Integers Test

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Integers Test - 11

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Weekly Quiz Competition

Question 1
1 / -0

Directions: The following number line shows the temperature in degree Celcius (^oC) on different days at a particular place in 20XX.

What is the temperature difference between Tuesday and Sunday?

A
12^οC

B
15^oC

C
18^oC

D
22^oC

Solution

On Tuesday, it was -3^oC and on Sunday, it was 9^oC.
Difference = -3 to 9 = 9 - (-3)
= 12^oC
Question 2
1 / -0

Directions: The following number line shows the temperature in degree Celcius (^oC) on different days at a particular place in 20XX.

The temperature difference between Monday and Tuesday is _____ the temperature difference between Wednesday and Saturday.

A
less than

B
more than

C
equal to

D
None of the above

Solution

Temperature on Wednesday = 0^oC
Temperature on Saturday = 6^oC
Difference = 6^oC
Temperature on Monday = -9^oC
Temperature on Tuesday = -3^oC
Difference = 6^oC
So, the temperature difference between Monday and Tuesday is equal to the temperature difference between Wednesday and Saturday.
Question 3
1 / -0

Evaluate^.

A
0

B
3

C
1

D
2

Solution

=

=

= 1

Question 4

1 / -0

Directions: Read the following statements and find M, N, O and P with the help of table given below.

(i) The sum of two integers is 94. If one of the numbers is 60, then the other integer is M .
(ii) The sum of a negative integer and a N integer is always a negative number.
(iii) When an even number gets multiplied by another even number, the result is always O .
(iv) The multiplicative inverse of 9 is P .

	M	N	O	P
A	34	negative	even	1/9
B	34	positive	odd	9
C	-34	positive	even/odd	-9
D	34	negative	even/odd	1/9

A

B

C

D

Solution

(i) Since, the sum of two integers is 94 and one of the numbers is 60, then the other integer, M = 94 - 60 = 34

(ii) Let the integer be -5.
According to question,
-5 + N = -10
N = -10 + 5
N = -5
So, N should always be a negative number.

(iii) When an even number gets multiplied by another even number, the result will always an even number.

(iv) P is the multiplicative inverse of 9.
By the property of multiplicative inverse,
P x 9 = 1 gives P = 1/9

Question 5
1 / -0

Which of the following statements is false?

A
Multiplying and dividing two integers with the same signs, the answer is always positive.

B
Multiplying and dividing two integers with different sign, the answer is always negative.

C
The sum of any integer and its opposite is equal to one.

D
An integer is a whole number that can be positive, negative or zero.

Solution

The sum of any integer and its opposite is equal to zero.
Question 6
1 / -0

The following number line represents the temperature in degree Celsius (°C). Which of the following explains the given condition?

A
-5 + 3

B
-5 + (-3)

C
5 + 3

D
0 - (-5)

Solution

In the given figure, we first go 5 steps to the left of the number line starting from zero and then, move 3 steps to the right.
Question 7
1 / -0

The value of (-6) x (-8) x (-2) x (0) x (1) + (5) x (2) x (3) x (6) is

A
120

B
180

C
-150

D
0

Solution

We have, (-6) x (-8) x (-2) x (0) x (1) + (5) x (2) x (3) x (6)
= 0 + 180
= 180
Question 8
1 / -0

Which of the following statements is/are correct?

Statement 1: Changing the order of the factors does not change the product.
Statement 2: Adding a zero to any number does not change the value of the number.

A
Only statement 1

B
Only statement 2

C
Both statements 1 and 2

D
Neither statement 1 nor 2

Solution

(1) Changing the order of the factors does not change the product. For example: (-3) x 8 = 8 x (-3)
(2) Adding a zero to any number does not change the value of the number. For example: -7 + 0 = -7
Question 9
1 / -0

In the following matrix, the product of every row and column is the same. What is the value of A and P?

A
-2, 5

B
-2, -2

C
2, -5

D
-2, -5

Solution

Product of row 1 = (-2) x 10 x (-1) = 20

Product of column 1 = (-2) x 5 x A = 20

= A =

= A = -2

Product of row 2 = 5 x (-2) x P = 20

P =

P = -2
Question 10
1 / -0

Find the value of the expression [(-8) x (-6) x (-15)] + [(-20) x (-7) x (-1)].

A
980

B
860

C
-860

D
-760

Solution

[(-8) x (-6) x (-15)] + [(-20) x (-7) x (-1)]
= [48 x (-15)] + [140 x (-1)]
= -720 + (-140)
= -720 - 140
= -860
Question 11
1 / -0

Which of the following statements is correct?

A
Integers can be written as fractions.

B
Rational numbers are the numbers in the form p/q.

C
All integers are whole numbers, but can be negative.

D
None of these

Solution

Integers can be written as fractions simply by giving them a denominator of one.
Question 12
1 / -0

The value of x in 16 - 4 + 2(-4) - (-8) + x + 52 = 84 is

A
15

B
16

C
20

D
22

Solution

16 - 4 + 2(-4) - (-8) + x + 52 = 84
12 - 8 + 8 + x + 52 = 84
64 + x = 84
x = 20
Question 13
1 / -0

What will be the sign, if we add -56 and +34?

A
Negative

B
Positive

C
Cannot say

D
Data is insufficient

Solution

-56 + 34 = -22
As the bigger number is negative, so the answer would be negative.
Question 14
1 / -0

Directions: Simplify the following.

22 - 40 + [28 - (-6 x 4) + 26] - 48

A
10

B
12

C
14

D
16

Solution

22 - 40 + [28 - (-6 x 4) + 26] - 48
= 22 - 40 + [28 - (-24) + 26] - 48
= 22 - 40 + [28 + 24 + 26] - 48
= 22 - 40 + 78 - 48
= 100 - 88
= 12
Question 15
1 / -0

Which of the following number pairs does not have a product equal to 48?

A
(-8, -6)

B
(2, 24)

C
(8, 6)

D
(-8, 6)

Solution

Product (-8, 6) = -48 ≠ 48
All other options have product equal to 48.
Question 16
1 / -0

Which of the following sets is in descending order?

A
12, 10, -2, -5, -7

B
10, -5, 13, -2, -6

C
18, 15, -17, -8, 4

D
-20, -18, -15, -12, -11

Solution

We know, Descending order means Biggest to smallest.
Hence, option 1 (12, 10, -2, -5, -7) is correct here.
Question 17
1 / -0

Which of the following represents 3 - 8?

A

B

C

D

Solution

This figure represents 3 - 8.

At first, we are going from 0 to 3 and then after that, we are moving 8 steps backward.
Question 18
1 / -0

Directions: Find the value of the following expression.

24 + 84 - (-24) - 28 + 8 + (-6 - 14) - (-8)

A
148

B
100

C
90

D
80

Solution

24 + 84 - (-24) - 28 + 8 + (-6 - 14) - (-8)
= 108 + 24 - 28 + 8 - 20 + 8
= 108 + 24 + 8 + 8 - 48
= 148 - 48
= 100
Question 19
1 / -0

The absolute value of -25 + 53 - 81 - 12 is

A
65

B
-65

C
-50

D
50

Solution

-25 + 53 - 81 - 12
= -118 + 53
= -65
Absolute value = 65
Question 20
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If a and b are negative numbers, then which of following is the absolute value for their addition?

A
Positive

B
Negative

C
Zero

D
Cannot be determined

Solution

a and b are negative numbers.
Example: -5 - 3 = -8
But, absolute value is always positive.
So, it would be 8.
Question 21
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In a G.K. test, 2 marks are given for every correct answer and 2 marks are also deducted for every incorrect answer. Mrinal answered all the questions and scored 30 marks, though he got 5 incorrect answers. Karan also answered all the questions and scored 20 marks, though he got 7 incorrect answers. How many correct answers did each get?

A
20, 17

B
15, 19

C
17, 15

D
10, 14

Solution

Let the number of correct answers be x for Mrinal and number of correct answers be y for Karan.

So, 2x - 2(5) = 30

2y - 2(7) = 20

So, x = 40/2 = 20 correct answers for Mrinal

y = 34/2 = 17 correct answers for Karan
Question 22
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A C.A. in a firm notes firm's income in positive numbers and its expenditure in negative numbers in the day book. There are some entries for 4 days like 53, -85, 75, -21, 48, 12, -35, 45 and 25. Find the net profit of 4 days in the firm.

A
100

B
115

C
117

D
120

Solution

Total income = 53 + 75 + 48 + 12 + 45 + 25 = 258

Total expenditure = 85 + 21 + 35 = 141

Net profit = 258 - 141 = 117
Question 23
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Roopa goes 66 km South from a point Q to point P. From P, she moves 54 km North along the same road. The distance travelled in the North direction is represented by a positive integer. How will you represent the distance travelled South and by which of the following integers will you represent her final position from Q?

A
Positive integer, 5 km

B
Positive integer, 8 km

C
Negative integer, 120 km

D
Negative integer, 12 km

Solution

Since South is represented by a negative integer, the final position of Roopa from point Q will be:
-66 + 54 = -12 km
Therefore, Roopa is 12 km away from point Q.
Question 24
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Sham has to cover 500 km. If his speed is 25 km/h and he has already covered 50 km, then how long will it take to cover the rest of the distance?

A
20 hours

B
22 hours

C
18 hours

D
15 hours

Solution

Distance to cover = (500 - 50) = 450 km

Speed = 25 km/h
Time required to cover the rest of the distance =
= 18 hours
Question 25
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A heater heats a room by 2 degree in an hour. If the temperature of the room at 10:00 am was 8 degree, then what will be the temperature of the room at 5:00 pm?

A
18 degrees

B
20 degrees

C
22 degrees

D
25 degrees

Solution

Temperature at 10 am = 8 degrees

Total time from 10 am to 5 pm = 7 hours

Heater heats the room by 2 degree per hour.

So, total rise in temperature of room due to heater, T = 7 × 2 degree = 14 degrees

Temperature at 5 pm = Temperature at 10 am + T = 8 + 14 = 22 degrees
Question 26
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Garvin makes a profit of Rs. 20 for every T-shirt he sells and a loss of Rs. 10 for every shirt he sells. He cannot sell only T-shirts, as customers need both things.

(a) If he gets an order to supply 500 T-shirts and 800 shirts, then find the profit or loss from the order.
(b) If he has to supply 50 shirts, then how many T-shirts does he need to supply, so that he makes neither loss nor profit in this order?

A
(a) Profit of Rs. 1,500 (b) 25

B
(a) Profit of Rs. 2,000 (b) 25

C
(a) Loss of Rs. 3,500 (b) 50

D
(a) Loss of Rs. 1,800 (b) 35

Solution

(a) Profit from 500 T-shirts = 500 × 20 = Rs. 10,000

Loss from 800 shirts = 800 × 10 = Rs. 8,000

Profit = 10000 - 8000 = Rs. 2,000

(b) 50 shirts = Loss of 50 × 10 = Rs. 500

To cover this loss from T-shirts, 500/20 = 25 T-shirts must be sold
Question 27
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Directions: The following number line shows the temperature in degree Celsius (°C) at different times of a day at a particular place. Find A, B and C in the statements given below.

(i) On the given day, the temperature difference, when the temperature was hottest and the coldest, is A .
(ii) The temperature difference at 6 a.m and 12 p.m. is B .
(iii) The temperature difference at 8 a.m and 6 p.m. is C .

A

B

C

D

Solution

(A) From the figure, the hottest temperature is 15°C and coldest temperature is 6°C.
So, the required difference = A = 15 - (-6) = 21°C

(B) Temperature at 6 a.m. = -6°C and temperature at 12 a.m. = 4°C
So, the required difference = B = 4 - (-6) = 10°C

(C) Temperature at 8 a.m. = 4°C and temperature at 6 p.m. = 10°C
So, the required difference = C = 10 - (-4) = 14°C

Question 28

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Directions: Match the following.

Column - 1	Column - 2
1. Zero property of multiplication	a. Adding 0 in any number does not change the value of the number
2. Identity property of addition	b. Changing the grouping of addends does not change the sum
3. Associative property of addition	c. Changing the order of addends does not change the sum
4. Commutative property of addition	d. The product of 0 and any number is zero

1 - a, 2 - d, 3 - c, 4 - b

1 - d, 2 - a, 3 - b, 4 - c

1 - c, 2 - a, 3 - d, 4 - b

1 - a, 2 - b, 3 - c, 4 - d

Solution

Column - 1	Column - 2
1. Zero property of multiplication	d. The product of 0 and any number is zero.
2. Identity property of addition	a. Adding 0 in any number does not change the value of the number.
3. Associative property of addition	b. Changing the grouping of addends does not change the sum.
4. Commutative property of addition	c. Changing the order of addends does not change the sum.

Hence, 1 - d, 2 - a, 3 - b, 4 - c is the correct answer.

Question 29
1 / -0

Directions: State 'T' for true statement and 'F' for false statement.

1. The multiplication or division of two positive integers will be positive.
2. The multiplication or division of two negative integers will be negative.
3. Adding a negative number is just like adding a positive number.
4. Fraction cannot be an integer.

A
1 - T, 2 - F, 3 - F, 4 - T

B
1 - T, 2 - T, 3 - F, 4 - T

C
1 - T, 2 - F, 3 - T, 4 - T

D
1 - T, 2 - F, 3 - T, 4 - F

Solution

1, If you multiply or divide two positive numbers, the result will be positive. (True)
2. If you multiply or divide two negative numbers, the result will be positive. The two negatives will cancel out each other. (False)
3. Adding a negative number is just like subtracting a positive number. (False)
4. Fraction cannot be an integer because Integers are whole numbers. (True)

1 - T, 2 - F, 3 - F, 4 - T is the correct answer.
Question 30
1 / -0

Directions: Fill in the blanks with >, < and =.

1. 35 × -4 + 18 ÷ 3 _____ 35 - 200 + 31
2. 88 ÷ 22 - 6 × 4 ______ 500 ÷ 25 - 100
3. 33 × 2 ÷ 11 + 7 _______ 54 × 2 ÷ 12 + 9

A
=, >, <

B
=, >, =

C
<, =, <

D
<, >, <

Solution

35 × -4 + 18 ÷ 3 = 35 - 200 + 31, (-134 = -134)

88 ÷ 22 - 6 × 4 > 500 ÷ 25 - 100, (-20 > -80)

33 × 2 ÷ 11 + 7 < 54 × 2 ÷ 12 + 9, (13 < 18)

Hence, option (1) is the correct answer.

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Re-Attempt Weekly Quiz Competition

Integers Test - 11

Result

Integers Test - 11

Score

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Rank

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SHARING IS CARING

Question 1

12οC

15oC

18oC

22oC

Solution

Question 2

less than

more than

equal to

None of the above

Solution

Question 3

0

3

1

2

Solution

Question 4

A

B

C

D

Solution

Question 5

Multiplying and dividing two integers with the same signs, the answer is always positive.

Multiplying and dividing two integers with different sign, the answer is always negative.

The sum of any integer and its opposite is equal to one.

An integer is a whole number that can be positive, negative or zero.

Solution

Question 6

-5 + 3

-5 + (-3)

5 + 3

0 - (-5)

Solution

Question 7

120

180

-150

0

Solution

Question 8

Only statement 1

Only statement 2

Both statements 1 and 2

Neither statement 1 nor 2

Solution

Question 9

-2, 5

-2, -2

2, -5

-2, -5

Solution

Question 10

980

860

-860

-760

Solution

Question 11

Integers can be written as fractions.

Rational numbers are the numbers in the form p/q.

All integers are whole numbers, but can be negative.

None of these

Solution

Question 12

15

16

20

22

Solution

12^οC

15^oC

18^oC

22^oC