SAT Mc Graw Hill 2011

CHAPTER 2 / DIAGNOSTIC SAT 69

18.D Think about how many options you have to fill

each place, from left to right. Since the first person

must be a girl, you have 6 options. Since the next must

be a boy, you have 5 options. Since the next must be a

boy, you have 4 options (one is already up there). Since

the next must be a girl, you have 5 options left. This

means that the total number of possible arrangements

is (6)(5)(4)(5) =600.

(Chapter 9, Lesson 5: Counting Problems)

19.D If the two lines are parallel, then they have the

same slope. The slope of lis , so the slope of m

must be

Cross-multiply: 3 k= 48

Divide by 3: k= 16

Therefore, the rectangle has a width of 16 and a

height of 12, so its area is (16)(12) =192.

(Chapter 10, Lesson 4: Coordinate Geometry)

20.E If vis the volume of the solid, then abc=v.

Solving this equation for agives ,so statement

II must be true. Now go to the answer choices, and

notice that you can eliminate any choice without II,

namely (A) and (C). Also notice from the original

equation that vcould not be odd if any of the integers

a, b, or cwere even, therefore they must all be odd.

This implies that a+b+cis odd, so statement I must be

true. This eliminates choice (D). To check statement

III, you need an expression for the surface area of the

solid, which is 2(ab) +2(bc) +2(ac) =2(ab+bc+ac).

Since this is a multiple of 2, it is even, so statement III

is also true.

(Chapter 9, Lesson 3: Numerical Reasoning Problems)

(Chapter 10, Lesson 7: Volumes and 3-D Geometry)

a

v

bc

=

3

4

12 3

4

as well. Therefore

k

=

9

12

3

4

=

To find the area of the triangle, you need to use the

formula area=base×height/2. Since the height di-

vides the triangle into two 30°− 60 °− 90 °triangles,

the other sides have lengths shown. The base of the

triangle is and the height is 3, so the area is

(Chapter 10, Lesson 3: The Pythagorean Theorem)

15.D The sum of the parts is 4 + 3 + 2 + 1 =10.

Therefore, the parts are of the

whole. The largest share, then, is ($50,000)(4/10) =

$20,000.

(Chapter 7, Lesson 4: Ratios and Proportions)

16.C Use the definition to translate the equation:

m{n} = 9

Translate: m^2 /n^2 = 9

Now think about what values of mand nwill

work. Notice that 3 and 1 will work, but so will − 3

and −1. Now plug these into the statements, and see

if any are false. Since −3 is not greater than −1,

statement I can be eliminated, and so can answers

(B), (D), and (E). Notice that this means you don’t

have to check statement II, because it’s in both

remaining answers. Statement III must be true

because if , then must equal 3 or –3.

Therefore, equals 1 or –1, so it is an integer.

(Chapter 6, Lesson 7: Thinking Logically and Checking)

(Chapter 9, Lesson 1: New Symbol or Term Problems)

17.C Let’s say there are xblue marbles in the jar. This

means there are 3xwhite marbles, and 2(3x) = 6 xred

marbles, for a total of 10xmarbles. Since 3xare white,

the probability of picking a white is 3x/10x=3/10.

(Chapter 9, Lesson 6: Probability Problems)

m

3 n

m

n

m

n

2

2 =^9

4

10

32

,

10

,

10

,and

1

10

63 3

2

93.

( )( )

=

63()

Section 3

1.A The fact that they rarely agreedimplies that

their opinions would often differ.

diverge=differ or move apart; coincide=fit together

or occur simultaneously; retreat=move away; assem-

ble=put together; truncate=cut short

2.D The sentence implies a contrast between what

once wasand what is now.If it is no longer an incon-

trovertible(irrefutable) truth,it must now be in doubt.

enacted=put into effect officially; irrefutable=

impossible to disprove; universal=true at all places

and times; dubious=doubtful; conclusive=acting as

final proof

13.D Remember that the word “is” can be inter-
preted as the equals sign (=). Therefore, “The number
of dogs is 3 fewer than 4 times the number of cats”
can be translated into d= 4c−3.
(Chapter 8, Lesson 7: Word Problems)

14.B Mark up the diagram with the information
given:

3 √ 3

30 °

P

6

R

6

30 °

S

60 ° 60 °

3

3 √ 3