Clock Times and Fibonacci Differences
XAT 2018 · Quantitative Ability & Data Interpretation · Hard · Quantitative Aptitude
An antique store has a collection of eight clocks. At a particular moment, the displayed times on seven of the eight clocks were as follows: 1:55 pm, 2:03 pm, 2:11 pm, 2:24 pm, 2:45 pm, 3:19 pm and 4:14 pm. If the displayed times of all eight clocks form a mathematical series, then what was the displayed time on the remaining clock?
- A.
1:53 pm
- B.
1:58 pm
- C.
2:18 pm
- D.
3:08 pm
- E.
5:08 pm
B
Explanation
Time gaps between consecutive given times: 8m, 8m, 13m, 21m, 34m, 55m. Notice 8, 13, 21, 34, 55 are Fibonacci numbers. The standard Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13... The initial 8 min gap between 1:55 and 2:03 can be split into 3 min and 5 min gaps. Inserting 1:58 pm gives gaps: 3m (1:55 to 1:58), 5m (1:58 to 2:03), 8m, 13m, 21m, 34m, 55m.
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