Find the missing sequence in the letter series below:
MNOP
To find the missing sequence in the given letter series, we need to analyze the pattern of letters in each segment. The series is presented as: A, CD, GHI, ?, UVWXY.
Letter Series Pattern Analysis
Let's examine two key aspects for each segment in the series:
- Number of Letters: We will count how many letters are present in each segment.
- Starting Letter Position: We will identify the alphabetical position of the first letter in each segment.
- Gap Between Segments: We will calculate how many letters are skipped between the end of one segment and the beginning of the next.
| Segment | Letters | Number of Letters | Last Letter & Position | Next Segment's Starting Letter & Position | Gap Calculation (Start of next - End of current) |
|---|---|---|---|---|---|
| A | A | 1 | A (1) | C (3) | \(3 - 1 = 2\) |
| CD | C, D | 2 | D (4) | G (7) | \(7 - 4 = 3\) |
| GHI | G, H, I | 3 | I (9) | ? (Missing) | ? |
| ? (Missing) | (To be found) | ? | (To be found) | U (21) | ? |
| UVWXY | U, V, W, X, Y | 5 | Y (25) | N/A | N/A |
Identifying the Missing Number of Letters
From the table above, let's observe the number of letters in each sequence of the letter series:
- Segment 1 (A): has 1 letter.
- Segment 2 (CD): has 2 letters.
- Segment 3 (GHI): has 3 letters.
- Segment 5 (UVWXY): has 5 letters.
There is a clear progression in the number of letters in each segment: 1, 2, 3, ?, 5. This indicates that the missing segment should contain 4 letters.
Determining the Starting Letter of the Missing Sequence
Next, let's analyze the gap between the end of one letter sequence and the start of the next:
- The gap after 'A' (which is at Position 1 in the alphabet) to 'C' (which is at Position 3) is \(3 - 1 = 2\).
- The gap after 'CD' (where 'D' is at Position 4) to 'G' (which is at Position 7) is \(7 - 4 = 3\).
We can see that the gap is increasing by 1 each time (2, 3, ...). Therefore, the next gap in the letter series should be 4.
The last letter of the previous known segment (GHI) is 'I', which is the 9th letter of the alphabet.
To find the starting letter of the missing sequence, we add the next gap (which is 4) to the alphabetical position of 'I':
\(\text{Starting letter position} = \text{Position of 'I'} + \text{Next Gap}\)
\(\text{Starting letter position} = 9 + 4 = 13\)
The 13th letter of the alphabet is 'M'. So, the missing sequence starts with 'M'.
Constructing the Missing Sequence
Based on our analysis, we determined that the missing sequence:
- Starts with 'M'.
- Contains 4 letters.
Therefore, counting 4 letters starting from 'M', the sequence will be: M, N, O, P.
So, the complete missing sequence in the letter series is MNOP.
Verification of the Letter Series Pattern
Let's verify if 'MNOP' fits correctly in the letter series by checking the subsequent segment (UVWXY):
- Our found missing sequence 'MNOP' ends with 'P', which is the 16th letter of the alphabet.
- The next expected gap in the pattern (which was 2, then 3, then 4) should be 5.
- The starting letter of the final segment 'UVWXY' is 'U', which is the 21st letter.
Let's apply the pattern to verify:
\(\text{Starting letter of UVWXY} = \text{Position of 'P'} + \text{Next Gap}\)
\(\text{Starting letter of UVWXY} = 16 + 5 = 21\)
Since the 21st letter is 'U', this confirms that 'MNOP' is indeed the correct missing sequence as it perfectly aligns with the established pattern for both the number of letters in each segment and the increasing gaps between segments in the letter series.
Important Questions from Critical Reasoning
As a responsible person, which of the following is not advisable?
- A, B, and C have a few chocolates among themselves. A gives to each of the other two half the number of chocolates they already have. Similarly B and C (in that order) give each of the other two half the number of chocolates each of them already has. Now, if each of them has the same number of chocolates, what could be the minimum number of chocolates they have among themselves?
Given question has main statement followed by four statements. Choose the ordered pair of statements, where the first statement implies the second, and the two statements are logically consistent with the main statement.
When she takes an examination, she clears it.
A. she took an examination
B. she did not take an examination
C. she cleared it.
D. she did not clear it.
You are alone in your house and there is a danger of thieves around. You hear a knock on the door. What should be your most logical action?
While traveling in a train, you notice that a lady from the coach behind you falls from the stairs of the train. What should be your best rational course of action?
