S.A.T. Math Testing Tactics

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

Replace Variables with Numbers

If a is equal to b multiplied by c, which of the following is equal to b divided by c?

A) B) C) D) E)

Example 6.1

a

bcab

ca

c 2

a

c2

a

bc

Replace variables with numbersA = B x C6 = 3 x 2

A=6B =3C =2

Solve ProblemB÷C3÷21.5

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)

B)

C)

D)

E)

Example 6.2

12

4

s

6

4

s

6

4

s

12

4

s

16

4

s

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?

A) B) C) D) E)

Example 6.3

cx

s

xs

cs

cxx

cscsx

Replace Variables with Numbers c= 4 cans each week for each student s = 10 students in school x = 80 cans of soup

Answer Question:4 x 10 = 40 cans each week

80 cans will last 2 weeks

Evaluate Answers:

A) (4 x 80) /10 =32

B) (80 x 10)/4 = 200

C) 10/(4x80) = .03125

D) 80/(4 x 10) = 2

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!

In Conclusion

S.A.T. Math Testing Tactics

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

Choose an Appropriate Number

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?

Example 7.1

Notice the two fractions: 3/5 and 1/4What is the LCD?

20

20 students at Central HS

3(20) 125

12 take Spanish, 8 left

1(8) 24

6 300

201000x

x students

2 take Italian, 6 left6 take French

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 C) ¼ D) 2/5 E) 5/12

Example 7.2

LCD: 2/3 , 3/8 , 3/5120

Start with 120 members

2/3 (120) = 80 men 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?

Example 7.3

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.

In Conclusion