Objective Type Questions: Negative Numbers and Integers | Mathematics (Maths) Class 6 PDF Download

 Page 1


 
 
 
 
 
 
Objective Type Questions                                                    page: 5.18 
Mark the correct alternative in each of the following: 
 
1. Which of the following statement is true? 
(a) - 7 > - 5              (b) - 7 < - 5                 (c) (- 7) + (- 5) > 0                       (d) (- 7) - (- 5) > 0 
Solution: 
 
The option (b) is correct answer. 
In option (a)  
We know that - 7 is to the left of – 5 
Hence, - 7 < - 5. 
In option (c)  
We know that (- 7) + (- 5) = - (7 + 5) = - 12. 
So - 12 is to the left of 0 
Hence (- 7) + (- 5) < 0. 
In option (d) 
(- 7) - (- 5) = (- 7) + (additive inverse of - 5) = (- 7) + (5) = - (7 - 5) = - 2 
We know that - 2 is to the left of 0, so (- 7) - (- 5) < 0. 
 
2. 5 less than - 2 is 
(a) 3                            (b) - 3                        (c) - 7                                 (d) 7 
Solution: 
 
The option (c) is correct answer. 
We know that, 5 less than - 2 = (- 2) - (5) = - 2 - 5 = - 7 
 
3. 6 more than - 7 is 
(a) 1                            (b) - 1                        (c) 13                                 (d) – 13 
Solution: 
 
The option (b) is correct answer. 
We know that, 6 more than - 7 = (- 7) + 6 = - (7 - 6) = - 1 
 
4. If x is a positive integer, then 
(a) x + |x| = 0              (b) x - |x| = 0                    (c) x + |x| = -2x                (d) x = - |x| 
Solution: 
 
The option (b) is correct answer. 
We know that if x is positive integer, then |x| = x  
Hence, x + |x| = x + x = 2x and x - |x| = x - x = 0 
 
5. If x is a negative integer, then 
(a) x + |x| = 0              (b) x - |x| = 0                    (c) x + |x| = 2x                (d) x - |x| = - 2x 
Solution: 
 
The option (a) is correct answer. 
We know that x is negative integer, then |x| = -x 
It can be written as 
x + |x| = x - x = 0 and x - |x| = x - (- x) = x + x = 2x 
Page 2


 
 
 
 
 
 
Objective Type Questions                                                    page: 5.18 
Mark the correct alternative in each of the following: 
 
1. Which of the following statement is true? 
(a) - 7 > - 5              (b) - 7 < - 5                 (c) (- 7) + (- 5) > 0                       (d) (- 7) - (- 5) > 0 
Solution: 
 
The option (b) is correct answer. 
In option (a)  
We know that - 7 is to the left of – 5 
Hence, - 7 < - 5. 
In option (c)  
We know that (- 7) + (- 5) = - (7 + 5) = - 12. 
So - 12 is to the left of 0 
Hence (- 7) + (- 5) < 0. 
In option (d) 
(- 7) - (- 5) = (- 7) + (additive inverse of - 5) = (- 7) + (5) = - (7 - 5) = - 2 
We know that - 2 is to the left of 0, so (- 7) - (- 5) < 0. 
 
2. 5 less than - 2 is 
(a) 3                            (b) - 3                        (c) - 7                                 (d) 7 
Solution: 
 
The option (c) is correct answer. 
We know that, 5 less than - 2 = (- 2) - (5) = - 2 - 5 = - 7 
 
3. 6 more than - 7 is 
(a) 1                            (b) - 1                        (c) 13                                 (d) – 13 
Solution: 
 
The option (b) is correct answer. 
We know that, 6 more than - 7 = (- 7) + 6 = - (7 - 6) = - 1 
 
4. If x is a positive integer, then 
(a) x + |x| = 0              (b) x - |x| = 0                    (c) x + |x| = -2x                (d) x = - |x| 
Solution: 
 
The option (b) is correct answer. 
We know that if x is positive integer, then |x| = x  
Hence, x + |x| = x + x = 2x and x - |x| = x - x = 0 
 
5. If x is a negative integer, then 
(a) x + |x| = 0              (b) x - |x| = 0                    (c) x + |x| = 2x                (d) x - |x| = - 2x 
Solution: 
 
The option (a) is correct answer. 
We know that x is negative integer, then |x| = -x 
It can be written as 
x + |x| = x - x = 0 and x - |x| = x - (- x) = x + x = 2x 
 
 
 
 
 
 
6. If x is greater than 2, then |2 - x| =  
(a) 2 - x              (b) x - 2                    (c) 2 + x                (d) - x – 2 
Solution: 
 
The option (b) is correct answer. 
We know that if a is negative integer, then |a| = - a  
It is given that x is greater than 2 where 2 - x is negative 
Hence, |2 - x| = - (2 - x) = - 2 + x = x - 2. 
 
7. 9 + |- 4| is equal to 
(a) 5                         (b) - 5                       (c) 13                            (d) -13 
Solution: 
 
The option (c) is correct answer. 
We know that, |- 4| = 4  
Hence 9 + |- 4| = 9 + 4 = 13 
 
8. (- 35) + (- 32) is equal to 
(a) 67                         (b) - 67                       (c) - 3                            (d) 3 
Solution: 
 
The option (b) is correct answer. 
It can be written as (- 35) + (- 32) = - (35 + 32) = - 67 
 
9. (- 29) + 5 is equal to 
(a) 24                         (b) 34                       (c) - 34                            (d) – 24 
Solution: 
 
The option (d) is correct answer. 
It can be written as (- 29) + 5 = - (29 - 5) = - 24 
 
10. |- |- 7| - 3| is equal to 
(a) - 7                       (b) 7                              (c) 10                                    (d) – 10 
Solution: 
 
The option (c) is correct answer. 
It can be written as |- |- 7| - 3| = |- 7 - 3| = |- 10| = 10                                           
 
11. The successor of - 22 is 
(a) - 23                       (b) - 21                              (c) 23                                    (d) 21 
Solution: 
 
The option (b) is correct answer. 
We know that if ‘a’ is an integer a + 1 is its successor.  
So the successor of - 22 = - 22 + 1 = - (22 - 1) = - 21 
 
12. The predecessor of – 14 is 
(a) – 15                        (b) 15                                  (c) 13                                (d) – 13 
Solution: 
 
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Objective Type Questions                                                    page: 5.18 
Mark the correct alternative in each of the following: 
 
1. Which of the following statement is true? 
(a) - 7 > - 5              (b) - 7 < - 5                 (c) (- 7) + (- 5) > 0                       (d) (- 7) - (- 5) > 0 
Solution: 
 
The option (b) is correct answer. 
In option (a)  
We know that - 7 is to the left of – 5 
Hence, - 7 < - 5. 
In option (c)  
We know that (- 7) + (- 5) = - (7 + 5) = - 12. 
So - 12 is to the left of 0 
Hence (- 7) + (- 5) < 0. 
In option (d) 
(- 7) - (- 5) = (- 7) + (additive inverse of - 5) = (- 7) + (5) = - (7 - 5) = - 2 
We know that - 2 is to the left of 0, so (- 7) - (- 5) < 0. 
 
2. 5 less than - 2 is 
(a) 3                            (b) - 3                        (c) - 7                                 (d) 7 
Solution: 
 
The option (c) is correct answer. 
We know that, 5 less than - 2 = (- 2) - (5) = - 2 - 5 = - 7 
 
3. 6 more than - 7 is 
(a) 1                            (b) - 1                        (c) 13                                 (d) – 13 
Solution: 
 
The option (b) is correct answer. 
We know that, 6 more than - 7 = (- 7) + 6 = - (7 - 6) = - 1 
 
4. If x is a positive integer, then 
(a) x + |x| = 0              (b) x - |x| = 0                    (c) x + |x| = -2x                (d) x = - |x| 
Solution: 
 
The option (b) is correct answer. 
We know that if x is positive integer, then |x| = x  
Hence, x + |x| = x + x = 2x and x - |x| = x - x = 0 
 
5. If x is a negative integer, then 
(a) x + |x| = 0              (b) x - |x| = 0                    (c) x + |x| = 2x                (d) x - |x| = - 2x 
Solution: 
 
The option (a) is correct answer. 
We know that x is negative integer, then |x| = -x 
It can be written as 
x + |x| = x - x = 0 and x - |x| = x - (- x) = x + x = 2x 
 
 
 
 
 
 
6. If x is greater than 2, then |2 - x| =  
(a) 2 - x              (b) x - 2                    (c) 2 + x                (d) - x – 2 
Solution: 
 
The option (b) is correct answer. 
We know that if a is negative integer, then |a| = - a  
It is given that x is greater than 2 where 2 - x is negative 
Hence, |2 - x| = - (2 - x) = - 2 + x = x - 2. 
 
7. 9 + |- 4| is equal to 
(a) 5                         (b) - 5                       (c) 13                            (d) -13 
Solution: 
 
The option (c) is correct answer. 
We know that, |- 4| = 4  
Hence 9 + |- 4| = 9 + 4 = 13 
 
8. (- 35) + (- 32) is equal to 
(a) 67                         (b) - 67                       (c) - 3                            (d) 3 
Solution: 
 
The option (b) is correct answer. 
It can be written as (- 35) + (- 32) = - (35 + 32) = - 67 
 
9. (- 29) + 5 is equal to 
(a) 24                         (b) 34                       (c) - 34                            (d) – 24 
Solution: 
 
The option (d) is correct answer. 
It can be written as (- 29) + 5 = - (29 - 5) = - 24 
 
10. |- |- 7| - 3| is equal to 
(a) - 7                       (b) 7                              (c) 10                                    (d) – 10 
Solution: 
 
The option (c) is correct answer. 
It can be written as |- |- 7| - 3| = |- 7 - 3| = |- 10| = 10                                           
 
11. The successor of - 22 is 
(a) - 23                       (b) - 21                              (c) 23                                    (d) 21 
Solution: 
 
The option (b) is correct answer. 
We know that if ‘a’ is an integer a + 1 is its successor.  
So the successor of - 22 = - 22 + 1 = - (22 - 1) = - 21 
 
12. The predecessor of – 14 is 
(a) – 15                        (b) 15                                  (c) 13                                (d) – 13 
Solution: 
 
 
 
 
 
 
 
The option (a) is correct answer. 
The predecessor of – 14 is – 15. 
 
13. If the sum of two integers is - 26 and one of them is 14, then the other integer is 
(a) - 12                       (b) 12                              (c) - 40                               (d) 40 
Solution: 
 
The option (c) is correct answer. 
It is given that the sum of two integers = - 26 
One of them = 14 
So the other integer = - 26 - 14 = - (26 + 14) = - 40 
 
14. Which of the following pairs of integers have 5 as a difference? 
(a) 10, 5                       (b) - 10, - 5                          (c) 15, - 20                               (d) both (a) and (b) 
Solution: 
 
The option (d) is correct answer. 
Consider option (a) 10 - 5 = 5 
Consider option (b) (- 5) - (- 10) = - 5 + 10 = 5 
Consider option (c) 15 - (- 20) = 15 + 20 = 35 
 
15. If the product of two integers is 72 and one of them is - 9, then the other integers is 
(a) - 8                       (b) 8                          (c) 81                               (d) 63 
Solution: 
 
The option (a) is correct answer. 
It is given that the product of two integers = 72 
One of them = - 9 
Hence, the other integers = 72 ÷ (- 9) = - 8 
 
16. On subtracting - 7 from - 14, we get 
(a) - 12                       (b) - 7                          (c) -14                               (d) 21 
Solution: 
 
The option (b) is correct answer. 
It can be written as 
Required number = - 14 - (- 7) = - 14 + 7 = - (14 - 7) = - 7 
 
17. The largest number that divides 64 and 72 and leave the remainders 12 and 7 respectively, is 
(a) 17                             (b) 13                                       (c) 14                                      (d) 18 
Solution: 
 
The option (b) is correct answer. 
By subtracting 12 and 7 from 64 and 72  
We get  
64 - 12 = 52 and 72 - 7 = 65 
So the required number is the HCF of 52 and 65. 
It can be written as 
52 = 4 × 13 and 65 = 5 × 13 
HCF of 52 and 65 = 13 
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Objective Type Questions                                                    page: 5.18 
Mark the correct alternative in each of the following: 
 
1. Which of the following statement is true? 
(a) - 7 > - 5              (b) - 7 < - 5                 (c) (- 7) + (- 5) > 0                       (d) (- 7) - (- 5) > 0 
Solution: 
 
The option (b) is correct answer. 
In option (a)  
We know that - 7 is to the left of – 5 
Hence, - 7 < - 5. 
In option (c)  
We know that (- 7) + (- 5) = - (7 + 5) = - 12. 
So - 12 is to the left of 0 
Hence (- 7) + (- 5) < 0. 
In option (d) 
(- 7) - (- 5) = (- 7) + (additive inverse of - 5) = (- 7) + (5) = - (7 - 5) = - 2 
We know that - 2 is to the left of 0, so (- 7) - (- 5) < 0. 
 
2. 5 less than - 2 is 
(a) 3                            (b) - 3                        (c) - 7                                 (d) 7 
Solution: 
 
The option (c) is correct answer. 
We know that, 5 less than - 2 = (- 2) - (5) = - 2 - 5 = - 7 
 
3. 6 more than - 7 is 
(a) 1                            (b) - 1                        (c) 13                                 (d) – 13 
Solution: 
 
The option (b) is correct answer. 
We know that, 6 more than - 7 = (- 7) + 6 = - (7 - 6) = - 1 
 
4. If x is a positive integer, then 
(a) x + |x| = 0              (b) x - |x| = 0                    (c) x + |x| = -2x                (d) x = - |x| 
Solution: 
 
The option (b) is correct answer. 
We know that if x is positive integer, then |x| = x  
Hence, x + |x| = x + x = 2x and x - |x| = x - x = 0 
 
5. If x is a negative integer, then 
(a) x + |x| = 0              (b) x - |x| = 0                    (c) x + |x| = 2x                (d) x - |x| = - 2x 
Solution: 
 
The option (a) is correct answer. 
We know that x is negative integer, then |x| = -x 
It can be written as 
x + |x| = x - x = 0 and x - |x| = x - (- x) = x + x = 2x 
 
 
 
 
 
 
6. If x is greater than 2, then |2 - x| =  
(a) 2 - x              (b) x - 2                    (c) 2 + x                (d) - x – 2 
Solution: 
 
The option (b) is correct answer. 
We know that if a is negative integer, then |a| = - a  
It is given that x is greater than 2 where 2 - x is negative 
Hence, |2 - x| = - (2 - x) = - 2 + x = x - 2. 
 
7. 9 + |- 4| is equal to 
(a) 5                         (b) - 5                       (c) 13                            (d) -13 
Solution: 
 
The option (c) is correct answer. 
We know that, |- 4| = 4  
Hence 9 + |- 4| = 9 + 4 = 13 
 
8. (- 35) + (- 32) is equal to 
(a) 67                         (b) - 67                       (c) - 3                            (d) 3 
Solution: 
 
The option (b) is correct answer. 
It can be written as (- 35) + (- 32) = - (35 + 32) = - 67 
 
9. (- 29) + 5 is equal to 
(a) 24                         (b) 34                       (c) - 34                            (d) – 24 
Solution: 
 
The option (d) is correct answer. 
It can be written as (- 29) + 5 = - (29 - 5) = - 24 
 
10. |- |- 7| - 3| is equal to 
(a) - 7                       (b) 7                              (c) 10                                    (d) – 10 
Solution: 
 
The option (c) is correct answer. 
It can be written as |- |- 7| - 3| = |- 7 - 3| = |- 10| = 10                                           
 
11. The successor of - 22 is 
(a) - 23                       (b) - 21                              (c) 23                                    (d) 21 
Solution: 
 
The option (b) is correct answer. 
We know that if ‘a’ is an integer a + 1 is its successor.  
So the successor of - 22 = - 22 + 1 = - (22 - 1) = - 21 
 
12. The predecessor of – 14 is 
(a) – 15                        (b) 15                                  (c) 13                                (d) – 13 
Solution: 
 
 
 
 
 
 
 
The option (a) is correct answer. 
The predecessor of – 14 is – 15. 
 
13. If the sum of two integers is - 26 and one of them is 14, then the other integer is 
(a) - 12                       (b) 12                              (c) - 40                               (d) 40 
Solution: 
 
The option (c) is correct answer. 
It is given that the sum of two integers = - 26 
One of them = 14 
So the other integer = - 26 - 14 = - (26 + 14) = - 40 
 
14. Which of the following pairs of integers have 5 as a difference? 
(a) 10, 5                       (b) - 10, - 5                          (c) 15, - 20                               (d) both (a) and (b) 
Solution: 
 
The option (d) is correct answer. 
Consider option (a) 10 - 5 = 5 
Consider option (b) (- 5) - (- 10) = - 5 + 10 = 5 
Consider option (c) 15 - (- 20) = 15 + 20 = 35 
 
15. If the product of two integers is 72 and one of them is - 9, then the other integers is 
(a) - 8                       (b) 8                          (c) 81                               (d) 63 
Solution: 
 
The option (a) is correct answer. 
It is given that the product of two integers = 72 
One of them = - 9 
Hence, the other integers = 72 ÷ (- 9) = - 8 
 
16. On subtracting - 7 from - 14, we get 
(a) - 12                       (b) - 7                          (c) -14                               (d) 21 
Solution: 
 
The option (b) is correct answer. 
It can be written as 
Required number = - 14 - (- 7) = - 14 + 7 = - (14 - 7) = - 7 
 
17. The largest number that divides 64 and 72 and leave the remainders 12 and 7 respectively, is 
(a) 17                             (b) 13                                       (c) 14                                      (d) 18 
Solution: 
 
The option (b) is correct answer. 
By subtracting 12 and 7 from 64 and 72  
We get  
64 - 12 = 52 and 72 - 7 = 65 
So the required number is the HCF of 52 and 65. 
It can be written as 
52 = 4 × 13 and 65 = 5 × 13 
HCF of 52 and 65 = 13 
 
 
Hence, the largest number that divides 64 and 72 and leave the remainders 12 and 7 respectively, is 13. 
18. The sum of two integers is - 23. If one of them is 18, then the other is
(a) -14 (b) 14 (c) 41 (d) -41
Solution:
The option (d) is correct answer. 
It is given that the sum of two integers = - 23 
One of them = 18 
So the other number = (- 23) - (18) = - 23 - 18 = - (23 + 18) = - 41 
Hence, the other number is - 41. 
19. The sum of two integers is - 35. If one of them is 40, then the other is
(a) 5 (b) - 75 (c) 75 (d) – 5
Solution:
The option (b) is correct answer. 
It is given that the sum of two integers = - 35 
One of them = 40 
So the other number = (- 35) - (40) = - 35 - 40 = - (35 + 40) = - 75 
Hence, the other number is - 75. 
20. On subtracting - 5 from 0, we get
(a) - 5 (b) 5 (c) 50 (d) 0
Solution:
The option (b) is correct answer. 
We know that, 0 - (- 5) = 0 + 5 = 5 
Hence by subtracting - 5 from 0, we obtain 5. 
21. (- 16) + 14 - (- 13) is equal to
(a) - 11 (b) 12 (c) 11 (d) – 15
Solution:
The option (c) is correct answer. 
It can be written as (- 16) + 14 - (- 13) = (- 16) + 14 + 13 = (- 16) + 27 = 27 - 16 = 11 
22. (- 2) × (- 3) × 6 × (- 1) is equal to
(a) 36 (b) - 36 (c) 6 (d) – 6
Solution:
The option (b) is correct answer. 
It can be written as (- 2) × (- 3) × 6 × (- 1) = (2 × 3) × 6 × (- 1) = 6 × 6 × (- 1) = 36 × (- 1) 
So we get (- 2) × (- 3) × 6 × (- 1) = - (36 × 1) = - 36 
23. 86 + (- 28) + 12 + (- 34) is equal to
(a) 36 (b) - 36 (c) 6 (d) – 6
Solution:
The option (a) is correct answer. 
Page 5


 
 
 
 
 
 
Objective Type Questions                                                    page: 5.18 
Mark the correct alternative in each of the following: 
 
1. Which of the following statement is true? 
(a) - 7 > - 5              (b) - 7 < - 5                 (c) (- 7) + (- 5) > 0                       (d) (- 7) - (- 5) > 0 
Solution: 
 
The option (b) is correct answer. 
In option (a)  
We know that - 7 is to the left of – 5 
Hence, - 7 < - 5. 
In option (c)  
We know that (- 7) + (- 5) = - (7 + 5) = - 12. 
So - 12 is to the left of 0 
Hence (- 7) + (- 5) < 0. 
In option (d) 
(- 7) - (- 5) = (- 7) + (additive inverse of - 5) = (- 7) + (5) = - (7 - 5) = - 2 
We know that - 2 is to the left of 0, so (- 7) - (- 5) < 0. 
 
2. 5 less than - 2 is 
(a) 3                            (b) - 3                        (c) - 7                                 (d) 7 
Solution: 
 
The option (c) is correct answer. 
We know that, 5 less than - 2 = (- 2) - (5) = - 2 - 5 = - 7 
 
3. 6 more than - 7 is 
(a) 1                            (b) - 1                        (c) 13                                 (d) – 13 
Solution: 
 
The option (b) is correct answer. 
We know that, 6 more than - 7 = (- 7) + 6 = - (7 - 6) = - 1 
 
4. If x is a positive integer, then 
(a) x + |x| = 0              (b) x - |x| = 0                    (c) x + |x| = -2x                (d) x = - |x| 
Solution: 
 
The option (b) is correct answer. 
We know that if x is positive integer, then |x| = x  
Hence, x + |x| = x + x = 2x and x - |x| = x - x = 0 
 
5. If x is a negative integer, then 
(a) x + |x| = 0              (b) x - |x| = 0                    (c) x + |x| = 2x                (d) x - |x| = - 2x 
Solution: 
 
The option (a) is correct answer. 
We know that x is negative integer, then |x| = -x 
It can be written as 
x + |x| = x - x = 0 and x - |x| = x - (- x) = x + x = 2x 
 
 
 
 
 
 
6. If x is greater than 2, then |2 - x| =  
(a) 2 - x              (b) x - 2                    (c) 2 + x                (d) - x – 2 
Solution: 
 
The option (b) is correct answer. 
We know that if a is negative integer, then |a| = - a  
It is given that x is greater than 2 where 2 - x is negative 
Hence, |2 - x| = - (2 - x) = - 2 + x = x - 2. 
 
7. 9 + |- 4| is equal to 
(a) 5                         (b) - 5                       (c) 13                            (d) -13 
Solution: 
 
The option (c) is correct answer. 
We know that, |- 4| = 4  
Hence 9 + |- 4| = 9 + 4 = 13 
 
8. (- 35) + (- 32) is equal to 
(a) 67                         (b) - 67                       (c) - 3                            (d) 3 
Solution: 
 
The option (b) is correct answer. 
It can be written as (- 35) + (- 32) = - (35 + 32) = - 67 
 
9. (- 29) + 5 is equal to 
(a) 24                         (b) 34                       (c) - 34                            (d) – 24 
Solution: 
 
The option (d) is correct answer. 
It can be written as (- 29) + 5 = - (29 - 5) = - 24 
 
10. |- |- 7| - 3| is equal to 
(a) - 7                       (b) 7                              (c) 10                                    (d) – 10 
Solution: 
 
The option (c) is correct answer. 
It can be written as |- |- 7| - 3| = |- 7 - 3| = |- 10| = 10                                           
 
11. The successor of - 22 is 
(a) - 23                       (b) - 21                              (c) 23                                    (d) 21 
Solution: 
 
The option (b) is correct answer. 
We know that if ‘a’ is an integer a + 1 is its successor.  
So the successor of - 22 = - 22 + 1 = - (22 - 1) = - 21 
 
12. The predecessor of – 14 is 
(a) – 15                        (b) 15                                  (c) 13                                (d) – 13 
Solution: 
 
 
 
 
 
 
 
The option (a) is correct answer. 
The predecessor of – 14 is – 15. 
 
13. If the sum of two integers is - 26 and one of them is 14, then the other integer is 
(a) - 12                       (b) 12                              (c) - 40                               (d) 40 
Solution: 
 
The option (c) is correct answer. 
It is given that the sum of two integers = - 26 
One of them = 14 
So the other integer = - 26 - 14 = - (26 + 14) = - 40 
 
14. Which of the following pairs of integers have 5 as a difference? 
(a) 10, 5                       (b) - 10, - 5                          (c) 15, - 20                               (d) both (a) and (b) 
Solution: 
 
The option (d) is correct answer. 
Consider option (a) 10 - 5 = 5 
Consider option (b) (- 5) - (- 10) = - 5 + 10 = 5 
Consider option (c) 15 - (- 20) = 15 + 20 = 35 
 
15. If the product of two integers is 72 and one of them is - 9, then the other integers is 
(a) - 8                       (b) 8                          (c) 81                               (d) 63 
Solution: 
 
The option (a) is correct answer. 
It is given that the product of two integers = 72 
One of them = - 9 
Hence, the other integers = 72 ÷ (- 9) = - 8 
 
16. On subtracting - 7 from - 14, we get 
(a) - 12                       (b) - 7                          (c) -14                               (d) 21 
Solution: 
 
The option (b) is correct answer. 
It can be written as 
Required number = - 14 - (- 7) = - 14 + 7 = - (14 - 7) = - 7 
 
17. The largest number that divides 64 and 72 and leave the remainders 12 and 7 respectively, is 
(a) 17                             (b) 13                                       (c) 14                                      (d) 18 
Solution: 
 
The option (b) is correct answer. 
By subtracting 12 and 7 from 64 and 72  
We get  
64 - 12 = 52 and 72 - 7 = 65 
So the required number is the HCF of 52 and 65. 
It can be written as 
52 = 4 × 13 and 65 = 5 × 13 
HCF of 52 and 65 = 13 
 
 
Hence, the largest number that divides 64 and 72 and leave the remainders 12 and 7 respectively, is 13. 
18. The sum of two integers is - 23. If one of them is 18, then the other is
(a) -14 (b) 14 (c) 41 (d) -41
Solution:
The option (d) is correct answer. 
It is given that the sum of two integers = - 23 
One of them = 18 
So the other number = (- 23) - (18) = - 23 - 18 = - (23 + 18) = - 41 
Hence, the other number is - 41. 
19. The sum of two integers is - 35. If one of them is 40, then the other is
(a) 5 (b) - 75 (c) 75 (d) – 5
Solution:
The option (b) is correct answer. 
It is given that the sum of two integers = - 35 
One of them = 40 
So the other number = (- 35) - (40) = - 35 - 40 = - (35 + 40) = - 75 
Hence, the other number is - 75. 
20. On subtracting - 5 from 0, we get
(a) - 5 (b) 5 (c) 50 (d) 0
Solution:
The option (b) is correct answer. 
We know that, 0 - (- 5) = 0 + 5 = 5 
Hence by subtracting - 5 from 0, we obtain 5. 
21. (- 16) + 14 - (- 13) is equal to
(a) - 11 (b) 12 (c) 11 (d) – 15
Solution:
The option (c) is correct answer. 
It can be written as (- 16) + 14 - (- 13) = (- 16) + 14 + 13 = (- 16) + 27 = 27 - 16 = 11 
22. (- 2) × (- 3) × 6 × (- 1) is equal to
(a) 36 (b) - 36 (c) 6 (d) – 6
Solution:
The option (b) is correct answer. 
It can be written as (- 2) × (- 3) × 6 × (- 1) = (2 × 3) × 6 × (- 1) = 6 × 6 × (- 1) = 36 × (- 1) 
So we get (- 2) × (- 3) × 6 × (- 1) = - (36 × 1) = - 36 
23. 86 + (- 28) + 12 + (- 34) is equal to
(a) 36 (b) - 36 (c) 6 (d) – 6
Solution:
The option (a) is correct answer. 
 
 
 
 
 
 
It can be written as 86 + (-28) + 12 + (-34) = 86 + (-28) - (34 - 12) = 86 + (-28) - 22 
On further calculation 
86 + (-28) + 12 + (-34) = (86 - 28) - (34 - 12) = (86 - 28) - 22 = 58 - 22 = 36 
 
24. (-12) × (-9) - 6 × (-8) is equal to 
(a) 156                             (b) 60                                (c) -156                                    (d) – 60 
Solution: 
 
The option (a) is correct answer. 
It can be written as (-12) × (-9) - 6 × (-8) = (12 × 9) - 6 × (-8) = 108 - 6 × (-8)  
On further calculation 
(-12) × (-9) - 6 × (-8) = 108 + 6 × 8 = 108 + 48 = 156