SAT Mc Graw Hill 2011

694 MCGRAW-HILL’S SAT

17. 52

Break a shape like
this into recogniz-
able four-sided
figures and trian-
gles that are easier
to deal with.

The area of the
rectangle on the
left is 7 × 4 =28.
The area of the rectangle on the right is 5 × 4 =20.
The sum of those two areas is 28 + 20 =48. The
area remaining for the triangle is the difference
78 − 48 =30. Set up an equation for the area of a
triangle to solve for x:
Area =^1 ⁄ 2 (base)(height)
30 =^1 ⁄ 2 (5)(height)
Divide by^1 ⁄ 2 : 60 =5(height)
Divide by 5: 12 =height

To find the hypotenuse of
the right triangle, set up
the Pythagorean theorem
and solve:
52 + 122 =c^2
25 + 144 =c^2
169 =c^2
c= 13

(Or just notice that it’s a 5-12-13 triangle!)

To find the perimeter of the figure, add up all of the
sides:

13 + 12 + 4 + 5 + 7 + 4 + 7 = 52

(Chapter 10, Lesson 5: Areas and Perimeters)
(Chapter 10, Lesson 3: The Pythagorean Theorem)

18. 225 Set up a three-circle Venn diagram to visual-
    ize this information.

Fifty students study two of the three languages, so let’s

say that 50 students study both Spanish and Latin. (It

doesn’t matter whichtwo languages those 50 students

take; the result turns out the same.) This means that

zero students study both Spanish and French, zero

students study both French and Latin, and zero

students study all three languages.

There are 120 Spanish students in all. There are there-

fore 120 − 50 =70 students who study Spanish alone.

There are 80 French students in all, all of whom study

just French, and there are 75 total Latin students in-

cluding 75 − 50 =25 students who study only Latin.

This means that there are 70 + 50 + 80 + 25 = 225

sophomores at Hillside High School.

(Chapter 9, Lesson 5: Counting Problems)

Section 5

1.C The clients were forced to seek more reliable

investment advice, so the manager must have man-

aged their funds badly. ineptitude=lack of skill

2.E Vartan is Armenian; he was born in Iran and

educated in Lebanon and is now president of the

American Brown University. He has a lot of worldly

experience. perpetual=lasting forever; authoritative=

showing authority; cosmopolitan=worldly

3.D They didn’t consider it in great detail, so the

reading must have been without great care. verbatim=

word for word; meandering=wandering; tormented=

feeling anguish or pain; cursory=quick and without

care; substantial=of substance, quite large

Spanish French

Latin

50 0

(^7080)
25
0
0
4

7

7

(^2844)

5

5

20

c x

4

7

7

(^284)
5
5
20
12
4
13