Understanding Letter Number Analogies

This question asks us to find a relationship between a letter and a number pair (Y 2 : 4) and apply the same relationship to another letter and number pair (V 2 : ?). This type of problem is called a letter number analogy, which tests your ability to find patterns involving both letters and numbers.

Analyzing the First Pair: Y 2 : 4

Let's look closely at the first pair given: Y 2 is related to 4. We have the letter Y and the number 2, resulting in the number 4. We need to figure out how 4 is derived from Y and 2.

• The letter Y is involved. Letters often relate to their position in the alphabet. Y is the 25th letter.
• The number 2 is given.
• The result is 4.

Let's think about common patterns in analogies:

• Alphabet Position: Y is the 25th letter. How can 25 and 2 relate to 4? $25 \div ? = 4$? $25 \times ? = 4$? No obvious simple arithmetic.
• Alphabet Position from the End: What if we consider the position of the letter from the end of the alphabet?
  • Z is the 1st letter from the end.
  • Y is the 2nd letter from the end.

Now, consider the number 2 given in 'Y 2'. If we combine the position from the end (which is 2 for Y) and the given number 2, we can see a pattern: $2^2 = 4$. This matches the number 4 in the analogy (Y 2 : 4). This seems like a plausible pattern.

Applying the Pattern to the Second Pair: V 2 : ?

Let's apply the same pattern to the second pair: V 2 : ? We have the letter V and the number 2. We need to find the related number.

• Identify the position of the letter V from the end of the alphabet.
  • Z is 1st from the end.
  • Y is 2nd from the end.
  • X is 3rd from the end.
  • W is 4th from the end.
  • V is 5th from the end.
• The letter V is the 5th letter from the end of the alphabet.
• The given number is 2.
• According to the pattern discovered, the related number should be the square of the letter's position from the end of the alphabet.

So, the calculation is:

\( (\text{Position of V from end})^2 = 5^2 \)

Let's calculate \(5^2\):

\( 5^2 = 5 \times 5 = 25 \)

Therefore, the number that completes the series is 25.

Checking the Options

Let's compare our result with the given options:

Our calculated number is 25, which matches option 2.

Conclusion

The pattern in this letter number analogy is that the result is obtained by squaring the position of the letter from the end of the alphabet. For Y, which is the 2nd from the end, $2^2 = 4$. For V, which is the 5th from the end, $5^2 = 25$.

Revision Table: Key Concepts

Additional Information on Letter Series and Analogies

Letter series and analogies are common in logical reasoning sections of various exams. They can involve various patterns:

• Alphabetical Position: Using the numerical position of letters (A=1, B=2, etc.). Patterns might involve adding, subtracting, multiplying, or dividing these positions.
• Position from the End: Using the reverse numerical position of letters (Z=1, Y=2, etc.).
• Skipping Letters: Patterns like skipping a certain number of letters (A, C, E, G...).
• Vowels/Consonants: Patterns based on whether a letter is a vowel or a consonant.
• Combination with Numbers: As seen in this problem, combining letter positions with numerical operations (addition, subtraction, multiplication, division, squaring, cubing, etc.).
• Reversing Letters: Patterns might involve reversing the letter order or using mirror images.

To solve these problems, it's helpful to know the alphabetical positions (both forward and backward) and to systematically look for different types of patterns.