Integers — The Other Side of Zero
24 Class 6 IMO Mathematics Olympiad practice questions on integers — the other side of zero, part of the Number Sense topic area. Every question below includes the correct answer and a full explanation.
Practice this topic interactively →1. What is the additive inverse of −8?
- A.−8
- B.0
- C.8
- D.16
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Answer: C. 8
The additive inverse of a number is the value that adds to it to make 0. −8 + 8 = 0, so the additive inverse of −8 is 8.
2. On a number line, which of these integers lies to the left of −3?
- A.−1
- B.0
- C.−5
- D.2
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Answer: C. −5
Numbers further left on the number line are smaller. −5 is smaller than −3, so it lies to the left of it.
3. What is −5 + 8?
- A.−13
- B.−3
- C.3
- D.13
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Answer: C. 3
Since 8 is larger, subtract: 8 − 5 = 3, and the sign follows the larger number (positive), giving 3.
4. A submarine is at a depth of 40 m below sea level. If sea level is taken as 0, which integer represents its position?
- A.40
- B.−40
- C.0
- D.−4
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Answer: B. −40
Below sea level is represented by a negative integer, so 40 m below sea level is −40.
5. Which integer is marked on the number line shown?
- A.3
- B.-3
- C.5
- D.-5
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Answer: A. 3
The marked point sits at 3 on the number line.
6. Which integer is marked on the number line shown?
- A.4
- B.-4
- C.6
- D.-6
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Answer: B. -4
The marked point sits at -4 on the number line.
7. What is −12 − (−5)?
- A.−17
- B.−7
- C.7
- D.17
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Answer: B. −7
Subtracting a negative is the same as adding the positive: −12 − (−5) = −12 + 5 = −7.
8. Which of the following is true?
- A.−8 > −3
- B.−3 > −8
- C.−8 = −3
- D.−3 < −8 always
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Answer: B. −3 > −8
Among negative numbers, the one with the smaller numerical value is greater. Since 3 < 8, −3 > −8.
9. Find the sum of −15 and −9.
- A.−24
- B.−6
- C.6
- D.24
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Answer: A. −24
Adding two negatives: add their values (15+9=24) and keep the negative sign, giving −24.
10. A lift goes down 6 floors from the 10th floor, then goes up 9 floors. Which floor is it on now?
- A.7
- B.11
- C.13
- D.15
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Answer: C. 13
10 − 6 + 9 = 13.
11. What is the successor (next integer) of −7?
- A.−8
- B.−6
- C.6
- D.8
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Answer: B. −6
The successor of any integer is 1 more than it. −7 + 1 = −6.
12. The number line shows a jump starting at -6. If the jump is +4, at which integer does it land?
- A.-10
- B.-2
- C.2
- D.10
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Answer: B. -2
-6 + 4 = -2.
13. The number line shows a jump starting at 5. If the jump is -9, at which integer does it land?
- A.-4
- B.-14
- C.4
- D.14
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Answer: A. -4
5 + (-9) = -4.
14. The number line shows a jump starting at -3. If the jump is -5, at which integer does it land?
- A.-8
- B.-2
- C.2
- D.8
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Answer: A. -8
-3 + (-5) = -8.
15. The temperature at 6 AM was −4°C. By noon it had risen by 11°C. What was the temperature at noon?
- A.5°C
- B.7°C
- C.9°C
- D.15°C
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Answer: B. 7°C
−4 + 11 = 7°C.
16. Find the value of 20 + (−35) − (−10).
- A.−25
- B.−5
- C.5
- D.45
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Answer: B. −5
20 + (−35) = −15, and −15 − (−10) = −15 + 10 = −5.
17. Which has the greater difference: (5 and −5), or (3 and −8)?
- A.5 and −5
- B.3 and −8
- C.Both are equal
- D.Cannot be determined
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Answer: B. 3 and −8
5 − (−5) = 10, but 3 − (−8) = 11. The second pair has the greater difference.
18. In a hollow integer grid, every row and column of the border must add up to the same 'border sum'. The top row is 4, −6, 5 (sum 3). The bottom row is x, −2, 1. What must x be for the bottom row to also sum to 3?
- A.2
- B.3
- C.4
- D.5
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Answer: C. 4
x + (−2) + 1 = 3, so x − 1 = 3, giving x = 4.
19. If M = −9 and N = 6, find the value of M − N.
- A.−15
- B.−3
- C.3
- D.15
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Answer: A. −15
M − N = −9 − 6 = −15.
20. On the number line shown, how many integers lie strictly between -6 and the marked point (not counting either one)?
- A.4
- B.5
- C.6
- D.7
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Answer: B. 5
The marked point is 0. Between -6 and 0 (exclusive) are -5, -4, -3, -2, -1 — that's 5 integers.
21. The sum of two integers is −18. If one of them is 25, find the other.
- A.−43
- B.−7
- C.7
- D.43
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Answer: A. −43
The other integer = −18 − 25 = −43.
22. A diver is 15 m below sea level. She dives down another 22 m, then rises 8 m. What is her final position relative to sea level?
- A.−37 m
- B.−29 m
- C.−21 m
- D.−13 m
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Answer: B. −29 m
−15 − 22 + 8 = −29 m.
23. Which of these is true? Statement I: The sum of a positive integer and its additive inverse is always 0. Statement II: Subtracting a negative integer always increases the value.
- A.Only I is true
- B.Only II is true
- C.Both I and II are true
- D.Neither is true
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Answer: C. Both I and II are true
I is the definition of an additive inverse, so it's always true. II is also true: subtracting a negative is the same as adding a positive, which increases the value.
24. Find the value of x if x + (−14) = −6.
- A.−20
- B.−8
- C.8
- D.20
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Answer: C. 8
x = −6 − (−14) = −6 + 14 = 8.