ITPEC IP October 2020 Question 32
In phone numbers that have the format below, eight billion numbers are to be created. What is the minimum number of digits required for the phone numbers? Here, “020” is included in the digits.
Explanation
13 digits — the fixed 020, one digit with 8 choices, and nine free digits give exactly eight billion numbers.
After 020 the first box allows 1–3 or 5–9, which is 8 choices (0 and 4 are excluded). Every further box allows 0–9, 10 choices. With n free boxes the number of phone numbers is 8 × 10n.
- •Needed: eight billion = 8 × 109
- •So 10n ≥ 109, which gives n = 9
- •Total digits: 020, the restricted digit and the free digits, 3 + 1 + 9 = 13
Answer (c)
Why not others:
- •(a) 11 — leaves 7 free digits: 8 × 107 is 80 million numbers, a hundredth of what is needed
- •(b) 12 — leaves 8 free digits: 8 × 108 is 800 million, one digit short
- •(d) 14 — 8 × 1010 is 80 billion numbers, enough but one digit more than the minimum
Key rule: The number of codes is the product of the choices at each position; each decimal digit multiplies it by 10, so find the fewest digits whose product reaches the need, then add the fixed digits.
Basic Theory · AI-written, may contain errors
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