352 MCGRAW-HILL’S SAT
SAT Practice 5: Counting Problems
- A pizzeria offers three different sizes of pizza,
two different kinds of crust, and eight different
choices for toppings. How many different one-
topping pizzas are there to choose from?
(A) 13 (B) 16 (C) 24
(D) 48 (E) 60
0, 2, 4, 6, 8
- How many different integers between 30 and
70 contain only digits from the list above?
(A) 7 (B) 10 (C) 15
(D) 20 (E) 25 - In how many ways can you arrange four different
paintings in a line on a wall?
(A) 12 (B) 24 (C) 36
(D) 48 (E) 64 - At Lincoln County High School, 36 students are
taking either calculus or physics or both, and 10
students are taking both calculus and physics.
If there are 31 students in the calculus class,
how many students are there in the physics
class?
(A) 5 (B) 8 (C) 11
(D) 15 (E) 21 - Dave’s stickball team has six players. How
many different six-player batting lineups can
they make if Dave must bat second and either
Zack or Paul must bat first?
(A) 48 (B) 96 (C) 192
(D) 256 (E) 720
6. Maria gave David xcards, gave Tina two more
cards than she gave David, and gave Samuel five
fewer cards than she gave Tina. In terms of x,
how many cards did Maria give Tina, David,
and Samuel all together?
(A) 3x+ 9 (B) 3x− 1
(C) 3x−3(D)x− 3
(E) x− 1
7. From a collection of six paintings, four are to be
chosen to hang on a wall. How many different
arrangements are possible if every painting is
different?
(A) 24 (B) 120 (C) 360
(D) 720 (E) 1,296
8. Every marble in a jar has either a dot, a stripe,
or both. The ratio of striped marbles to non-
striped marbles is 3:1, and the ratio of dotted
marbles to nondotted marbles is 2:3. If six mar-
bles have both a dot and a stripe, how many
marbles are there all together?
(A) 16 (B) 18 (C) 20
(D) 36 (E) 40
9. An ant must walk from one vertex of a cube to
the “opposite” vertex (that is, the vertex that is
farthest from the starting vertex) and back
again to its starting position.
It may only walk along the
edges of the cube. For the
entire trip, its path must tra-
verse exactly six edges, and
it maytravel on the same
edge twice. How many dif-
ferent six-edge paths can the
ant choose from?
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