Sat math Essentials

14.
c.
The surface area of a cube is equal to 6
e
2
, where
e
is the length of one edge of the cube; 6
e
2
= 384
cm,
e
2
= 64,
e
= 8 cm. The volume of a cube is
equal to 
e
3
; (8 cm)
3
= 512 cm
3
.
15.
b.
There are 180 degrees in a line: (
x
+ (supplement
of angle 
x
)) + (
y
+ (supplement of angle 
y
)) +
(
z
+ (supplement of angle 
z
)) = 540. The supple-
ment of angle 
x
, the supplement of angle 
y
, and
the supplement of angle 
z
are the interior angles
of a triangle. There are 180 degrees in a triangle,
so those supplements sum to 180. Therefore,
x
+
y
+ 
z
+ 180 = 540, and 
x
+ 
y
+ 
z
= 360.
16.
e.
The measure of an angle in the exterior of a cir-
cle formed by a tangent and a secant is equal to
half the difference of the intercepted arcs. The
two intercepted arcs are AB, which is 60°, and
AC, which is 110°. Find half of the difference of
the two arcs;
1
2
(110 – 60) = 
1
2
(50) = 25°.
17.
d.
If Carlos buys ten balloons, he will pay
(10)($0.90) = $9. In order to total 2,000 bal-
loons, Carlos will have to make this purchase
2,
1
0
0
00
= 200 times. It will cost him a total of
(200)($9) = $1,800. If Carlos buys 1,000 bal-
loons, he will pay (1,000)($0.60) = $600. In
order to total 2,000 balloons, Carlos will have to
make this purchase 
2
1
,
,
0
0
0
0
0
0
= 2 times. It will cost
him a total of (2)($600) = $1,200. It will save
Carlos $1,800 – $1,200 = $600 to buy the bal-
loons 1,000 at a time.