Competency Based Questions Chapter 6 Integers

Hint: Represent integers with their signs in order to differentiate positive number, negative number and zero from each other

Question.1. Which set shows all numbers less than 0?

(a) 12, 23, 37
(b) –15, 0, 15
(c) –28, –9, 0
(d) –54, –43, –39

Question.2. The number -x is a negative integer. Which of these is a valid conclusion about x?

(a) x is any integer greater than or equal to 0.
(b) x is any integer less than or equal to 0.
(c) x is any integer greater than 0.
(d) x is any integer less than 0.

Ans.1. (d) –54, –43, –39
Ans.2. (c) x is any integer greater than 0.

Hint: Denote numbers with their signs in order to represent real life situations like temperature scale, credit debit etc.

Question.3. The depth of a submarine is 542 meters below the sea level. If 0 represents the sea level, what is the elevation of the submarine?

(a) 542
(b) –542
(c) \frac{1}{542}
(d) -\frac{1}{542}

Question.4. Aakriti has a certain amount of money. She spends more money than she has by borrowing some money from her friend. Aakriti made the following statements.
Statement I: The initial amount of money she has is represented by a positive integer.
Statement II: The amount she spent is represented by a negative integer.
Which of these statements is/are true?

(a) Only statement I
(b) Only statement II
(c) Both statements I and II
(d) Neither statement I nor statement II

Ans.3. (b) –542
Ans.4. (c) Both statements I and II

Hint: Represent the integer on Number Line in order to determine its position with respect to other integers.

Question.5. Ajay plots two points A and B on the number line.

• Point A lies 3 points to the left of zero.
• Point B lies 5 points to the right of point A.

Which of these options correctly represents the points A and B?

(a) (b) (c) (d)

Question.6. A point U lies 3 steps to the left of an integer n, as shown below:

• Point U is moved 9 steps to its right to get point V.
• Point V is moved 5 steps to its left to get point W.

Which of these represents the position of point W with respect to n?

(a) It lies 1 step to the right of n.
(b) It lies 1 step to the left of n.
(c) It lies 4 steps to the right of n.
(d) It lies 4 steps to the left of n.

Ans.5. (b) Ans.6. (a) It lies 1 step to the right of n.

Hint: Determine one more and one less of a given integers in order to find its predecessor and successor.

Question.7. What is the successor of the predecessor of –12?

(a) –11
(b) –12
(c) –13
(d) –14

Question.8. The predecessor of an integer is k+13 and the successor of the integer is -k+5. What is the integer?

(a) –3
(b) –4
(c) –5
(d) –6

Ans.7. (b) –12
Ans.8. (c) –5

Hint: Determine the order of integers in order to represent them on number line and draw comparison between them.

Question.9. Which of these can be used to prove that −4 > −7 using a number line?83

(a) On the number line 4 is to the left of –7.
(b) On the number line –4 is to the left of –7.
(c) On the number line 4 is to the right of –7.
(d) On the number line–4 is to the right of –7.

Question.10. Given that m is a positive integer and n is a negative integer. Which of these statements is correct?

(a) The predecessor of m will be always greater than the successor of n.
(b) The predecessor of m will be always less than the successor of n.
(c) The predecessor of m and successor of n can never be equal.
(d) The predecessor of m and successor of n can be equal.

Ans.9. (d) On the number line –4 is to the right of –7.
Ans.10. (d) The predecessor of m and successor of n can be equal.

Hint: Represent the integers on number line in order to perform arithmetic operations on them.

Question.11. Which number line shows the addition of −4 and its successor?

(a) (b) (c) (d)

Question.12. The value of 7-3+p is the greatest negative integer. Which number line shows the value of p?

(a) (b) (c) (d)

Ans.11. (b) Ans.12. (c)

Hint: Apply the rules of integer’s operations in order to perform arithmetic operations on them.

Question.13. What is the result obtained on subtracting 98 from the sum of –126 and 154?

(a) 126
(b) 70
(c) –7084
(d) –126

Question.14. If p = −54 and q = 29, what is the largest negative integer that should be added to (p+q)-(p-q) so that the result is a negative integer?

(a) –59
(b) –58
(c) –47
(d) –39

Ans.13. (c) –7084
Ans.14. (a) –59