Solving Letter and Number Analogy Questions

This question asks us to find the relationship between a letter and a number and apply that same relationship to another letter to find its corresponding number. The analogy is given as F : 216 :: L : ?

Let's break down the analogy:

• F is related to 216.
• L is related to an unknown number.

Identifying the Pattern: F to 216

First, we need to determine the position of the letter 'F' in the English alphabet. The alphabet starts with A=1, B=2, C=3, and so on.

• A = 1
• B = 2
• C = 3
• D = 4
• E = 5
• F = 6

So, the alphabetical position of F is 6.

Now, let's look at the number 216. Can we find a mathematical relationship between 6 and 216? We can try simple operations like squaring or cubing the number.

• $6^2 = 6 \times 6 = 36$
• $6^3 = 6 \times 6 \times 6 = 36 \times 6 = 216$

We can see that 216 is the cube of the alphabetical position of the letter F.

The pattern seems to be: Number = (Alphabetical Position of Letter)$^3$

Applying the Pattern: L to ?

Now, let's apply this same pattern to the letter 'L'.

Find the alphabetical position of 'L':

• A = 1, ..., F = 6, ..., K = 11, L = 12

The alphabetical position of L is 12.

According to the pattern, the related number for L should be the cube of its alphabetical position (12).

Calculate $12^3$:

$\text{Number} = 12^3 = 12 \times 12 \times 12$

First, calculate $12 \times 12 = 144$.

Next, calculate $144 \times 12$:

Using multiplication:

  144
x  12
-----
  288 (144 x 2)
1440 (144 x 10)
-----
1728

So, $12^3 = 1728$.

Comparing with Options

The number related to L based on the pattern is 1728. Let's check the given options:

1. 1728
2. 1700
3. 1600
4. 1723

Our calculated number, 1728, matches the first option.

Conclusion on Letter and Number Analogy

The relationship in this analogy is that the number is the cube of the alphabetical position of the letter. F is the 6th letter, and $6^3 = 216$. L is the 12th letter, and $12^3 = 1728$.

Revision Table: Key Concepts for Analogies

Additional Information: Solving Letter-Number Reasoning

Letter-number reasoning questions often combine alphabetical positions with mathematical operations. To solve these questions effectively, it's helpful to:

• Know the alphabetical positions of letters instantly.
• Be familiar with common mathematical patterns (squares, cubes, prime numbers, arithmetic/geometric progressions).
• Look for patterns in the differences or ratios between numbers if direct operations on the position don't work.
• Sometimes, the pattern might involve reverse alphabetical order (Z=1, Y=2, etc.).
• Consider vowel/consonant positions or groups.

Practice with different types of letter-number analogy and series questions helps in quickly identifying the underlying rule.