Whole Numbers Test

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Whole Numbers Test - 12

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Weekly Quiz Competition

Question 1
1 / -0

The number 289 can be represented by a 17 × 17 square grid. Which of the following can also be represented on a square grid?

A
77

B
99

C
361

D
440

Solution

From the given options we notice that:

77 = 7 x 11.

99 = 9 x 11.

Also,

440 cannot be a square number because there is only one zero at the end.

Hence we are left with 361.

Now if we notice:
there is a 1 at the the end:

Hence:

9 x 9 = 81.

or 19 x 19 = 361.

Hence 361 can be represented on a square grid.
Question 2
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Directions: Study the given statement carefully and choose the correct option.

If two numbers perform an operation and that operation produces different set of numbers, then operation is not closed under

A
Closure property

B
Fixed property

C
Associate property

D
None of these

Solution

Closure property is the process for a closed set. When two numbers perform an operation and that operation produces different set of numbers, then its operation is not closed under closure property.
According to closure property, the positive integers are closed under addition and multiplication, but not under subtraction.

For example:
1 + 2 = 3, which is a positive integer.
1 - 2 = -1; which is not a positive integer, even though both 1 and 2 are positive integers.
Question 3
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The addition of (-144) and (-54) is closed. It is an example of which of the following properties?

A
Associative

B
Distributive

C
Closure

D
Commutative

Solution

(-144) and (-54) are both negative integers. We take the sum of their numerical values and put the negative sign.

144
+ 54
198

(-144) + (-54) = -(144 + 54) = -198
-198 is a negative integer.
Closure property of integers under addition is true.
Question 4
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Which of the following options will replace the question mark?

Place value of 7 in 5,87,154. 91 (?) Place value of 7 in 7,219.54.

A
>

B
<

C
=

D
None of these

Solution

Place value of 7 in 5,87,154. 91 = 7,000
Place value of 7 in 7,219.54 = 7,000
So, (?) is replaced by (=) because 7,000 = 7,000
Question 5
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Multiplicative identity means________ to any number and it keeps its identity same.

A
multiply 1

B
divide 1

C
add 1

D
subtract 1

Solution

Multiplicative identity means that you can multiply 1 to any number and it keeps its identity the same and the number stays the same.

25 x 1 = 25
Question 6
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Which of the following statements is false?

A
The predecessor of a whole number is one less than the given number.

B
The whole number 0 does not have any predecessor.

C
The successor of a whole number is the number obtained by adding 2 to it.

D
None of these

Solution

1. The predecessor of a whole number is one less than the given number. (Correct)
2. The whole number 0 does not have any predecessor. (Correct)
3. The successor of a whole number is the number obtained by adding 2 to it. (Incorrect - The successor of a whole number is the number obtained by adding 1 to it is the right statement.)
Question 7
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The predecessor of 99,999 is

A
9,999

B
99,997

C
99,998

D
1,00,000

Solution

Predecessor means before number (99,999 - 1) = 99,998
Question 8
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If number 'z' is a factor of a number 'y', then 'y' divided by 'z' gives the remainder

A
0

B
1

C
2

D
3

Solution

Factors are the numbers that we can multiply together to get another number.

Example: 2 and 3 are factors of 6, because 2 × 3 = 6.
In this example, take 2 or 3 equal to 'z' and 6 equal to 'y'.

Now, 'y' divided by 'z' means 6 divided by 2 or 3.
When 6 is divided by 2 or 3, then 6 will be completely divisible by 2 or 3 and the remainder will be zero.

Therefore, when a number 'z' is a factor of a number 'y', then 'y' divided by 'z' gives the remainder 'zero'.
Question 9
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How many whole numbers are there between 127 and 159?

A
30

B
31

C
32

D
33

Solution

All the natural numbers along with zero are called whole numbers.
When we count to the right of 127 up to 159 on the number line, we find that there are 31 whole numbers between 127 and 159 (we do not include 127 and 159).
Therefore, 31 is the correct answer.
Question 10
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Which of the following sets of numbers will make the number sentence true?

_____ - ______ + _____ = 23

A
13, 7, 29

B
5, 13, 19

C
29, 13, 7

D
37, 15, 18

Solution

(1) 13 - 7 + 29 = 35
(2) 5 - 13 + 19 = 11
(3) 29 - 13 + 7 = 23 (Correct)
(4) 37 - 15 + 18 = 40
Question 11
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Which of the following is false?

A
(19 × 7) + 13 = (17 × 9) - 7

B
(78 ÷ 2) + 27 = (96 ÷ 3) + 34

C
(55 × 3) ÷ 5 = (15 × 7) - 55

D
None of these

Solution

Option 1:
L.H.S
= (19 × 7) + 13
= 133 + 13 = 146
R.H.S
= (17 × 9) - 7
= 153 - 7 = 146
L.H.S = R.H.S (True)

Option 2:
L.H.S
= (78 ÷ 2) + 27
= 39 + 27 = 66
R.H.S
= (96 ÷ 3) + 34
= 32 + 34 = 66
L.H.S = R.H.S (True)

Option (3) is false.
L.H.S
= (55 × 3) ÷ 5
= 165 ÷ 5 = 33
R.H.S
= (15 × 7) - 55
= 105 - 55 = 50
L.H.S is not equal to R.H.S (False)

Hence, option 3 is false statement.
Question 12
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What does the given number line represent?

A
3 × 2

B
4 × 5

C
18 ÷ 3

D
6 ÷ 3

Solution

In the given number line, we start from 0 and jump 3 units to the right. Then, we make another such jump from 3 to reach 6.
It means that we make two jumps, covering 3 units in each of them towards the right.
It can be represented as:
(3 units) × 2 = 6 units.
Therefore, 3 × 2 = 6 is the correct answer.
Question 13
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The commutative law does not apply to

A
addition

B
subtraction and division

C
multiplication

D
addition and multiplication

Solution

Commutative Law state that one can apply an operation on two numbers in any order. For example: we can add and multiply any 2 whole numbers in any order. i.e.
3 + 4 = 4 + 3
3 × 4 = 4 × 3.

But in case of subtraction and division it is not possible. For example:
6 - 3 = 3
3 - 6 = -3 which is not a whole number
Similarly,
6 ÷ 3 = 2
3 ÷ 6 = 1/2 = 0.5.
Therefore, the commutative law does not apply to subtraction and division.
Question 14
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Zero is

A
a natural number

B
a whole number

C
the successor of 1

D
a negative integer

Solution

Zero is not a natural number. It is the predecessor of 1 and considered a whole number.
Question 15
1 / -0

The multiplicative identity of 56 is

A
0

B
1

C
-1

D
None of these

Solution

Multiplicative identity means that you can multiply 1 to any number and it keeps its identity the same and the number stays the same.
To write out this property using variables, we can say that n × 1 = n. It does not matter if n equals one, one million or 3.566879. The property always hold true.
Therefore, 56 × 1 = 56.
Hence, option 2 is true.
Question 16
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Garvin prepares 10 boxes of fruits, each containing 20 apples, 30 mangoes and 50 strawberries. Using which of the following properties can you calculate the total number of fruits in 10 boxes?

A
Distributive property

B
Associative property

C
Commutative property

D
None of these

Solution

Number of apples in each box = 20
Number of apples in 10 boxes = 10 x 20

Number of mangoes in each box = 30
Number of mangoes in 10 boxes = 10 x 30

Number of strawberries in each box = 50
Number of strawberries in 10 boxes = 10 x 50

Now, Garvin prepares 10 boxes containing these fruits.
So, total number of fruits in all 10 boxes = 10 x 20 + 10 x 30 + 10 x 50

By distributive property: 10 x (20 + 30 + 50) fruits
= 10 x 100 = 1000 fruits

Hence, distributive property is the correct answer.
Question 17
1 / -0

Which of the following statements is false?

A
1 + 1 = 2

B
1 x 1 = 1

C
1 ÷ 1 = 0

D
1 - 1 = 0

Solution

1 ÷ 1 = 0 is false because when we divide any number by 1, it remains the same.
(1 ÷ 1 = 1)
Question 18
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In closure property of subtraction, the difference between any two whole numbers will not always be a ________ number.

A
whole

B
real

C
same

D
decimal

Solution

In closure property of subtraction, the difference between any two whole numbers will not always be a whole number.
Example:
7 - 15 = -8
In the above example, 7 as well as 15 are whole numbers, but -8 is not a whole number.
Therefore, in closure property, whole numbers are closed under addition and also under multiplication.
Question 19
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By using dot pattern, which of the following numbers can be used to make a line, a triangle and a rectangle?

A
5

B
6

C
7

D
9

Solution

The number 6 can be shown as a line given above.
The number 6 can also be shown as a triangle given above.
The number 6 can also be shown as a rectangle in (2 × 3) or (3 × 2) grid given above.

Option 1: 5 can be used to make line but cannot be used to make rectangle and triangle.
Option 3: 7 can be used to make line but cannot be used to make rectangle and triangle.
Option 4: 9 can be used to make line and square but cannot be used to make rectangle and triangle.
Question 20
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Which of the following equations represents the associative property?

A
a + (b + c) = (a + b) + c

B
a + b = b - a

C
a(b + c) = ab + abc

D
None of these

Solution

Associative property states that you can add or multiply, regardless of how the numbers are grouped.
a + (b + c) = (a + b) + c represents the associative property.
So, a + (b + c) = (a + b) + c is the correct answer.
Question 21
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A contractor hires 23 workers in the morning to do a work and 12 workers in the evening to do the work. If he pays Rs. 300 to each worker for his shift, then how much money does the contractor spend on workers each day?

A
Rs. 10,000

B
Rs. 10,500

C
Rs. 10,612

D
Rs. 10,950

Solution

Number of workers in the morning = 23
Number of workers in the evening = 12
Total number of workers in one day = 23 + 12 = 35
Money he pays to one worker = Rs. 300
Money he will pay in total = 300 x 35 = Rs. 10,500
or,
300 x (23 + 12) = 300 x 35 = Rs. 10,500
Question 22
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Amit has 12 chocolate candies, 28 lemon candies and 15 orange candies with him. Rohit has 18 chocolate candies, 23 lemon candies and 20 orange candies with him. How many candies do they have in total?

A
116

B
118

C
120

D
122

Solution

Number of candies Amit has in total = 12 + 28 + 15 = 55
Number of candies Rohit has in total = 18 + 23 + 20 = 61
Total candies they have = 61 + 55 = 116
Question 23
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One car is able to transport 85 boxes. How many cars would be needed to transport 1,020 boxes?

A
10

B
11

C
12

D
13

Solution

85 boxes are transported in 1 car.

1 box is transported incar.
1,020 boxes can be transported incars.
= 12 cars
Question 24
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In a box, there are 123 black beads. A person takes out 8 black beads and replaces them by 16 white beads. He kept repeating the pattern, till there are only white beads left in the box. How many white beads are present in the box in the end?

A
246

B
250

C
252

D
260

Solution

Number of black beads = 123
8 black beads are replaced by 16 white beads.
1 black bead is replaced by 16 ÷ 8 = 2 white beads.
So, for every 1 black bead, 2 white beads are put in the bag.
123 black beads would be replaced by 123 x 2 = 246 white beads.
Question 25
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One year's savings of Mohak is Rs. 23,512. He invested Rs. 10,562 in a policy. He gave Rs. 5,254 to charity and Rs. 5,500 to his wife. How much money is left with him?

A
Rs. 1,900

B
Rs. 2,011

C
Rs. 2,196

D
Rs. 2,250

Solution

Total savings = Rs. 23,512
Money invested in policy = Rs. 10,562
Money given to charity = Rs. 5,254
Money given to wife = Rs. 5,500
Money left with him
= 23,512 - (10,562 + 5,254 + 5,500)
= 23,512 - 21,316
= Rs. 2,196

Question 26

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Directions: Match the following.

Column - I	Column - II
(i) a × b = 0	(a) Multiplication by inverse of itself
(ii) a × b = a	(b) Multiplication by 0
(iii) a × b = 1	(c) Multiplication by 1

(i) (ii) (iii)

(b) (c) (a)

(i) (ii) (iii)

(a) (c) (b)

(i) (ii) (iii)

(c) (b) (a)

(i) (ii) (iii)

(a) (b) (c)

Solution

When we multiply a number by 0, we always get 0 as the answer.For example: 2 × 0 = 0
When we multiply a number by 1, we always get answer as the number itself.For example: 2 × 1 = 2
When we multiply a number by inverse of itself, we always get 1 as the answer.
For example:

Question 27
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Directions: State T for true and F for false.

(i) Multiplication can be done in any order.
(ii) Addition and subtraction can be done in any order.
(iii) Sum of two whole numbers is always a whole number.

A

(i) (ii) (iii)

T F T

B

(i) (ii) (iii)

F F T

C

(i) (ii) (iii)

T T T

D

(i) (ii) (iii)

T F F

Solution

Multiplication can be done in any order. It is called commutative property.
For example: 2 × 3 = 3 × 2 = 6 (True)

Addition can be done in any order, but subtraction cannot be done in any order.
For example: 2 + 3 = 3 + 2 = 5
But in case of subtraction we have,
3 - 2 = 1
2 - 3 = -1
Therefore, the result is not equal always. (False)

Sum of two whole numbers would always be a whole number.
2 + 3 = 5, which is a whole number (True)
Question 28
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Directions: Study the following statements.

Statement I. if 'a' is a whole number, then 3a will always be an odd number.
Statement II. If 'a' is a whole number, then 2a will always be an even number.

Which of the following options hold?

A
Both statements I and II are true

B
Statement I is true, but statement II is false

C
Statement I is false, but statement II is true

D
Both statements I and II are false

Solution

According to statement I, if 'a' is a whole number, then 3a is always an odd number, which is not true.
If a = 2, then 3a = 3 × 2 = 6, which is even. Hence, statement I is false.

According to statement II, if 'a' is a whole number, then 2a is an even number, which is always true.
Let a = 9, then 2a = 9 × 2 = 18, which is even. hence, statement II is true.

Therefore, option 3 is correct.

Question 29

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Directions: Match the following.

Column - I	Column - II
(i) When 8 is divided by 2 two times	(a) 0
(ii) Greatest even number between 1 and 11	(b) 2
(iii) Whole number which has no predecessor, is	(c) 10

(i) (ii) (iii)

(b) (a) (c)

(i) (ii) (iii)

(b) (c) (a)

(i) (ii) (iii)

(a) (b) (c)

(i) (ii) (iii)

(a) (c) (b)

Solution

(i) When 8 is divided by 2 two times, the answer is 2.
8 ÷ 2 = 4, 4 ÷ 2 = 2
(ii) Even numbers between 1 and 11 are 2, 4, 6, 8 and 10. Greatest one is 10.
(iii) Zero is the smallest whole number which has no predecessor.

Question 30
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Directions: Fill in the blanks.

(i) ____ x 23 = 23 x 12
(ii) _______ is an identity of multiplication.
(iii) If ______ is added to a number, the sum will remain the same.
(iv) Division by __________ is not defined.

A

(i) (ii) (iii) (iv)

12 1 0 0

B

(i) (ii) (iii) (iv)

12 0 1 0

C

(i) (ii) (iii) (iv)

10 1 0 0

D

(i) (ii) (iii) (iv)

12 1 0 1

Solution

(i) 12 x 23 = 23 x 12
(ii) 1 is an identity of multiplication.
(iii) If 0 is added to a number, then the sum will remain the same.
(iv) Division by 0 is not defined.

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Whole Numbers Test - 12

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Whole Numbers Test - 12

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Question 1

77

99

361

440

Solution

Question 2

Closure property

Fixed property

Associate property

None of these

Solution

Question 3

Associative

Distributive

Closure

Commutative

Solution

Question 4

>

<

=

None of these

Solution

Question 5

multiply 1

divide 1

add 1

subtract 1

Solution

Question 6

The predecessor of a whole number is one less than the given number.

The whole number 0 does not have any predecessor.

The successor of a whole number is the number obtained by adding 2 to it.

None of these

Solution

Question 7

9,999

99,997

99,998

1,00,000

Solution

Question 8

0

1

2

3

Solution

Question 9

30

31

32

33

Solution

Question 10

13, 7, 29

5, 13, 19

29, 13, 7

37, 15, 18

Solution

Question 11

(19 × 7) + 13 = (17 × 9) - 7

(78 ÷ 2) + 27 = (96 ÷ 3) + 34

(55 × 3) ÷ 5 = (15 × 7) - 55

None of these

Solution

Question 12

3 × 2

4 × 5

18 ÷ 3

6 ÷ 3

Solution