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Calculating in the IT exam: Percentages, rule of three and data volumes

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tagsglossar, ihk, rechnen

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Calculating in the IT exam: Percentages, rule of three and data volumes

In short: IT exams repeatedly feature the same types of calculation: percentage and rule-of-three calculations, conversion of data volumes and transfer times, plus power consumption and availability.

In more detail: With a few formulas and a clean way of calculating you win easy points. Important: calculate with units, note intermediate results, check the result for plausibility.

In Depth

Percentages and rule of three

  • Percentage value = base value × percentage / 100. Example: 19 % of 250 € = 250 × 0.19 = 47.50 €.
  • Base value = percentage value / percentage × 100. Percentage = percentage value / base value × 100.
  • Gross/net: gross = net × 1.19 (19 % VAT), net = gross / 1.19.
  • Rule of three: Proportional (more → more): 5 licences cost 40 €, 8 licences cost 40 € / 5 × 8 = 64 €. Inversely proportional (more → less): 5 computers need 40 min, 8 computers need 5 × 40 / 8 = 25 min.
  • Availability = (total time − downtime) / total time; 99.9 % in a year ≈ 8.76 hours of downtime.

Data volumes and units

  • 1 byte = 8 bits. Decimal: 1 KB = 1000 B, 1 MB = 1000 KB, 1 GB = 1000 MB. Binary (IEC): 1 KiB = 1024 B, 1 MiB = 1024 KiB, 1 GiB = 1024 MiB.
  • Hard drives advertise decimal, operating systems often show binary: 500 GB ≈ 465 GiB.
  • Data rate: Mbit/s (bit!) ≠ MB/s (byte): 100 Mbit/s = 12.5 MB/s.
  • Transfer time = data volume / data rate. Example: 600 MB over 50 Mbit/s: 600 MB × 8 = 4,800 Mbit; 4,800 / 50 = 96 s.

Storage need and capacity

  • Uncompressed image: width × height × colour depth (bytes) → 1920 × 1080 × 3 B ≈ 6.2 MB.
  • Video/audio: data rate × duration (e.g. 5 Mbit/s × 3600 s = 18,000 Mbit = 2.25 GB).
  • Number of possibilities: n bits → 2^n values (8 bits: 256; 16 bits: 65,536).
  • RAID capacity (n disks): RAID 0: n × C; RAID 1: C; RAID 5: (n−1) × C; RAID 6: (n−2) × C; RAID 10: n/2 × C.
  • Password combinations: characters^length (62^8 ≈ 2.2·10

Power, costs and profitability

  • Energy (kWh) = power (kW) × time (h). 150 W × 8 h = 1.2 kWh. Cost = kWh × price (e.g. 1.2 × 0.35 €/kWh = 0.42 €).
  • Leasing/purchase: compare total costs over the term (purchase + operation − residual value), see TCO.
  • Straight-line depreciation = acquisition cost / useful life.
  • Payback period = investment / annual savings. Tips: write down the calculation (partial credit!), state the unit, round sensibly, and check plausibility (is the result realistic?).

See also: Storage units, Units and conversion, Kilowatt hour, Payback calculation and TCO, Subnetting and CIDR