# Free Integers Subjective Test 02 Practice Test - 7th grade

What will be the sign of the product if we multiply 12 negative integers together?  [1 MARK]

#### SOLUTION

Solution :

As we know that the product of two negative integers is always positive. Hence, when we multiply 12 negative integers, we can treat these 12 integers like 6 pairs of negative integers. Each pair will give us a positive integer. Hence the overall multiple will be a positive integer.

Define commutative property of addition of integers with the help of an example.  [2 MARKS]

#### SOLUTION

Solution :

Definition: 1 Mark
Example: 1 Mark

The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around.
So, if we add any number of integers in any order the result will be the same.

For addition, the rule is "a + b = b + a".

Example
2 + 3 = 3 + 2 = 5.

Arrange the following integers in ascending order and represent them on the number line: 2, 5, (-1), (-4), (-5)
[2 MARKS]

#### SOLUTION

Solution :

Ascending Order : 1 Mark
Representation on number line : 1 Mark

Integers in ascending order: (-5), (-4), (-1), 2, 5 What will be the output of the equation:
(a ÷ b) × (c) where 'a' and 'b' are positive integers and 'c' is a negative integer?  [2 MARKS]

#### SOLUTION

Solution :

Concept: 1 Mark
Result: 1 Mark

The result will be a negative integer as multiplication of one negative and one positive integer will result in a negative integer.

(a ÷ b) = + integer

(+)×()=() integer

Verify that a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c) for each of the following values of a, b and c.
(a) a = 12, b = −4, c = 2
(b) a = (− 10), b = 1, c = 1
[2 MARKS]

#### SOLUTION

Solution : Each option: 1 Mark

(a) a = 12, b = −4, c = 2

÷ (b + c) = 12 ÷ (− 4 + 2) = 12 ÷ (−2)
= −6

(a ÷ b) + (a ÷ c) = [12 ÷ (−4)] + [12 ÷ 2] = −3 + 6 = 3

Hence, a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c)

(b) a = −10, b = 1, c = 1

÷ (b + c) = (−10) ÷ (1 + 1) = (−10) ÷ 2
= −5

(a ÷ b) + (a ÷ c) = [(−10) ÷ 1] + [(−10) ÷ 1]
= − 10 − 10 = −20

Hence, a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c)

Using the number line find the integer in the following cases : [3 MARKS]

(a) Sum of 5 and -3

(b) 5 less than 3

(c) 4 more than -1

#### SOLUTION

Solution :

Each option: 1 Mark

(a) We first move to the right of 0 by 5 steps reaching 5. Then we move 3 steps to the left of 5 reaching 2. We get, (+5)+(3)=2

(b) We want to know an integer which is 5 less than 3 for that we need to start from 3 and move to the left by 5 steps and obtain –2 as shown below: (c) We want to know the integer which is 4 more than –1. So, we start from –1 and proceed 4 steps to the right of –1 to reach 3 as shown below: In a class test (+ 3) marks are given for every correct answer and (−2) marks are given for every incorrect answer and no marks for not attempting any question.
(i) Radhika scored 20 marks. If she has got 12 correct answers, how many questions has she attempted incorrectly?
(ii) Mohini scores − 5 marks in this test, though she has got 7 correct answers. How many questions has she attempted incorrectly?  [3 MARKS]

#### SOLUTION

Solution :

Each option:1.5 Marks

As per the question
Marks obtained for 1 right answer = +3
Marks obtained for 1 wrong answer = −2

(i) Marks scored by Radhika = 20

Marks obtained for 12 correct answers = 12 × 3 = 36

Marks obtained for incorrect answers = Total score − Marks obtained for 12 correct answers
= 20 − 36 = −16

Marks obtained for 1 wrong answer = −2

= (−16) ÷ (−2) = 8

(ii) Marks scored by Mohini = −5

Marks obtained for 7 correct answers
= 7 × 3 = 21

Marks obtained for incorrect answers = Total score − Marks obtained for 12 correct answers
= − 5 − 21 = −26

Marks obtained for 1 wrong answer = −2

= (−26) ÷ (−2) = 13

(i) Evaluate:

(a)(2)×(3)×(4)

(b)2×(3)×(4)

(c)26×(3)×410

(ii)
Use the sign of >, < or = in the box to make the statements true.

(a)(8)+(4)  (8)+(4)

(b)(3)+7(19)  158+(9)

(c)2341+11  234111          [3 MARKS]

#### SOLUTION

Solution :

Each part: 1.5 Marks

(i) Multiplication of even no. of negative integers gives a positive integer whereas multiple of odd no. of negative integers gives a negative integer.

(a) We have multiplication of three negative integers. So, the product will be negative integers.
(2)×(3)×(4)=6×(4)=(24)

(b) We have multiplication of two negative integers and one positive integer. So, the product will be positive integers.
2×(3)×(4)=12×2=24

(c) 26×(3)×410
=13×3×25
=25

(ii)
(a) 12<4

(b) 15<2

(c) 7>29

A shopkeeper earns a profit of Re 1 by selling one pen and incurs a loss of 40 paise per pencil while selling pencils of her old stock.

(i) In a particular month, she incurs a loss of Rs 5. In this period, she sold 45 pens. How many pencils did she sell in this period?

(ii) In the next month, she earns neither profit nor loss. If she sold 70 pens, how many pencils did she sell? [3 MARKS]

#### SOLUTION

Solution :

Steps: 2 Marks
Result: 1 Mark

(i) Profit earned by selling one pen = Re 1
Profit earned by selling 45 pens = Rs 45, which we denote by + Rs 45
Total loss = Rs 5, which we denote by (– Rs 5)

Profit earned + Loss incurred = Total loss
Therefore, Loss incurred = Total Loss – Profit earned
= Rs (– 5 – 45) = Rs (–50) = (– 5000 paise)
Loss incurred by selling one pencil = 40paise
which we write as (– 40paise)

So, number of pencils sold
=(5000)÷(40)=125 pencils.

(ii) In the next month, there is neither profit nor loss.
So, Profit earned + Loss incurred = 0
i.e., Profit earned = – Loss incurred.

Now, profit earned by selling 70 pens = Rs 70
Hence, the loss incurred by selling pencils = Rs 70 which we indicate by (– Rs 70) or (– 7,000 paise).
Total number of pencils sold
=(7000)÷(40)=175 pencils.

An elevator descends into a mine shaft at the rate of 6 m/min. If the descent starts from 10 m above the ground level, how long will it take to reach −350m? [4 MARKS]

#### SOLUTION

Solution :

Calculations: 1 Mark
Steps: 2 Marks
Result: 1 Mark

Given that
An elevator descends into a mine shaft at the rate of 6 m/min.
The descent starts from 10m above the ground level.

Now, the distance descended is denoted by a negative integer.
Initial height = +10 m
Final depth = −350 m
Total distance to be descended by the elevator = (−350) − (+10) = −360 m
Time taken by the elevator to descend −6 m = 1 min
Thus, time taken by the elevator to descend −360 m = (−360) ÷ (−6)
= 60 minutes = 1 hour

Hence it will take 1 hour to reach -350m.

A helicopter is flying at a height of 1500 m. There is a helipad which is just below the helicopter at a height of 600 m from the ground. Taking upward movement of the helicopter as positive and downward movement as negative. Find the distance of helipad from the helicopter? How much time will it take for the helicopter to reach the helipad if the speed of the helicopter is 50 meters per second?
[4 MARKS]

#### SOLUTION

Solution :

Steps: 2 Marks
Result: 2 Marks

Upward movement is taken as positive while downward movement is taken as negative. Hence, from the question we can conclude that helicopter is moving downward. So, the distance of helipad from the helicopter will be negative integers.

=1500m+600m

=900m

Given that the speed of the helicopter is 50 meters per second.
Total distance to be covered = 900 m
Time taken by the helicopter to reach the helipad = 900 ÷ 50 =18 seconds
Hence, the helicopter will reach the helipad in 18 seconds.

Tesla makes a profit of Rs 100 on each car it sells, while it makes a loss of Rs 150 each time they send a rocket into space. They have sent 10 rockets into space this year. If Tesla wants to make a net profit of Rs 3000, how many cars they must sell this year? If 10 cars have already been sold, how many more cars need to be sold so as to meet the target. [4 MARKS]

#### SOLUTION

Solution : Steps: 2 Marks

It is given that
Tesla makes a profit of Rs 100 on each car it sells
While it makes a loss of Rs 150 each time they send a rocket into space.
Tesla wants to make a profit of Rs 3000.
Total number of rockets sent to space this year = 10
Total Loss due to the rockets = 10 × 1500 = Rs 1500
Let x number of cars be sold, so as to make a profit of Rs 3000.
Net Profit = Profit from selling cars - loss due to sending of rockets
So on substituting the values, we get:
3000 = 100 × x - 1500
x = (3000 + 1500) ÷ (100)
x = 4500 ÷ 100
x = 45

So, the total number of cars that need to be sold to make a profit of Rs 3000 are 45.
It is given that, 10 cars have already been sold.
Number of cars that need to be sold to meet the target = 45 - 10 = 35
So, 35 more cars need to be sold to meet the target.

Find the product, using suitable properties:
(a) 26
× (− 48) + (− 48) × (− 36)
(b) 15
× (− 25) × (− 4) × (− 10)
[4 MARKS]

#### SOLUTION

Solution : Each option: 2 Marks

(a) 26 × (−48) + (−48) × (−36)
= (−48) × 26 + (−48) × (−36)
( (b × a = a × b))
= (−48) [26 − 36] (a × b + a × c) = a (b + c)
= (−48) × (−10) = 480

(b) 15 × (−25) × (−4) × (−10)
= 15 × [(−25) × (−4)] × (−10)
= 15 ×  × (−10)
= 15 × (−1000) = −15000

At Srinagar temperature was 5C on Monday and then it dropped by 2C on Tuesday. What was the temperature of Srinagar on Tuesday? On Wednesday, it rose by 4C. What was the temperature on Wednesday? If the temperature drops by 2 each day after Wednesday, then, find the temperature on Saturday.  [4 MARKS]

#### SOLUTION

Solution : Steps: 1 Mark
Temperature on Tuesday: 1 Mark
Temperature on Wednesday: 1 Mark
Temperature on Saturday: 1 Mark

Temperature on Monday =5C

Temperature on Tuesday = Temperature on Monday 2C

=5C2C=7C

Temperature on Wednesday = Temperature on Tuesday +4C

=7C+4C=3C

Therefore, the temperature on Tuesday and Wednesday was 7C and 3C respectively.

Given that
The temperature drops by 2 each day after Wednesday
The temperature on Wednesday = 3C
The temperature on Saturday
=3(2×3)=36=9C

The temperature on Saturday is 9C

A cement company earns a profit of Rs 8 per bag of old white cements and a loss of Rs 5 per bag of old grey cements. What is the number of white cement bags it must sell to have neither profit nor loss, if the number of grey bags sold is 6,400 bags?  [4 MARKS]

#### SOLUTION

Solution : Steps: 2 Marks
Result: 2 Marks

As per the question
Loss incurred while selling 1 bag of grey cement = -Rs 5
Loss incurred while selling 6400 bags of grey cement = (- 5) × 6400 = - 32000
Let the number of bags of white cement to be sold be x.
Profit earned while selling 1 bag of white cement=Rs 8
Profit earned while selling x bags of white cement
= x × 8
=8x

In condition of no profit no loss,
Profit earned + Loss incurred = 0
8x + (-32000) = 0
8x = 32000
x = 4000
Therefore, 4000 bags of white cement must be sold.