Number Play: Practice 4 | Homework Practice

Section A: Core Practice

Question 1mcq

A three-digit number is

100a+10b+c

. The reversed number is

100c+10b+a

. What is the difference original minus reversed?

A.

99(a-c)

B.

99(b-c)

C.

9(a-c)

D.

90(a-c)

Question 2mcq

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

A.Ignore the digits and choose a formula randomly.

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

C.Use only mental guessing.

D.Check one example and stop.

Question 3mcq

Use the digit-sum test. Is

1116

divisible by

3

?

A.Divisible by

3

B.Cannot be decided from digits

C.Always divisible by

9

D.Divisible by

5

only

Question 4mcq

Use the digit-sum test. Is

2505

divisible by

3

?

A.Divisible by

5

only

B.Always divisible by

9

C.Cannot be decided from digits

D.Divisible by

3

Question 5mcq

What is the greatest proper factor of

48

?

A.

1

B.

48

C.

16

D.

24

Question 6mcq

What is the difference between the two-digit number

46

and the number formed by reversing its digits?

A.

2

B.

18

C.

27

D.

2

Section B: Reasoning and Application

Question 7mcq

What is the difference between the two-digit number

28

and the number formed by reversing its digits?

A.

6

B.

6

C.

63

D.

54

Question 8mcq

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

9

.

B.It is always odd.

C.It is always a multiple of

5

.

D.It is always prime.

Question 9mcq

A three-digit number is

100a+10b+c

. The reversed number is

100c+10b+a

. What is the difference original minus reversed?

A.

99(a-c)

B.

90(a-c)

C.

99(b-c)

D.

9(a-c)

Question 10mcq

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

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

B.Use only mental guessing.

C.Ignore the digits and choose a formula randomly.

D.Check one example and stop.

Question 11mcq

Use the digit-sum test. Is

1116

divisible by

3

?

A.Always divisible by

9

B.Divisible by

3

C.Divisible by

5

only

D.Cannot be decided from digits

Question 12mcq

Use the digit-sum test. Is

2505

divisible by

3

?

A.Cannot be decided from digits

B.Always divisible by

9

C.Divisible by

3

D.Divisible by

5

only