The value of Floor(8.4) + Ceil(9.9) is:
2021
The value of Floor(8.4) + Ceil(9.9) is:
Answer: A. 18 — The floor function ⌊x⌋ gives the greatest integer that is less than or equal to x, so it always moves down to the nearest whole number and never rounds up.…
- A.
18
- B.
19
- C.
20
- D.
17
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Correct answer: A
The floor function ⌊x⌋ gives the greatest integer that is less than or equal to x, so it always moves down to the nearest whole number and never rounds up.
The ceiling function ⌈x⌉ gives the least integer that is greater than or equal to x, so it always moves up to the nearest whole number whenever a fractional part exists.
Applying this to the given expression:
Since 8 ≤ 8.4 < 9, the greatest integer not exceeding 8.4 is 8; so Floor(8.4) = 8.
Since 9 < 9.9 ≤ 10, the least integer not less than 9.9 is 10; so Ceil(9.9) = 10.
Adding these: 8 + 10 = 18.
As an independent check, 8.4 lies strictly between 8 and 9, and the floor always selects the lower of the two regardless of how large the decimal part is; 9.9 lies strictly between 9 and 10, and the ceiling always selects the upper of the two regardless of how small the remaining gap is. This confirms Floor(8.4) + Ceil(9.9) = 8 + 10 = 18.