Sat math Essentials

9.
a.
When a base is raised to a fractional exponent,
raise the base to the power given by the numer-
ator and take the root given by the denominator.
Raise the base,
a
, to the 
b
th power, since 
b
is the
numerator of the exponent. Then, take the 
c
th
rooth of that:
c
a
b
.
10.
e.
No penguins live at the North Pole, so anything
that lives at the North Pole must not be a pen-
guin. If Flipper lives at the North Pole, then he,
like all things at the North Pole, is not a penguin.
11.
e.
If
p
< 0 and 
q
> 0, then 
p
< 
q
. Since 
p
< 
q
,
p
plus
any value will be less than 
q
plus that same value
(whether positive or negative). Therefore,
p
+
r
< 
r
+ 
q
.
12.
d.
22% of the movies rented were action movies;
250(0.22) = 55 movies; 12% of the movies
rented were horror movies; 250(0.12) = 30
movies. There were 55 – 30 = 25 more action
movies rented than horror movies.
13.
b.
The circumference of a circle is equal to 2
π
r
,
where 
r
is the radius of the circle. If the circum-
ference of the circle = 20
π
units, then the radius
of the circle is equal to ten units. The base of tri-
angle 
ABC
is the diameter of the circle, which is
twice the radius. The base of the triangle is 20
units and the height of the triangle is eight units.
The area of a triangle is equal to 
1
2
bh
, where 
b
is
the base of the triangle and 
h
is the height of the
triangle. The area of triangle 
ABC
= 
1
2
(8)(20) =
1
2
(160) = 80 square units.