Whole Numbers Test

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Whole Numbers Test - 11

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Question 1
1 / -0

Number 169 can be arranged in a 13 x 13 grid. In which of the following grids will 256 be arranged?

A
13 x 13

B
14 x 14

C
15 x 15

D
16 x 16

Solution

13 x 13 = 169
Similarly, 16 x 16 = 256
Hence, 256 can be arranged in a grid of 16 x 16.
Hence, option (4) is correct.
Question 2
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The property satisfied by division of whole numbers is

A
commutative property

B
closure property

C
additive identity

D
None of these

Solution

None of the properties given here is a property of division.

Commutative property is for addition and multiplication.
Closure property is addition and multiplication.
Additive is for addition and multiplication.
So, none of the given properties is satisfied by the division of numbers.

Hence, option (4) is correct.
Question 3
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26(23 - 24) = (26 × 23) - (26 × 24) is an example of ____ property.

A
commutative

B
associative

C
distributive

D
closure

Solution

The product of a whole number with the difference of the two other whole numbers is equal to the difference of the products of the whole number with other two whole numbers. This is called the distributive property of multiplication over subtraction. If a, b and c are any three whole numbers, then a(b - c) =

Hence, option (3) is correct.
Question 4
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What will replace the (?) in the following?

Place Value of 4 in 24,58,658 ? Place Value of 5 in 22,57,646

A
>

B
<

C
=

D
None of these

Solution

Place Value of 4 in 24,58,658 = 4,00,000
Place Value of 5 in 22,57,646 = 50,000
Hence, 4,00,000 > 50,000
Hence, option (1) is correct.
Question 5
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Which of the following statements is false?

A
1,00,001 is a successor of 1,00,000.

B
9,99,999 is a predecessor of 1,00,000.

C
0 is a whole number.

D
Every positive number is a whole number.

Solution

Predecessor is a number before the given number.
The number before 1,00,000 is 99,999.
So, statement (2) is not true.
Hence, option (2) is correct.
Question 6
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The successor of 1,00,000 is

A
99,999

B
99,998

C
1,00,001

D
9,99,999

Solution

A successor is a thing that succeeds another thing.
So, successor of 1,00,000 is 1,00,001.
1,00,000 + 1 = 1,00,001
Hence, option (3) is correct.
Question 7
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If p and q are whole numbers, then commutative law is true in division, if and only if

A
p = q

B
p > q

C
p < q

D
None of these

Solution

If p = q, then p ÷ q = p ÷ p = 1 and q ÷ p = q ÷ q = 1
Hence, option (1) is correct.
Question 8
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How many whole numbers are before 36?

A
0

B
35

C
36

D
Infinite

Solution

Whole numbers start from 0.
So, whole numbers before 36 will be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13................. 34, 35.
So, there are 36 whole numbers before 36.
Hence, option (3) is correct.
Question 9
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Which of the following numbers will make the number sentence true?

_____ + 2 + ____ = _____

A
(5, 7, 14)

B
(5, 2, 7)

C
(2, 7, 17)

D
(2, 5, 14)

Solution

5 + 2 + 7 = 14
5 + 2 + 2 = 9, which is not equal to 7.
2 + 2 + 7 = 11, which is not equal to 17.
2 + 2 + 5 = 9, which is not equal to 14.
Hence, option (1) is correct.
Question 10
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Which of the following is false?

A
16 ÷ 8 = 2

B
8 ÷ 0 = 0

C
25(7 - 8) = 25 x 7 - 25 x 8

D
5 - 2 is not equal to 2 - 5

Solution

Any number divided by 0 is always infinite.
So, 8 ÷ 0 = 0 is false.
Hence, option (2) is correct.
Question 11
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What does the given number line represent?

A
8 - 4

B
4 × 8

C
4 + 8

D
4 + 12

Solution

The number line represents 4 + 8 = 12
Hence, option (3) is correct.
Question 12
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Which of the following defines commutative law of addition?

A
Zero added to any number is the number itself

B
Addition can be done in any order

C
Odd number added to an odd number equals an even number

D
Addition is inverse of subtraction

Solution

As per commutative law of addition, you can change the position of numbers in an addition expression without changing the sum.
Hence, option (2) is correct. For example, if a and b are any two whole numbers then commutative law of addition gives -
a + b = b + a
Question 13
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Every whole number is the predecessor of a/an

A
natural number

B
integer

C
negative number

D
None of these

Solution

Every whole number is the predecessor of a natural number.
We know that whole numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, ....
Natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, .......
The successor of a whole number is the number obtained by adding 1 to it.
We can say that every whole number is the predecessor of a natural number.
Hence, option (1) is correct.
Question 14
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Sum of two even numbers will be

A
always odd

B
always even

C
sometimes even

D
sometimes odd

Solution

Sum of two even numbers will be always even.
For example: 2 + 4 = 6
10 + 16 = 26
Similarly, whenever we are going to add two even numbers, we will always get an even number as the answer.
So, option (2) is correct.
Question 15
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Sarah is preparing some gift boxes for her friends. Each box contains a teddy for Rs. 50, a chocolate for Rs. 20 and a pen for Rs. 30. She makes 8 of these boxes. Find the cost of these 8 boxes.

A
Rs. 800

B
Rs. 500

C
Rs. 100

D
None of these

Solution

Cost of 1 box = (50 + 20 + 30) = Rs. 100
Cost of 8 boxes = (100 x 8) = Rs. 800
So, cost of these 8 boxes = Rs. 800
Hence, option (1) is correct.
Question 16
1 / -0

Any number divided by zero is

A
not defined

B
zero

C
the number itself

D
one

Solution

Any number divided by zero is always not defined.
For example:
5 divided by 0 = Infinite
Hence, option (1) is correct.
Question 17
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Which of the following statements is false?

A
1 x 1 = 1

B
1 - 1 = 1

C
1 + 1 = 2

D
1 ÷ 1 = 1

Solution

1 - 1 = 0 and not 1.
So, 1 - 1 = 1
This statement is false.
Hence, option (2) is correct.
Question 18
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Whole numbers are closed in

A
multiplication and addition

B
addition and subtraction

C
subtraction and division

D
multiplication and division

Solution

Whole numbers are closed under addition and multiplication. Whole numbers are not closed under subtraction and division.
If a and b are any two whole numbers, then (a + b) and (a x b) are also whole numbers. The sum of two whole numbers is the same, no matter in which order they are added.
So, we can say that whole numbers are closed under addition and subtraction.
Hence, option (1) is correct.
Question 19
1 / -0

How many different rectangular patterns can be represented by the number 12?

A
1

B
2

C
3

D
4

Solution

The number 12 can represent two different rectangles.
They are:
(i) 3 4 = 12
(ii) 2 6 = 12
Question 20
1 / -0

Which of the following properties is/are applicable for addition of whole numbers?

A
Closure property

B
Commutative property

C
Property of opposites

D
All of the above

Solution

Closure property, commutative property and property of opposites are the properties of addition of whole numbers.
So, all the given three properties are properties of addition of whole numbers.
Hence, option (4) is correct.
Question 21
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Simon bought 167 packets of crisps on Monday and 98 packets of crisps on Tuesday. Each packet cost Rs. 18. How much money did he pay to the shopkeeper?

A
Rs. 4,707

B
Rs. 4,770

C
Rs. 4,077

D
Rs. 4,777

Solution

Number of packets bought on Monday = 167
Number of packets bought on Tuesday = 98
Cost of each packet = Rs. 18
Total packets = 167 + 98 = 265
Cost of 265 packets = 265 x 18 = Rs. 4,770
Hence, option (2) is correct.
Question 22
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Aman and Param went to Kasauli for a month. Aman bought 145 bottles of water in the first week and 187 bottles in the second week. Then, Param bought 254 bottles in the third week and 67 bottles in the fourth week. How many bottles did they buy in total?

A
563

B
653

C
635

D
569

Solution

Number of bottles bought by Aman in the first week = 145
Number of bottles bought in the second week = 187
Number of bottles bought by Param in the third week = 254
Number of bottles bought in the fourth week = 67
Total number of bottles = 145 + 187 + 254 + 67 = 653
Hence, option (2) is correct.
Question 23
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78 keyboards can be packed in a single wooden carton. If there are 35,568 keyboards, then how many wooden cartons are needed to pack all the keyboards?

A
436 cartons

B
456 cartons

C
465 cartons

D
546 cartons

Solution

Number of keyboards that can be packed in 1 carton = 78
Number of cartons needed to pack 35,568 keyboards == 456 cartons
Hence, option (2) is correct.
Question 24
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There are 512 ball bearings in a container. A worker replaced 8 ball bearings with 16 cranks. He continued the same process, until all the ball bearings were replaced by cranks. How many cranks did he put in the container?

A
1,204 cranks

B
1,024 cranks

C
924 cranks

D
947 cranks

Solution

Let n be the number of steps.
Then, 512 - 8 x n = 0
8n = 512
n = 64
Now, number of cranks added = 16
Therefore, total number of cranks added = = 1,024 cranks
Hence, option (2) is correct.

Alternate Solution:
There are 512 ball bearings in a container and every time 8 ball bearings are replaced by 16 cranks.
This means every ball bearing is replaced by 2 cranks.
Therefore, number cranks added = 512 2 = 1024.
Question 25
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Prahlad had Rs. 11,20,000 in the beginning. He gave Rs. 2,75,000 to Keshav and bought a second hand car from his colleague Daya for Rs. 4,26,000. Then, he bought a puppy from his friend Abhishek for Rs. 34,600. How much money is left with him now?

A
Rs. 3,88,400

B
Rs. 3,84,400

C
Rs. 3,48,400

D
Rs. 3,84,800

Solution

Total money Prahlad had in the beginning = Rs. 11,20,000
Amount given to Keshav = Rs. 2,75,000
Cost of car = Rs. 4,26,000
Cost of puppy = Rs. 34,600
Total amount spent = 2,75,000 + 4,26,000 + 34,600 = Rs. 7,35,600
Amount left with him = 11,20,000 - 7,35,600 = Rs. 3,84,400
Hence, option (2) is correct.

Question 26

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Directions: Match the following.

Column I	Column II
i. (x x y) x z = x x (y x z)	a. Distributive property of multiplication over addition
ii. x (y + z) = x(y) + y(z)	b. Distributive property for division
iii. (x + y) / z = x/z + y/z	c. Associative property of multiplication

If x, y and z are whole numbers.

i ii iii

a b c

i ii iii

c a b

i ii iii

b a c

i ii iii

b c a

Solution

Distributive property for division means that any given quantity can be split up into smaller chunks that are easier to divide.
Hence, (x + y) / z = x/z + y/z is an example of distributive property for division.

Distributive property of multiplication over addition means that multiplying a sum of numbers or variables by a number equals to the same result as multiplying each number or variable by the number and then, adding the products together.
Hence, x(y + z) = x(y) + y(z) is an example of distributive property of multiplication over addition.

Associative property of multiplication states that you can add or multiply, regardless of how the numbers are grouped.
Hence, (x x y) x z = x x (y x z) is an example of associative property of multiplication.

Hence, option (2) is correct.

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

I. Multiplying two odd numbers gives an odd number.
II. The subtraction of two whole numbers is more than their product.
III. The sum of three odd numbers is always an even number.

A

I II III

T F F

B

I II III

F T F

C

I II III

F F T

D

I II III

T F T

Solution

I. Multiplying two odd numbers always gives an odd number = True
II. The subtraction of two whole numbers is more than their product = False
III. The sum of three odd numbers is always an even number = False
Hence, option (1) is correct.
Question 28
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Directions: Study the following statements.

Statement 1: Subtraction and division are not associative for whole numbers.
Statement 2: Multiplication of whole numbers is distributive over subtraction.

Which of the following options hold?

A
Both statements are true.

B
Statement 1 is true, but statement 2 is false

C
Statement 1 is false, but statement 2 is true

D
Both statements are false.

Solution

Statement (1) that says that subtraction and division are not associative for whole numbers, is true. Statement (2) that says that multiplication of whole numbers is distributive over subtraction, is false.
Hence, option (2) is correct.

Question 29

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Directions: Match the following.

Column I	Column II
i. The smallest 2 digit even number is	a. 8
ii. When the biggest 1 digit odd number is divided by the second smallest 1 digit odd number, it gives the answer	b. 10
iii. The biggest 1 digit even number is	c. 3

i ii iii

a b c

i ii iii

c b a

i ii iii

a c b

i ii iii

b c a

Solution

i	ii	iii
b	c	a

i. The smallest 2 digit even number = 10
ii. When the biggest 1 digit odd number is divided by the second smallest 1 digit odd number, it gives 3 as the answer.
The biggest 1 digit odd number = 9
The second smallest 1 digit odd number = 3
Therefore, 9 ÷ 3 = 3
iii. The biggest 1 digit even number = 8
Hence, option (4) is correct.

Question 30
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Directions: Choose the correct option.

(i) The product of a whole number and an even number is always an ____ number.
(ii) If x = y, then the subtraction of both the numbers will be
(iii) The product of smallest natural number and a whole number will always be
(iv) If we divide any two positive integers, then it will always be

A

i ii iii iv

odd 1 the number itself positive

B

i ii iii iv

even 0 the number itself positive

C

i ii iii iv

even negative 0 the number itself

D

i ii iii iv

odd 1 the number itself 0

Solution

(i) The product of a whole number and an even number will always be an even number.
(ii) If x = y, then the subtraction of both the numbers will be 0.
(iii) The product of the smallest natural number and a whole number will always be the number itself.
(iv) If we divide any two positive integers, then it will always be positive.
Hence, option (2) is correct.

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Whole Numbers Test - 11

Result

Whole Numbers Test - 11

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Question 1

13 x 13

14 x 14

15 x 15

16 x 16

Solution

Question 2

commutative property

closure property

additive identity

None of these

Solution

Question 3

commutative

associative

distributive

closure

Solution

Question 4

>

<

=

None of these

Solution

Question 5

1,00,001 is a successor of 1,00,000.

9,99,999 is a predecessor of 1,00,000.

0 is a whole number.

Every positive number is a whole number.

Solution

Question 6

99,999

99,998

1,00,001

9,99,999

Solution

Question 7

p = q

p > q

p < q

None of these

Solution

Question 8

0

35

36

Infinite

Solution

Question 9

(5, 7, 14)

(5, 2, 7)

(2, 7, 17)

(2, 5, 14)

Solution

Question 10

16 ÷ 8 = 2

8 ÷ 0 = 0

25(7 - 8) = 25 x 7 - 25 x 8

5 - 2 is not equal to 2 - 5

Solution

Question 11

8 - 4

4 × 8

4 + 8

4 + 12

Solution

Question 12

Zero added to any number is the number itself

Addition can be done in any order

Odd number added to an odd number equals an even number

Addition is inverse of subtraction

Solution