Solving the Letter Series Completion Problem

The question asks us to find the sequence of letters that will complete the given letter series by filling in the blanks.

The given letter series is:

N M L _ J N _ L J J _ M L J _ N M _ J J

There are 5 blanks in the series.

We need to examine the series carefully to identify a repeating pattern or rule that governs the sequence of letters.

Let's look at the provided options and see if substituting the letters from any option into the blanks reveals a consistent pattern.

Analyzing the Pattern in the Letter Series

Let's try the first option, which is J M N J L. Substituting these letters into the blanks from left to right gives:

N M L J J N M L J J N M L J J N M L J J

Now, let's look at the complete series with the blanks filled using option 1:

N M L J J N M L J J N M L J J N M L J J N M L J J

Observing this filled series, we can see a clear repeating pattern of five letters: N M L J J. This sequence repeats itself 5 times to form the entire series.

Let's verify if this pattern fits the original series structure:

• The first five letters are N M L J J. This matches the start of the original series up to the first blank (N M L _ J). The first blank is filled with J.
• The next five letters are N M L J J. This matches the original series from the letter 'N' after the first blank up to the second blank (N _ L J J). The second blank is filled with M.
• The next five letters are N M L J J. This matches the original series from the letter 'N' after the second blank up to the third blank (_ M L J). The third blank is filled with N. (Note: The original series has J J after the second blank. This chunk should be _ M L J _, but the option filling gives N M L J J). Let's re-check the original series and the filled one carefully.

Original Series with blanks (underscores):

N M L _ J N _ L J J _ M L J _ N M _ J J

Number of characters: 22 letters + 5 blanks = 27 positions.

Let's fill the blanks with option 1 (J M N J L):

N M L J J N M L J J N M L J J N M L J J

Let's segment this filled series into groups of 5:

• Group 1: N M L J J (Matches N M L _ J where blank is J)
• Group 2: N M L J J (Matches N _ L J J where blank is M)
• Group 3: N M L J J (Matches _ M L J J where blank is N)
• Group 4: N M L J J (Matches _ M L J _ where blank is J) - No, this doesn't match. The filled series segment is NMLJJ, but the original segment structure is _ M L J _. Let's re-align.

Let's write out the original series with position numbers:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

N M L _ J N _ L J J _ M L J _ N M _ J J

Now, let's insert the letters from Option 1 (J, M, N, J, L) into the blank positions (4, 7, 11, 15, 18):

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

N M L J J N M L J J N M L J J N M L J J

The complete series with option 1 letters filled is:

N M L J J N M L J J N M L J J N M L J J N M L J J

This clearly shows the repeating pattern "NMLJJ". The series is simply "NMLJJ" repeated 5 times.

Verification with the Pattern

Let's check if the blanks align with this repeating NMLJJ pattern:

• Position 4 is blank in the original series. In NMLJJ, position 4 is J. Option 1 provides J for the first blank.
• Position 7 is blank. The series is NMLJJ | NMLJJ | ... Position 6 is N, Position 7 should be M. Option 1 provides M for the second blank.
• Position 11 is blank. NMLJJ | NMLJJ | NMLJJ | ... Position 11 is the first letter of the third NMLJJ block, which is N. Option 1 provides N for the third blank.
• Position 15 is blank. NMLJJ | NMLJJ | NMLJJ | NMLJJ | ... Position 15 is the fourth letter of the third NMLJJ block, which is J. Option 1 provides J for the fourth blank. (Correction: Position 15 is the fifth letter of the third block or the fourth letter of the fourth block. Let's count carefully: N M L J J (1-5) N M L J J (6-10) N M L J J (11-15). Position 15 is the 5th letter of the 3rd block, which is J. Option 1 provides J. Let's re-check the original series structure N M L J _ N M _ J J. Original position 15 is after NMLJ. NMLJJ. Yes, the 5th position is J.)
• Position 18 is blank. NMLJJ | NMLJJ | NMLJJ | NMLJJ | NMLJJ. Position 16 is N, Position 17 is M, Position 18 should be L. Option 1 provides L for the fifth blank.

Let's map the original series and the filled blanks based on the NMLJJ pattern:

There seems to be a small discrepancy in the original series structure provided versus how the NMLJJ pattern fits the blanks based on option 1. Let's re-read the original string exactly: `N M L _ J N _ L J J _ M L J _ N M _ J J`. The blanks are at positions 4, 7, 11, 15, 18. The total length of the original string with blanks is 22 letters + 5 blanks = 27 characters.

Let's apply the NMLJJ pattern repeatedly to 27 positions:

N M L J J | N M L J J | N M L J J | N M L J J | N M L J J | N M

This would give 27 characters. Let's compare this with the original series:

• Positions 1-3: N M L (Matches)
• Position 4: Blank, Pattern is J. Option 1 provides J. (Matches)
• Position 5: J (Matches)
• Position 6: N (Matches)
• Position 7: Blank, Pattern is M. Option 1 provides M. (Matches)
• Position 8-10: L J J (Matches)
• Position 11: Blank, Pattern is N. Option 1 provides N. (Matches)
• Position 12-14: M L J (Matches)
• Position 15: Blank, Pattern is J. Option 1 provides J. (Matches)
• Position 16-17: N M (Matches)
• Position 18: Blank, Pattern is L. Option 1 provides L. (Matches)
• Position 19-20: J J (Matches)

The total length of the original series with blanks is 27 characters. The pattern NMLJJ is 5 characters long. $27 \div 5 = 5$ with a remainder of 2. So the pattern repeats 5 times, followed by the first 2 letters of the pattern.

Full predicted series based on pattern NMLJJ repeated 5 times + first 2 letters:

N M L J J N M L J J N M L J J N M L J J N M L J J N M

Original Series with blanks:

N M L _ J N _ L J J _ M L J _ N M _ J J

Comparing these two strings, we can see that the original series given in the question does not fully match the pattern NMLJJ repeated 5 times followed by NM. The original series has J J at the end, making its length 27 characters. NMLJJ repeated 5 times is 25 characters. So the series seems to end with NMLJJ repeated 5 times exactly.

Let's re-count the characters in the original series: N(1) M(2) L(3) _ J(5) N(6) _ L(8) J(9) J(10) _ M(12) L(13) J(14) _ N(16) M(17) _ J(19) J(20). This is 20 given characters + 5 blanks = 25 total positions. Let's assume the series is 25 characters long.

Original series (25 positions): N M L _ J N _ L J J _ M L J _ N M _ J J

Blanks are at positions: 4, 7, 11, 15, 18 (assuming 1-based indexing of the 25 positions).

Applying Option 1 (J M N J L) to these blanks:

N M L J J N M L J J N M L J J N M L J J

Let's divide this into groups of 5:

• N M L J J (Positions 1-5)
• N M L J J (Positions 6-10)
• N M L J J (Positions 11-15)
• N M L J J (Positions 16-20)
• N M L J J (Positions 21-25)

This sequence NMLJJ repeated 5 times perfectly matches the filled series of length 25. Let's check the blanks against this pattern:

• Blank 1 (Pos 4): Pattern position 4 is J. Option 1 provides J. Correct.
• Blank 2 (Pos 7): Pattern position 2 of the second block (Pos 5+2=7) is M. Option 1 provides M. Correct.
• Blank 3 (Pos 11): Pattern position 1 of the third block (Pos 10+1=11) is N. Option 1 provides N. Correct.
• Blank 4 (Pos 15): Pattern position 5 of the third block (Pos 10+5=15) or position 4 of the fourth block (Pos 11+4=15)? Let's see. NMLJJ (1-5), NMLJJ (6-10), NMLJJ (11-15). Position 15 is the 5th character of the 3rd block, which is J. Option 1 provides J. Correct.
• Blank 5 (Pos 18): Pattern position 3 of the fourth block (Pos 15+3=18) is L. Option 1 provides L. Correct.

The sequence J M N J L from option 1 successfully completes the series to form the repeating pattern NMLJJ.

The letters that complete the series are J, M, N, J, L.

Summary of the Solution

The given letter series is N M L _ J N _ L J J _ M L J _ N M _ J J. By testing the options, we find that inserting the letters J, M, N, J, L into the blanks creates a series where the sequence NMLJJ repeats 5 times. This indicates that the underlying pattern is NMLJJ.

Revision Table: Letter Series Pattern Analysis

Additional Information: Types of Letter Series Patterns

Letter series questions can have various types of patterns, including:

• Repeating Patterns: A fixed group of letters repeats (e.g., ABCABCABC...). This was the type in our problem (NMLJJNMLJJ...).
• Alphabetical Progression: Letters move forward or backward in the alphabet by a fixed number of steps (e.g., A, C, E, G...).
• Skipping Letters: Letters are skipped in a sequence (e.g., A, D, G, J... skipping 2 letters each time).
• Combination Patterns: A combination of different rules, such as alternating between different step counts, or combining letter positions with numbers.
• Reverse Order: Letters appear in reverse alphabetical order.

To solve letter series problems effectively, it is helpful to:

• Write down the position of each letter in the alphabet (A=1, B=2, ... Z=26).
• Look for differences between consecutive letters.
• Look for patterns within blocks of letters.
• Check for alternating patterns.
• Consider repeating blocks.

Practicing various types of letter series helps improve pattern recognition skills for logical reasoning tests.