Select the option that is related to the fifth term in the same way as the second term is related to the first term and the fourth term is related to the third term.
H64 : J100 :: L144 : N196 :: U441 : ?

Question

Select the option that is related to the fifth term in the same way as the second term is related to the first term and the fourth term is related to the third term.

H64 : J100 :: L144 : N196 :: U441 : ?

Prepp Team · Accepted Answer

Understanding Analogy Patterns in Letter and Number Series

This question is an example of a letter-number analogy, where we need to find the relationship between the elements in the first pair and the third pair to apply it to the fifth term. Let's analyze the given pairs:

H64 : J100
L144 : N196
U441 : ?

Analyzing the First Analogy Pair: H64 : J100

Let's look at the relationship between the letters and the numbers separately.

Letters: H and J. In the English alphabet, H is the 8th letter, and J is the 10th letter. The difference in their positions is $10 - 8 = 2$. So, the second letter is 2 positions after the first letter.
Numbers: 64 and 100. We can observe that $64$ is the square of $8$ ($8^2$) and $100$ is the square of $10$ ($10^2$).

Combining the letter and number patterns, if the first letter is at position 'n', the number is $n^2$. The second letter is at position 'n+2', and the number is $(n+2)^2$.

Analyzing the Second Analogy Pair: L144 : N196

Let's check if the same pattern holds for the second pair.

Letters: L and N. In the English alphabet, L is the 12th letter, and N is the 14th letter. The difference in their positions is $14 - 12 = 2$. This matches the +2 pattern from the first pair.
Numbers: 144 and 196. We see that $144$ is the square of $12$ ($12^2$) and $196$ is the square of $14$ ($14^2$). This also matches the pattern where the number is the square of the corresponding letter's position.

The pattern is consistently applied: take the letter's position, square it for the number. The next term uses a letter two positions ahead and the square of its position.

Applying the Pattern to the Fifth Term: U441

Now, let's apply this established pattern to the fifth term, U441, to find the missing term.

Letter: U. In the English alphabet, U is the 21st letter.
Number: 441. We can confirm that $441$ is the square of $21$ ($21^2$). This fits the pattern $n^2$ for the first part of the term.

Following the pattern, the next term should:

Start with a letter that is 2 positions after U. Since U is the 21st letter, the letter will be the 21 + 2 = 23rd letter of the alphabet, which is W.
Be followed by the square of the position of the new letter (W). The position of W is 23. The square of 23 is $23^2$.

Let's calculate $23^2$:

$23^2 = 23 \times 23$

$23 \times 20 = 460$

$23 \times 3 = 69$

$460 + 69 = 529$

So, $23^2 = 529$.

The missing term is W529.

Concluding the Analogy

The pattern is clear: Letter at position 'n' paired with $n^2$, followed by the letter at position 'n+2' paired with $(n+2)^2$. Applying this to U441 (U is the 21st letter, $441 = 21^2$), the next term is W (23rd letter, $23 = 21 + 2$) paired with $23^2 = 529$. The missing term is W529.

Term 1	Term 2	Pattern Applied
H64	J100	H (8th) $\rightarrow$ 8²=64, J (10th) $\rightarrow$ 10²=100. Letters: +2 pos. Numbers: square of letter pos.
L144	N196	L (12th) $\rightarrow$ 12²=144, N (14th) $\rightarrow$ 14²=196. Letters: +2 pos. Numbers: square of letter pos.
U441	?	U (21st) $\rightarrow$ 21²=441, ? (23rd) $\rightarrow$ 23²=529. Letters: +2 pos. Numbers: square of letter pos.

Revision Table: Letter & Number Analogy

Concept	Description	Example (from question)
Letter Position	The numerical order of a letter in the alphabet (A=1, B=2, ... Z=26).	H=8, J=10, L=12, N=14, U=21, W=23
Letter Pattern	The rule for how letters change between terms (e.g., adding a fixed number of positions).	H (+2) $\rightarrow$ J, L (+2) $\rightarrow$ N, U (+2) $\rightarrow$ W
Number Pattern	The rule for how numbers change between terms (e.g., squaring the letter's position, adding a fixed number, etc.).	64 = 8², 100 = 10², 144 = 12², 196 = 14², 441 = 21², 529 = 23²
Combined Pattern	The rule connecting the letter and number components within each term and between terms.	Letter at 'n', number n² followed by Letter at 'n+2', number (n+2)²

Additional Information: Solving Letter-Number Series Questions

Letter-number series and analogy questions are common in reasoning tests. To solve them effectively, consider these strategies:

Identify Letter Pattern: Look at the sequence of letters. Are they alphabetical? Is there a fixed gap between them (+1, +2, -1, -2, etc.)? Is there a pattern based on vowels or consonants?
Assign Numerical Values to Letters: Often, converting letters to their position numbers (A=1, B=2, ...) helps reveal a numerical pattern related to the letters.
Identify Number Pattern: Look at the sequence of numbers. Are they increasing or decreasing? By a fixed amount (arithmetic progression)? By a fixed ratio (geometric progression)? Are they squares, cubes, primes, or following another sequence?
Look for Relationship Between Letter and Number: Is the number related to the letter's position (e.g., position number, square of position, double the position)?
Check for Alternating Patterns: Sometimes, the pattern might alternate between different rules or apply separately to odd and even terms.
Break Down Complex Terms: If a term has multiple parts (like a letter and a number), analyze each part's sequence independently first, then look for connections.

Practicing with various types of series helps in quickly identifying the underlying logic and applying it correctly to find the missing terms.

Prepp Team · Answer

W582

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V484

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V221