Tactic 6: Replace Variables with Numbers


Many S.A.T. questions will ask you about a
generic situation using variables. Your
answer choices will not be numbers.
To make these problems easier:
◦ Replace each variable with an easy to use number
◦ Solve the problem using those numbers
◦ Evaluate each of the 5 choices to see which
expression is equivalent to your specific answer
If a is equal to b multiplied by c, which of the
following is equal to b divided by c?
a
A) bc
B)
ab
c
Replace variables with numbers
A=BxC
6=3x2
A=6
B =3
C =2
C)
a
c
D)
Solve Problem
B÷C
3÷2
1.5
a
c2
E)
a
bc 2
Test Answer Choices
A) 6/(3x2) = 1
B) (6x3)/2 = 9
C) 6/2 = 3
D) 6/22 = 1.5
E) 6/(3x22) = 0.5
If the sum of four consecutive odd integers is s, then,
in terms of s, what is the greatest of these integers?
A)
s  12
4
B) s  6
4
C) s  6
4
D)
E)
s  12
4
s  16
4
Replace Variables with Numbers:
1 + 3+ 5 + 7 = 16 = S
Largest = 7
Evaluate Answer Choices:
A) (16-12)/4 = 1
B) (16-6)/4 = 2.5
C) (16+6)/4 = 5.5
D) (16+12)/4 = 7
If a school cafeteria needs c cans of soup each week
for each student and there are exactly s students in
the school, for how many weeks will x cans of soup
last?
xs
s
cx
x
A)
B) c
C) cx
D)
E) csx
s
cs

Replace Variables with Numbers
c= 4 cans each week for each student
s = 10 students in school
x = 80 cans of soup
Evaluate Answers:
A) (4 x 80) /10 =32
B) (80 x 10)/4 = 200
Answer Question:
4 x 10 = 40 cans each week
C) 10/(4x80) = .03125
80 cans will last
D) 80/(4 x 10) = 2
2 weeks
E) 4x10x80 = 3200
There is no reason to
deal with an
abstract problem.
Instead, make up
your own numbers
and find the
solution that works!
Replace Variables
with Numbers!
Tactic 7: Choose an Appropriate Number

Tactic 7 and Tactic 6 are very similar.
In Tactic 6, we chose easy-to-substitute numbers to
replace our variables.
In Tactic 7, we are going to choose a nice, friendly
number as a starting value.

In general:
Problems dealing with fractions– choose the Least
Common Denominator
Problems dealing with percents – choose 100 or 1000

At Central High School each student studies exactly
one foreign language. Three-fifths of the students
take Spanish and one-fourth of the remaining
students take Italian. If 300 students take French,
how many students are enrolled at Central High?
Notice the two fractions: 3/5 and 1/4
What is the LCD?
20
20 students at Central HS
3
(20)  12
5
12 take Spanish, 8 left
1
(8)  2
4
2 take Italian, 6 left
6 take French
6 300

20
x
x  1000 students
On a certain Russian-American committee, 2/3 of the
members are men, and 3/8 of the men are Americans. If
3/5 of the committee members are Russians, what fraction
of the members are American women?
A) 3/20
B) 11/60
LCD: 2/3 , 3/8 , 3/5
120
Start with 120 members
C) ¼
D) 2/5
2/3 (120) = 80 men
E) 5/12
so
40 women
3/8 (80) = 30 USA men so 50 Russ men
3/5 (120) = 72 Russians so 48 USA
48 USA – 30 USA men = 18 USA women
18/120 = .15
At Books, Books, Books, Inc., 40% of all books purchased are
paperback. Of the paperbacks, 35% are mysteries. Of the
non-mystery paperbacks, 25% are romance novels. What
percent of all books purchased are either paperback
mysteries or romance novels?
Since we are taking a percent of a percentage, let’s start with 1000 books.
.40 (1000) = 400 paperbacks
.35 (400) = 140 mysteries,
260 other paperbacks
.25 (260) = 65 romance
140 + 65 = 205
205/1000 = .205
20.5%


When dealing with
fractions, choose
the LCD as your
starting population.
When dealing with
percents, choose a
multiple of 100 to
be your starting
population.