Number Play: Final Assessment | Homework Practice

Section A: Concepts

Question 1mcq

Use the digit-sum test. Is

372

divisible by

3

?

A.Cannot be decided from digits

B.Divisible by

3

C.Divisible by

5

only

D.Always divisible by

9

Question 2mcq

Use the digit-sum test. Is

845

divisible by

3

?

A.Cannot be decided from digits

B.Divisible by

5

only

C.Not divisible by

3

D.Always divisible by

9

Question 3mcq

What is the greatest proper factor of

72

?

A.

1

B.

72

C.

24

D.

36

Question 4mcq

What is the difference between the two-digit number

59

and the number formed by reversing its digits?

A.

45

B.

36

C.

4

D.

4

Question 5mcq

What is the difference between the two-digit number

37

and the number formed by reversing its digits?

A.

4

B.

4

C.

45

D.

36

Question 6mcq

Choose any two-digit number and subtract the sum of its digits from it. What is always true of the result?

A.It is always a multiple of

5

.

B.It is always prime.

C.It is always odd.

D.It is always a multiple of

9

.

Question 7mcq

A three-digit number is

100a+10b+c

. The reversed number is

100c+10b+a

. What is the difference original minus reversed?

A.

9(a-c)

B.

99(b-c)

C.

90(a-c)

D.

99(a-c)

Question 8mcq

Which approach is best for proving a number-game pattern?

A.Check one example and stop.

B.Use only mental guessing.

C.Ignore the digits and choose a formula randomly.

D.Test small cases, find a pattern, then express it using variables.

Section B: Skills

Question 9mcq

Use the digit-sum test. Is

845

divisible by

3

?

A.Not divisible by

3

B.Divisible by

5

only

C.Always divisible by

9

D.Cannot be decided from digits

Question 10mcq

Use the digit-sum test. Is

1116

divisible by

3

?

A.Divisible by

3

B.Cannot be decided from digits

C.Divisible by

5

only

D.Always divisible by

9

Question 11mcq

What is the greatest proper factor of

84

?

A.

28

B.

84

C.

1

D.

42

Question 12mcq

What is the difference between the two-digit number

37

and the number formed by reversing its digits?

A.

45

B.

4

C.

36

D.

4

Question 13mcq

What is the difference between the two-digit number

46

and the number formed by reversing its digits?

A.

2

B.

27

C.

2

D.

18

Question 14mcq

Choose any two-digit number and subtract the sum of its digits from it. What is always true of the result?

A.It is always prime.

B.It is always a multiple of

9

.

C.It is always odd.

D.It is always a multiple of

5

.

Question 15mcq

A three-digit number is

100a+10b+c

. The reversed number is

100c+10b+a

. What is the difference original minus reversed?

A.

90(a-c)

B.

99(b-c)

C.

9(a-c)

D.

99(a-c)

Question 16mcq

Which approach is best for proving a number-game pattern?

A.Ignore the digits and choose a formula randomly.

B.Use only mental guessing.

C.Check one example and stop.

D.Test small cases, find a pattern, then express it using variables.

Section C: Applications

Question 17mcq

Use the digit-sum test. Is

1116

divisible by

3

?

A.Divisible by

5

only

B.Always divisible by

9

C.Divisible by

3

D.Cannot be decided from digits

Question 18mcq

Use the digit-sum test. Is

2505

divisible by

3

?

A.Divisible by

5

only

B.Divisible by

3

C.Always divisible by

9

D.Cannot be decided from digits

Question 19mcq

What is the greatest proper factor of

48

?

A.

1

B.

48

C.

16

D.

24

Question 20mcq

What is the difference between the two-digit number

46

and the number formed by reversing its digits?

A.

27

B.

2

C.

2

D.

18

Question 21mcq

What is the difference between the two-digit number

28

and the number formed by reversing its digits?

A.

54

B.

6

C.

6

D.

63

Question 22mcq

Choose any two-digit number and subtract the sum of its digits from it. What is always true of the result?

A.It is always odd.

B.It is always a multiple of

9

.

C.It is always prime.

D.It is always a multiple of

5

.

Question 23mcq

A three-digit number is

100a+10b+c

. The reversed number is

100c+10b+a

. What is the difference original minus reversed?

A.

99(b-c)

B.

9(a-c)

C.

99(a-c)

D.

90(a-c)

Question 24mcq

Which approach is best for proving a number-game pattern?

A.Check one example and stop.

B.Use only mental guessing.

C.Ignore the digits and choose a formula randomly.

D.Test small cases, find a pattern, then express it using variables.

Section D: Reasoning

Question 25mcq

Use the digit-sum test. Is

2505

divisible by

3

?

A.Divisible by

3

B.Divisible by

5

only

C.Always divisible by

9

D.Cannot be decided from digits

Question 26mcq

Use the digit-sum test. Is

372

divisible by

3

?

A.Divisible by

5

only

B.Always divisible by

9

C.Divisible by

3

D.Cannot be decided from digits

Question 27mcq

What is the greatest proper factor of

60

?

A.

30

B.

20

C.

1

D.

60

Question 28mcq

What is the difference between the two-digit number

28

and the number formed by reversing its digits?

A.

54

B.

63

C.

6

D.

6

Question 29mcq

What is the difference between the two-digit number

59

and the number formed by reversing its digits?

A.

45

B.

4

C.

36

D.

4

Question 30mcq

Choose any two-digit number and subtract the sum of its digits from it. What is always true of the result?

A.It is always prime.

B.It is always a multiple of

9

.

C.It is always a multiple of

5

.

D.It is always odd.

Question 31mcq

A three-digit number is

100a+10b+c

. The reversed number is

100c+10b+a

. What is the difference original minus reversed?

A.

99(b-c)

B.

9(a-c)

C.

90(a-c)

D.

99(a-c)

Question 32mcq

Which approach is best for proving a number-game pattern?

A.Ignore the digits and choose a formula randomly.

B.Check one example and stop.

C.Test small cases, find a pattern, then express it using variables.

D.Use only mental guessing.