Integers Test

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Integers Test - 12

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Weekly Quiz Competition

Question 1
1 / -0

The following number line shows the balances in bank accounts of different customers:

Find the difference between the balances of Anil and Aman.

A
600

B
200

C
400

D
-200

Solution

Balance of Anil = -300
Balance of Aman = 100
Difference = 100 - (-300) = 400
Question 2
1 / -0

The following number line shows the balances in bank accounts of different customers:

The total balance in the accounts of Anil and Aman is _______ the total balance in the accounts of Amar and Sunil.

A
less than

B
more than

C
the same as

D
Cannot be determined

Solution

Total balance in accounts of Anil and Aman = -300 + 100 = -200
Total balance in accounts of Amar and Sunil = -400 + 300 = -100
-200 < -100
Option 1 is correct.
Question 3
1 / -0

Evaluate .

A
-1

B
1

C
2

D
-2

Solution

= -1

Question 4

1 / -0

Directions: Read the statements given below and choose the correct values of A, B, C and D from the options given in the table below.

(i) The sum of two numbers is 8. If one of them is -2, then the other integer is A .
(ii) The difference between a positive integer and a negative integer is -3. If one of them is -2, then the other integer is B .
(iii) For any integer b, [(-2) × b] is equal to C .
(iv) The greatest negative integer is D .

Options	A	B	C	D
P	10	-1	2b	1
Q	-10	-1	2b	-1
R	10	1	-2b	1
S	10	1	-2b	-1

P

Q

R

S

Solution

(i) Sum = 8
So, (-2) + (10) = -2 + 10 = 8
So, A = 10

(ii) Difference between a positive integer and a negative integer is -3.
One of them = -2
-2 - 1 = -3
So, B = 1

(iii) -2 × b = -2b
C = -2b

(iv) The greatest negative integer is -1.
D = -1

Question 5
1 / -0

Write whether the following statements are True (T) or False (F).

(A) Multiplying certain integers will give the same result every time regardless of the order of their multiplication.

(B) The numbers to the left of zero on a number line have a larger value than those to its right.

(C) Addition is not associative for integers.

(D) When we multiply two negative integers, we just multiply them as whole numbers and put the positive sign before the product.

A
A - T, B - F, C - F, D - T

B
A - T, B - T, C - F, D - T

C
A - T, B - F, C - T, D - F

D
A - F, B - T, C - F, D - F

Solution

(A) Multiplying certain integers will give the same result every time regardless of the order of their multiplication - True
Commutative property of multiplication:
2 × (4 × 3) = 24
(2 × 3) × 4 = 24
(2 × 4) × 3 = 24
(B) The numbers to the left of zero on a number line have a larger value than those to its right - False
The numbers to the left of zero on the number line are negative and therefore smaller in value as compared to those to its right.
(C) Addition is not associative for integers - False
Addition is associative for integers: 2 + (3 + 5) = (2 + 3) + 5
(D) When we multiply two negative integers, we just multiply them as whole numbers and put the positive sign before the product - True
-2 × -3 = +6
Question 6
1 / -0

Which of the following number sentences best describes the problem shown on the number line below?

A
-8 + 5

B
-5 + 8

C
-5 - 8

D
-8 - 5

Solution

First, we move to the left of 0 up to -8.
From there, we move 5 places to the right to reach -3.
So, -8 + 5 = -3
Question 7
1 / -0

Find the value of (8) × (-4) × (2) × 0 × (5) × (-6) + 0 × (4) × (-5) × (1) × (3) × (6).

A
0

B
420

C
300

D
350

Solution

Any value multiplied by 0 gives 0.
So, 0 + 0 = 0
Question 8
1 / -0

Which of the following statements is/are correct?

Statement 1: When multiplying a positive integer by a negative integer, we multiply them as whole numbers and put a negative sign (-) before the product. We thus get a negative integer as the product.

Statement 2: Multiplication of whole numbers is the same as repeated addition.

A
Both statements 1 and 2

B
Only statement 1

C
Only statement 2

D
Neither 1 nor 2

Solution

Statement 1 is correct: (-2 × 4) = -8

Statement 2 is correct: 5 × 5 = 25

Repeated addition = 5 + 5 + 5 + 5 + 5 = 5 × 5 = 25
Question 9
1 / -0

In a magic square, each row, column and diagonal gives the same sum. One such square is given below:

-2 -9 -4

-7 A -3

B -1 -8

The values of A and B, respectively, are

A
-5 and -6

B
-6 and -4

C
-6 and -5

D
-4 and -5

Solution

First row: (-2) + (-9) + (-4) = -15

Second row: (-7) + A + (-3) = -15
A = -5

Third row: B + (-1) + (-8) = -15
B = -6
Question 10
1 / -0

The value of is

A
12

B
24

C
6

D
2

Solution

= = 12
Question 11
1 / -0

Which of the following is not true?

(a) A prime number is a natural number that can only be divided by one and itself.
(b) A prime number has exactly two factors.
(c) 7 is a prime number.
(d) 1 is a prime number.

A
(a)

B
(b)

C
(c)

D
(d)

Solution

1 is not prime number, since it has only one divisor or factor, namely 1.
Question 12
1 / -0

The value of x in -15 × (-12 + (-6) + 23) = -15 × (-4 × 3 + (-x) + 19 - (-4)) is

A
6

B
7

C
8

D
9

Solution

-15 × (-12 + (-6) + 23) = -15 × (-4 × 3 + (-x) + 19 - (-4))

-15 × (-12 - 6 + 23) = -15 × (-12 + (-x) + 19 + 4)

-15 × (5) = -15 × (-12 + (-x) + 19 + 4)

-15 × (5) = -15(11 - x)

-75 = -165 + 15x

15x = 90

x = 6
Question 13
1 / -0

What will be the sign of the product obtained when we multiply 102 positive integers, 3 negative integers and 50 positive integers?

A
Negative

B
Positive

C
Cannot be determined

D
Data insufficient

Solution

Product of odd number of negative integers is always negative, and product of even number of negative integers is always positive.

So, 102 positive integers × 3 negative integers × 50 positive integers = Negative

(Positive × Negative × Positive = Negative)
Question 14
1 / -0

Find the value of 221 - [{56 + (25 - (3 + (-7) + 2 × 52 + 111))}].

A
11

B
15

C
16

D
21

Solution

221 - [{56 + (25 - (3 + (-7) + 2 × 52 + 111))}]
= 221 - [{56 + (25 - (3 + (-7) + 2 × 52 + 111))}]
= 221 - [{56 + (25 - (3 - 7) + 104 + 111))}]
= 221 - [{56 + 25 + 4 + 104 + 111))}]
= 221 - [{300}]
= 221 - 200

= 21
Question 15
1 / -0

Which of the following groups of integers has a sum equal to -72?

A
{-2, -20, -50}

B
{-2, 20, 54}

C
{4, 40, -28}

D
{2, 20, 50}

Solution

The required group is: {-2, -20, -50}

Adding them all, we get: (-2) + (-20) + (-50) = -2 - 20 - 50 = -22 - 50 = -72

Therefore, option 1 is the correct answer.
Question 16
1 / -0

Which of the following options shows numbers in descending order?

A
26, 13, -26, -15, -5

B
26, 13, -5, -15, -26

C
-26, -15, -5, 13, 26

D
-5, 13, -15, -26, 26

Solution

26 > 13 > -5 > -15 > -26

As we move towards the left on the number line, the value of the numbers decreases.
Question 17
1 / -0

Which of the following number lines represents -3 + 5?

A

B

C

D

Solution

The number line above represents -3 + 5 = 2.
Question 18
1 / -0

Find the value of the given expression:

(-25) - 45 + 50 - (-65) - 20 - (-120) - 40

A
145

B
50

C
105

D
-95

Solution

(-25) - 45 + 50 - (-65) - 20 - (-120) - 40

= -25 - 45 + 50 + 65 - 20 + 120 - 40

= -130 + 235

= 105
Question 19
1 / -0

The absolute value of 58 - 25 + 80 - 95 is

A
66

B
18

C
-53

D
-34

Solution

58 - 25 + 80 - 95

= 138 - 120 = 18
Question 20
1 / -0

If x is a positive integer and y is a negative integer, then which of the following is correct?

A
x + y = y + x

B
y - 0 = 0 - y = y

C
x = -y = 0

D
x + y = y - x

Solution

x = positive
y = negative

Now, we are given:
x + y = y + x

Putting the values:

x - y = -y + x, which is correct.
Question 21
1 / -0

In an Olympiad test, 2 marks are awarded for every correct answer and mark is deducted for every incorrect answer. A student X answers all the questions and scores 50 marks, answering 30 correctly. Anotherstudent Y also answers all the questions and scores 7 marks, answering 15 correctly.

How many questions does each of them answer incorrectly?

A
X - 10, Y - 23

B
X - 20, Y - 46

C
X - 25, Y - 30

D
X - 14, Y - 20

Solution

For X:

Let the number of incorrect answers be a.
Then, 30(2) + a() = 50
60 -= 50
= 60 - 50

a = 10 × 2

a = 20

Hence, X answered 20 questions incorrectly.

For Y:

Let the number of incorrect answers be b.
Then, 15(2) + b() = 7
30 -= 7
= 30 - 7

b = 23 × 2

b = 46

Hence, Y answered 46 questions incorrectly.
Question 22
1 / -0

In his diary, a shopkeeper writes the selling prices of goods as positive numbers and the cost prices of the same goods as negative numbers. These were the entries in diary:

20, -15, 35, -20, 50, -10, 20, -30

Calculate the total profit made by the shopkeeper.

A
50

B
60

C
70

D
80

Solution

Profit = Total SP - Total CP

Total SP = 20 + 35 + 50 + 20 = 125

Total CP = 15 + 20 + 10 + 30 = 75

So, profit = 125 - 75 = 50
Question 23
1 / -0

A man travelled 80 km northwards from A to B. From B, he travelled 70 km towards south along the same path. If the distance travelled along the north is represented in positive numbers, then how will the distance travelled along the south be represented? By which integer will you represent his final position from A?

A
In negative numbers, 10 km

B
In negative numbers, 20 km

C
In positive numbers, 10 km

D
In positive numbers, 15 km

Solution

Distance of final position from A = 80 - 70 = 10 km.

If north indicates positive, then south must indicate negative.
Question 24
1 / -0

An elevator in a mall ascends at the rate of 5 m/min. If the ascent starts 15 m below the ground level, then how long will it take to reach 220 m above the ground level?

A
40 minutes

B
42 minutes

C
45 minutes

D
47 minutes

Solution

Total distance covered from A to C = 15 + 220 = 235 m.

Speed = 5 m/min.

Time =

Time =

Time = 47 min
Question 25
1 / -0

Meteorologists forecast that the temperature will drop 6°C every hour. If at 12:00 noon, the temperature is 40°C, then what will be the temperature at 8:00 pm?

A
-2°C

B
10°C

C
-8°C

D
5°C

Solution

At 12:00 noon, temperature = 40°C
Now, the temperature drops 6°C every hour.
At 8:00 pm, temperature = 40 - (6 × 8) = 40 - 48 = -8°C
Question 26
1 / -0

In a Chemistry test, there are 20 questions. For every correct answer, 3 marks are awarded and for every incorrect answer, 1 mark is deducted. If Geetika attempts 19 questions, out of which 13 are correctly answered, then how many marks does she get?

A
33

B
44

C
51

D
56

Solution

Marks awarded for each correct answer = 3
Marks deducted for each wrong answer = 1
Total questions attempted = 19
Correct answers = 13
Incorrect answers = 6
Total marks scored = 13 × 3 + {6 × (-1)}
= 39 - 6 = 33
Question 27
1 / -0

The number line given below, ranging from -10 to 10, indicates the level of water in a river. Using the given information for three months, state the values of A, B and C respectively.

(i) The difference between the highest and the lowest levels is ___A___.

(ii) The water level rose ___B___ units from June to July.

(iii) The water level rose ___C___ units from May to June.

A
15, 9, 6

B
16, 10, 7

C
17, 11, 8

D
None of the above

Solution

(i) The difference between the highest and the lowest levels is 8-(-7) = 15.

(ii) The water level rose -1 to 8 i.e. 9 units from June to July.

(iii) The water level rose -7 to -1 i.e. 6 units from May to June.

Question 28

1 / -0

Match the following:

Column 1	Column 2
(i) On a number line	(A) the associative property of operations.
(ii) (a + b) + c = a + (b + c) is	(B) the addition and subtraction can be represented.
(iii) a × b = b × a is	(C) the commutative property of the operations.

(i) - (A), (ii) - (C), (iii) - (B)

(i) - (A), (ii) - (B), (iii) - (C)

(i) - (B), (ii) - (A), (iii) - (C)

None of the above

Solution

(i) On a number line, the addition and subtraction can be represented.

(ii) (a + b) + c = a + (b + c) is the associative property of operations.

(iii) a × b = b × a is the commutative property of operations.

Question 29
1 / -0

Find the incorrect statement from the following.

A
5 × 2 = 2 × 5 denotes the distributive property of multiplication operation.

B
The division of a negative integer by another negative integer results in a positive number.

C
On multiplying two negative numbers, we get a positive number.

D
All of the above

Solution

5 × 2 = 2 × 5 denotes the commutative property of multiplication operation. Rest all statements are correct.
Question 30
1 / -0

Fill in the boxes using symbols <, > or =.

(i) 5 × (-6) - (-9) (-9) × (8) + (-8)

(ii) 15 - (-10) - (-6) (-15) + (6) + (-6)

(iii) 4 + (5) × (9) (-9) + (-8) × (-8)

A
>, >, <

B
>, <, <

C
>, >, =

D
None of the above

Solution

(i) 5 × (-6) - (-9) > (-9) × (8) + (-8)

-30 + 9 > -72 - 8

-21 > -80, true

(ii) 15 - (-10) - (-6) > (-15) + (6) + (-6)

15 + 10 + 6 > -15 + 6 - 6

31 > -15, true

(iii) 4 + (5) × (9) < (-9) + (-8) × (-8)

4 + 45 < -9 + 64

49 < 55, true

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Re-Attempt Weekly Quiz Competition

Integers Test - 12

Result

Integers Test - 12

Score

-

Rank

-

SHARING IS CARING

Question 1

600

200

400

-200

Solution

Question 2

less than

more than

the same as

Cannot be determined

Solution

Question 3

-1

1

2

-2

Solution

Question 4

P

Q

R

S

Solution

Question 5

A - T, B - F, C - F, D - T

A - T, B - T, C - F, D - T

A - T, B - F, C - T, D - F

A - F, B - T, C - F, D - F

Solution

Question 6

-8 + 5

-5 + 8

-5 - 8

-8 - 5

Solution

Question 7

0

420

300

350

Solution

Question 8

Both statements 1 and 2

Only statement 1

Only statement 2

Neither 1 nor 2

Solution

Question 9

-5 and -6

-6 and -4

-6 and -5

-4 and -5

Solution

Question 10

12

24

6

2

Solution

Question 11

(a)

(b)

(c)

(d)

Solution

Question 12

6

7

8

9

Solution