Which of the following letter-clusters will replace the question mark (?) in the given series to make it logically complete?
HP 16, ?, NV 64, QY 100, TB 144

Question

Which of the following letter-clusters will replace the question mark (?) in the given series to make it logically complete?HP 16, ?, NV 64, QY 100, TB 144

Prepp Team · Accepted Answer

Understanding the Letter Cluster and Number Series

The question asks us to find the letter-cluster and number that will replace the question mark (?) in the given series to make it logically complete. The series is:

HP 16, ?, NV 64, QY 100, TB 144

Let's analyze the pattern in the numbers and the letter clusters separately.

Analyzing the Number Pattern

The numbers in the series are 16, ?, 64, 100, and 144. Let's look at these numbers:

16 is the square of 4 ($4^2$).
64 is the square of 8 ($8^2$).
100 is the square of 10 ($10^2$).
144 is the square of 12 ($12^2$).

The bases of these squares are 4, 8, 10, 12. Let's look at the pattern in these bases:

\(10 - 8 = 2\)

\(12 - 10 = 2\)

It appears the bases are increasing by 2. If this pattern holds throughout the series, the base before 8 should be $8 - 2 = 6$, and the base after 4 should be $4 + 2 = 6$.

So, the missing number should be the square of 6:

\(6^2 = 36\)

The pattern for the numbers is the square of consecutive even numbers starting from 4: $4^2, 6^2, 8^2, 10^2, 12^2$.

Analyzing the Letter Cluster Pattern (First Letter)

The first letters of the clusters are H, ?, N, Q, T. Let's find their positions in the English alphabet:

H is the 8th letter.
N is the 14th letter.
Q is the 17th letter.
T is the 20th letter.

Let's look at the difference in positions between consecutive known letters:

\(17 - 14 = 3\)

\(20 - 17 = 3\)

This suggests the first letters are increasing by 3 positions each time. Let's apply this pattern to find the missing letter:

From H (8th position), moving forward by 3 positions: $8 + 3 = 11$. The 11th letter is K.
From K (11th position), moving forward by 3 positions: $11 + 3 = 14$. The 14th letter is N, which matches the next cluster.

So, the missing first letter is K.

Analyzing the Letter Cluster Pattern (Second Letter)

The second letters of the clusters are P, ?, V, Y, B. Let's find their positions in the English alphabet:

P is the 16th letter.
V is the 22nd letter.
Y is the 25th letter.
B is the 2nd letter (or 28th if we wrap around after Z).

Let's look at the difference in positions between consecutive known letters:

\(25 - 22 = 3\)

\(28 - 25 = 3\) (considering B as 28th after Y)

This suggests the second letters are also increasing by 3 positions each time (with wrap-around from Z to A if needed). Let's apply this pattern to find the missing letter:

From P (16th position), moving forward by 3 positions: $16 + 3 = 19$. The 19th letter is S.
From S (19th position), moving forward by 3 positions: $19 + 3 = 22$. The 22nd letter is V, which matches the next cluster.

So, the missing second letter is S.

Combining the Patterns

Based on our analysis:

The missing letter cluster starts with K and ends with S.
The missing number is 36.

Therefore, the missing term in the series is KS 36.

Conclusion

The complete series is HP 16, KS 36, NV 64, QY 100, TB 144.

Looking at the options, KS 36 is the correct replacement for the question mark.

Element	HP 16	?	NV 64	QY 100	TB 144
First Letter (Position)	H (8)	K (11)	N (14)	Q (17)	T (20)
Pattern		+3	+3	+3	+3
Second Letter (Position)	P (16)	S (19)	V (22)	Y (25)	B (2)
Pattern		+3	+3	+3	+3
Number	16	36	64	100	144
Pattern (Base)	$4^2$	$6^2$	$8^2$	$10^2$	$12^2$

Revision Table: Key Concepts for Series Completion

Concept	Description	Example (from this problem)
Number Series	Look for arithmetic, geometric, squares, cubes, prime numbers, or mixed patterns in the sequence of numbers.	The numbers are squares of even numbers: $4^2, 6^2, 8^2, ...$
Letter Series	Convert letters to their alphabetical positions. Look for patterns in the positions (arithmetic progression, skips, etc.). Consider wrap-around from Z to A.	First letters: H(8), K(11), N(14), ... (add 3). Second letters: P(16), S(19), V(22), ... (add 3).
Mixed Series	Analyze each component (letters, numbers, symbols) separately first, then look for interaction if any.	This series combines a letter pattern and a number pattern independently.

Additional Information: Types of Series Patterns

Series completion questions test your ability to identify patterns in sequences. Common patterns include:

Arithmetic Progression: Each term is obtained by adding a constant value to the previous term. Example: 2, 5, 8, 11, ... (+3)
Geometric Progression: Each term is obtained by multiplying the previous term by a constant value. Example: 3, 6, 12, 24, ... (x2)
Difference Series: The difference between consecutive terms follows a pattern (e.g., arithmetic progression). Example: 1, 2, 4, 7, 11, ... (Differences: 1, 2, 3, 4, ...)
Square/Cube Series: Terms are squares or cubes of natural numbers, even numbers, odd numbers, etc. Example: 1, 4, 9, 16, ... ($1^2, 2^2, 3^2, 4^2$)
Alphabetical Position Series: Patterns based on the positions of letters in the alphabet. Example: A, C, E, G, ... (1, 3, 5, 7, ... adding 2)
Mixed Series: A combination of two or more different patterns within the same series, applied to different elements (like letters and numbers, or interleaved sequences).

Solving series questions requires careful observation and breaking down the sequence into simpler parts.

Prepp Team · Answer

JS 36

Prepp Team · Answer

JR 36

Prepp Team · Answer

KR 49