# NUMBER THEORY AND THE REAL NUMBERS

5. The dimensions of a rectangular court are measured to
be 83.6 by

50.5 feet. What is the area of this court?

a. 4200 sq ft

b. 4222 sq ft

c. 4221.8 sq ft

d. 4220 sq ft

e. 4221.80 sq ft

6 . The circumference of a ball is measured as 11.5 in.
What is the

diameter of this ball? (Use π ≈ 3.14.)

a. 3.662 in.

b. 3.7 in.

c. 3.66 in.

d. 3.6624 in.

e. None of these

7 . Written as a decimal, 5.75% is

a. 0.575

b. 0.00575

c. 0.0575

d. 5.75

e. None of these

8 . Written as a percent, correct to one decimal place ,5/9 is

a. 0.6%

b. 5.6%

c. 56%

d. 55.6%

e. None of these

9 . A 2-liter bottle of soda sells for 69 cents and costs
the store 49 cents.

Find the percent of profit, correct to two decimal places.

a. 28%

b. 40.82%

c. 28.99%

d. 40.80%

e. None of these

1 0 . 50 of the employees of Company A make between
$25,000 and

$50,000 annually. If this represents 20% of all the employees, how

many employees does Company A have?

a. 200

b. 250

c. 500

d. 400

e. None of these

1 1 . In simplified form ,

1 2 . In simplified form,

1 3 . In simplified form,

14.

15. Which one of the following is an arithmetic sequence ?

a. 2, 3, 5, 8, . . .

b. 4, 8, 16, 32, . . .

c. 2, 5, 8, 11, . . .

d. 1, 0, 1, 0, . . .

e. 0, 2, 3, 7, . . .

1 6 . The sum of the first ten terms of the sequence 2, 5, 8, 11, . . . is

a. 185

b. 155

c. 220

d. 370

e. None of these

17. For the sequence
which of the following is

correct? (Note: S6 means the sum of the first six terms .)

1 8 . The repeating decimal 1.888 . . . =

1 9 . The underlined word in the sentence "This is the fifth test." is used as:

a. a cardinal number

b . an ordinal number

c. identification

d . a natural number

e. None of these

20. What addition properties of the system of natural
numbers are used

in the equation : 7 + 6 + 3 = 7 + 3 + 6 = (7 + 3) + 6 ?

a . Associativity only

b . Commutativity only

c. The distributive property only

d . The associative and the distributive properties only

e . Commutativity and associativity only

2 1 . Written as a product of primes , 286 =

a. 2•143

b . 2•11•1 3

c. 1•2•11•1 3

d. 22•1 3

e . None of these

2 2 . All the prime numbers between 50 and 60 are:

a . 51, 53 and 57

b. 53 and 59

c. 51, 57 and 59

d . 53 and 57

e. None of these

2 3 . The number 123 is:

a . a prime number

b . a composite number

c. an even number

d . neither prime nor composite

e . None of these

2 4 . The number 45 is divisible by :

a . 5 only

b . 1, 3, and 5 only

c. 1, 3 and 15 only

d . 1, 3, 5, 9, and 15 only

e . 1, 3, 5, 9, 15 and 45 only

2 5 . The GCF of 135 and 225 is

a. 3

b. 5

c. 15

d. 4 5

e . 9

2 6 . When written in simplest reduced form

2 7 . The LCM of 12, 24 and 30 is

a. 2

b. 3

c. 6

d . 3 0

e . 1 2 0

2 8 . When written in simplest reduced form ,

2 9 . A pattern for a wedding outfit calls for
yards of lace trim for t h e

dress and 6 yards of lace trim for the veil.
How many yards of lace

trim does the pattern call for?

3 0 . -4 - (-12) =

a . 6

b . -16

c. 8

d . - 8

e . None of these

31. 48 ÷ 8 × 3 + 19 =

a . 1 2 6

b . 2 1

c. 3 7

d . 1.12

e . None of these

3 2 . The reciprocal of is:

3 3 .

3 4 . Written as a decimal, 5/6 =

3 5 . Written as the quotient of two integers

3 6 . Written in standard decimal notation,

a . 3,860,000

b . 386 × 10,000

c. 386,000

d . 386 × 100,000

e . None of these

3 7 . In scientific notation,

3 8 . Which one of the following numbers is irrational?

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