A clock strikes only at each full hour, as many times as the hour: once at 1 o’clock, twice at 2 o’clock, and so on up to 12 times at 12 o’clock. How many times in all does it strike from 9 a.m. to 3 p.m., both included?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 48
Add the strikes of every full hour in the period. After 12 noon the clock starts again from 1, so the hours from 1 p.m. are struck as 1, 2, 3, not 13, 14, 15.
Full hours from 9 a.m. to 3 p.m., both included: 9, 10, 11, 12, 1, 2, 3
Strikes \(=9+10+11+12=42\) in the morning up to noon
Strikes \(=1+2+3=6\) in the afternoon
Total \(=42+6=48\)
Why the other options are incorrect
Option (2) 36 — Incorrect. This leaves out both end hours, 9 a.m. and 3 p.m.
Option (3) 45 — Incorrect. This leaves out the 3 strikes at 3 p.m.
Option (4) 84 — Incorrect. This counts the afternoon hours as 13, 14 and 15 strikes; the clock strikes 1, 2 and 3.