An antique store has a collection of eight clocks. At a particular mom

Question

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 an evenly spaced sequence (arithmetic progression), 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

A 1:53 pm
B 1:58 pm
C 2:18 pm
D 3:08 pm
E 5:08 pm

mavr1k · Answer

b - 1:58PM

The increments are a Fibonacci sequence, - 3,5,8,13,21,34,55 and so on.
so from 1.55 + 3 = 1.58. and then 1.58 + 05 = 2:03 pm.

yashikaaggarwal · Answer

1:55 - 2:03 = 8 min

2:03 - 2:11 = 8 min
2:11 - 2:24 = 13 min (
2:24 - 2:45 = 21 min (13+8)
2:45 - 3:19 = 34 min (21+13)
3:19 - 4:14 = 55 min (21+34)

Time has to be less than 2:11 to be in sequence.

A) 1:53:1-55 = 2 min
1:55-2:03 = 8 min
2:03 - 2:11 = 8 min (not in sequence)

B) 1:55:1-58 = 3 min
1:58-2:03 = 5 min
2:03 - 2:11 = 8 min ( in sequence)

B is answer

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HNS · Answer

How is this an Arithmetic Sequence ?

luisdicampo · Answer

Deconstructing the Question  
The problem asks for the missing clock time in a sequence.
Convert all times to minutes from a reference (e.g., 12:00 pm) to find the pattern.

Given Times: 
1:55 pm = 115 min
2:03 pm = 123 min
2:11 pm = 131 min
2:24 pm = 144 min
2:45 pm = 165 min
3:19 pm = 199 min
4:14 pm = 254 min

Step 1: Analyze Differences  
Calculate the difference between consecutive terms:
123 - 115 =  8 
131 - 123 =  8 
144 - 131 =  13 
165 - 144 =  21 
199 - 165 =  34 
254 - 199 =  55

The sequence of differences is: 8, 8, 13, 21, 34, 55.
Notice the Fibonacci relationship for the later terms:
13 + 21 = 34
21 + 34 = 55
8 + 13 = 21

However, the beginning (8, 8) breaks the pattern. Working backwards from 13, the previous terms should be 5 and 3 (since 5+8=13 and 3+5=8).
The first gap of "8" in our data (between 1:55 and 2:03) is actually the sum of the missing  3  and  5  intervals. This implies the missing clock is inside this first interval.

Step 2: Find the Missing Value  
We need to split the interval between 1:55 pm and 2:03 pm.
Start with the smallest Fibonacci difference expected:  3 .
1:55 pm + 3 minutes =  1:58 pm .

Check the next interval:
2:03 pm - 1:58 pm = 5 minutes.
This completes the Fibonacci difference sequence:  3, 5, 8, 13, 21, 34, 55 .

Answer:  B

An antique store has a collection of eight clocks. At a particular mom

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An antique store has a collection of eight clocks. At a particular mom

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