difference of squares” factor-
ing formula: a^2 −b^2 =(a−b)(a+b)
Substitute: 10 =(2)(a+b)
Divide by 2: 5 =a+b
(Chapter 8, Lesson 5: Factoring)
5.A
To find the value of f(14), find all the factors of 14:
1, 2, 7, 14
There are two prime factors, 2 and 7.
2 + 7 = 9
f(14) = 9To find the value of f(6), find all the factors of 6:
1, 2, 3, 6
There are two prime factors, 2 and 3.
2 + 3 = 5
f(6) = 5
f(14) −f(6) = 9 − 5 = 4(Chapter 11, Lesson 2: Functions)
6.D First write an equation to find the average.Multiply by 4: a+b+c+d= 80
If you want ato be as large as possible, make b, c,and
das small as possible. You are told that they are all
differentpositive integers: a+b+c+d= 80
Let b=1, c=2, d=3: a+ 1 + 2 + 3 = 80
Combine like terms: a+ 6 = 80
Subtract 6: a= 74
(Chapter 9, Lesson 2: Mean/Median/Mode Problems)
7.B Let the radius of circle A =aand the radius of
circle B =b.It is given that a= 2 b.The circumference
of a circle can be found with the equation C= 2 πr.
The sum of their circumferences is 36π:
36 π= 2 πa+ 2 πb
Divide by π: 36 = 2 a+ 2 b
Substitute for a: 36 =2(2b) + 2 b
Simplify: 36 = 4 b+ 2 b
Combine like terms: 36 = 6 b
Divide by 6: 6 =b
Solve for a: a=2(b) =2(6) = 12
(Chapter 10, Lesson 5: Areas and Perimeters)
abcd+++
=
420
8.C This is a visualization problem. The six possi-
ble planes are illustrated below. Notice that the six
faces of the cube “don’t count,” because each of those
contains four edges of the cube.(Chapter 10, Lesson 7: Volumes and 3-D Geometry)- 16 Set up an equation: 2 x− 10 = 22
Add 10: 2 x= 32
Divide by 2: x= 16
(Chapter 8, Lesson 1: Solving Equations) - 36
There are 180°on one side of a line:
2 y+y+y+y= 180 °
Combine like terms: 5 y= 180 °
Divide by 5: y= 36 °
(Chapter 10, Lesson 1: Lines and Angles)2 y°y°
y°
y°