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Question (31)

QN0030243

If the sum of two integers is S and their difference (first − second) is D, then the first number equals:

(A) (S − D) ÷ 2
(B) S − D
(C) (S + D) ÷ 2
(D) S + D

Correct Answer: C

Explanation:

Adding the two equations: first + second = S and first − second = D gives 2 × first = S + D

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Question (32)

QN0030244

If sum = 4 and difference = 12, the second number is:

(A) 8
(B) −4
(C) 4
(D) −8

Correct Answer: B

Explanation:

Second = (S − D)/2 = (4 − 12)/2 = −4

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Question (33)

QN0030245

The number line used for the carrom coin model extends:

(A) Only to the right (positive side)
(B) Only to the left (negative side)
(C) In both directions from 0
(D) Only between −5 and +5

Correct Answer: C

Explanation:

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Question (34)

QN0030246

Two integers have a sum of 0 and a difference of 10. The pair with difference −10 is obtained by:

(A) Adding 10 to both numbers
(B) Multiplying both numbers by −1
(C) Swapping the two numbers
(D) Subtracting 10 from both numbers

Correct Answer: C

Explanation:

Swapping first and second number changes first − second to second − first, reversing the sign

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Question (35)

QN0030247

Which of the following pairs satisfies sum = −7 and difference = −13?

(A) (−10, 3)
(B) (3, −10)
(C) (−3, −4)
(D) (−4, 3)

Correct Answer: A

Explanation:

−10 + 3 = −7 and −10 − 3 = −13, both conditions satisfied

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Question (36)

QN0030248

A coin at position 0 moves first by +5 and then lands at −2. What was the second movement?

(A) +7
(B) −7
(C) +3
(D) −3

Correct Answer: B

Explanation:

5 + x = −2 gives x = −7

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Question (37)

QN0030249

In the carrom coin model, if a coin starts at 0 and ends to the left of 0 after two strikes both leftward, which conclusion is correct?

(A) Both movements are positive
(B) Both movements are negative
(C) One movement is positive and one is negative
(D) Both movements equal zero

Correct Answer: B

Explanation:

Leftward movements are represented as negative integers

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Question (38)

QN0030250

A coin starts at 0, moves right by 'a' units and then left by 'b' units, ending at a position to the right of 0. Which condition must hold?

(A) a < b
(B) a = b
(C) a > b
(D) a + b = 0

Correct Answer: C

Explanation:

For the final position a + (−b) to be positive, a must be greater than b

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Question (39)

QN0030251

What is the second number when two integers have a sum of −7 and a difference of −1?

(A) −4
(B) −3
(C) −6
(D) −1

Correct Answer: B

Explanation:

Second = (S − D)/2 = (−7 − (−1))/2 = −6/2 = −3

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Question (40)

QN0030252

A student answers 6 questions incorrectly in a test. Each wrong answer carries a penalty represented as −2 marks. Using the integer model, what is the total penalty?

(A) −12
(B) 12
(C) −8
(D) 8

Correct Answer: A

Explanation:

6 × (−2) = −12

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Question (31)

If the sum of two integers is S and their difference (first − second) is D, then the first number equals:

Explanation:

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Question (32)

If sum = 4 and difference = 12, the second number is:

Explanation:

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Question (33)

The number line used for the carrom coin model extends:

Explanation:

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Question (34)

Two integers have a sum of 0 and a difference of 10. The pair with difference −10 is obtained by:

Explanation:

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Question (35)

Which of the following pairs satisfies sum = −7 and difference = −13?

Explanation:

Link:

Question (36)

A coin at position 0 moves first by +5 and then lands at −2. What was the second movement?

Explanation:

Link:

Question (37)

In the carrom coin model, if a coin starts at 0 and ends to the left of 0 after two strikes both leftward, which conclusion is correct?

Explanation:

Link:

Question (38)

A coin starts at 0, moves right by 'a' units and then left by 'b' units, ending at a position to the right of 0. Which condition must hold?

Explanation:

Link:

Question (39)

What is the second number when two integers have a sum of −7 and a difference of −1?

Explanation:

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Question (40)

A student answers 6 questions incorrectly in a test. Each wrong answer carries a penalty represented as −2 marks. Using the integer model, what is the total penalty?

Explanation:

Link:

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