Sat math Essentials

–
M AT H P R E T E S T
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2 4

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24.
8
3
1
2
Each term is equal to the previous term mul-
tiplied by 
3
2
. The fifth term in the sequence is
9
8
3
2
2
1
7
6
, and the sixth term is 
2
1
7
6
3
2
8
3
1
2
.
25.
–
1
4
The question is asking you to find the 
y
-inter-
cept of the equation 
2
x
3
–
y
3
4. Multiply both
sides by 3y and divide by 12:
y
1
6
x
– 
1
4
. The
graph of the equation crosses the 
y
-axis at
(0,–
1
4
).
26.
100
Set the measures of the angles equal to 1
x
, 3
x
,
and 5
x
. The sum of the angle measures of a
triangle is equal to 180 degrees:
1
x
3
x
5
x
180
9
x
180
x
20
The angles of the triangle measure 20 degrees,
60 degrees, and 100 degrees.
27.
54
One face of the prism has a surface area of
nine square units and another face has a sur-
face area of 21 square units. These faces share
a common edge. Three is the only factor
common to 9 and 21 (other than one), which
means that one face measures three units by
three units and the other measures three units
by seven units. The face of the prism that is
identical to the face of the cube is in the shape
of a square, since every face of a cube is in the
shape of a square. The surface area of the
square face is equal to nine square units, so
surface area of one face of the cube is nine
square units. A cube has six faces, so the sur-
face area of the cube is 9 
6 
54 square
units.