SAT Mc Graw Hill 2011

68 McGRAW-HILL’S SAT

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Section 2

1.C Substitute k= 10 into 2m+ k= 12 to get
2 m+ 10 = 12
Subtract 10: 2m= 2
Divide by 2:m= 1
(Chapter 8, Lesson 1: Solving Equations)

2.E If the average of three numbers is 50, then
their sum must be 3(50) = 150. If two of the numbers
are 35 and 50, then the third is 150 − 35 −50 = 65
(Chapter 9, Lesson 2: Mean/Median/Mode Problems)

3.D Since the ones column has only one A, it is
easy to figure out its value from there. The only value
for A that yields a 7 in the ones column is 4.
(Chapter 9, Lesson 3: Numerical Reasoning Problems)

4.E The problem is best solved with a proportion:

. Cross-multiply: 25x= 2025
Divide by 25:x= 81
(Chapter 7, Lesson 4: Ratios and Proportions)

5.B Since 32 = 2^5 , we can substitute: 2x−^1 = 32
2 x−^1 = 2^5
x−1 = 5
Add 1:x= 6
(Chapter 8, Lesson 3: Working with Exponents)

6.A Since there were 59 yes votes, 26 of which were
from men, 59 − 26 = 33 of them were from women.
Since there were 76 women in total, 33 of whom voted
yes, 76 − 33 = 43 of them must have voted no.
(Chapter 11, Lesson 5: Data Analysis)

7.D They both start with xcards. After Mike gives
Kenny 12 cards, Mike has x−12 and Kenny has x+ 12
cards. If Kenny has twice as many as Mike, then
x+ 12 = 2(x−12)
Distribute: x+ 12 = 2x− 24
Add 24: x+ 36 = 2x
Subtract x: 36 = x
Since they each had 36 cards to start, they had a total
of 36 + 36 = 72.
(Chapter 8, Lesson 7: Word Problems)

8.C The fraction that is walnuts equals the amount

of walnuts divided by the total amount:

Simplify:

(Chapter 7, Lesson 4: Ratios and Proportions)

x

()x+ 35

x

()x++15 20

9

25 225

=

x

9.B You might simplify this problem by plugging

in possible values for the angle measures, remember-

ing the parallel lines theorem. Your diagram might

look like this:

This example shows that a+ d+ f+ g= 360°, and the

only other sum among the choices that equals 360°

is (B).

(Chapter 10, Lesson 1: Lines and Angles)

10.A Either plug in the ordered pairs to check, or

draw a graph, as long as you can do it quickly. Notice

that the point (7, −1) satisfies both inequalities:

2(7) + 3(−1) > 6 and 7 −(−1) > 6.

(Chapter 8, Lesson 6: Inequalities, Absolute Value,

and Plugging In)

11.A If nhas a remainder of 6 when it is divided by

12, it must be 6 more than a multiple of 12. Pick any

one you like: 18, for example. When 18 is divided by

6, the remainder is 0.

(Chapter 7, Lesson 7: Divisibility)

12.B Any five-sided polygon can be divided into

three triangles like so:

Since the sum of the angles in a triangle is 180°, the sum

of the angles in this figure is 3(180) = 540°. The average

measure of the five angles, then, is 540/5 = 108°.

(Chapter 10, Lesson 2: Triangles)