In a code language, if PEN is written as 17717, then how will CAP be written in the same language?

Question

Prepp Team · Accepted Answer

Understanding the Code Language Pattern

This question involves decoding a simple code language based on a given example. We are told that the word PEN is coded as 17717. We need to find the code for the word CAP using the same logic.

Analysing the Code for PEN (17717)

Let's look at the letters in PEN and their positions in the English alphabet:

P is the 16th letter.
E is the 5th letter.
N is the 14th letter.

Now, let's compare these positions with the coded digits 17717. The coded form has five digits, but the word PEN has only three letters. However, the coded form can be seen as three separate numbers corresponding to the three letters: 17, 7, and 17.

Let's see if there's a pattern relating the letter positions to these numbers:

For P (16th letter), the code is 17. The difference is \(17 - 16 = 1\).
For E (5th letter), the code is 7. The difference is \(7 - 5 = 2\).
For N (14th letter), the code is 17. The difference is \(17 - 14 = 3\).

It appears the pattern is to take the alphabetical position of the letter and add a number based on its position in the word (1st letter adds 1, 2nd letter adds 2, 3rd letter adds 3). Let's verify this pattern with PEN:

1st letter is P: Position is 16. Add 1. \(16 + 1 = 17\). This matches the first part of the code.
2nd letter is E: Position is 5. Add 2. \(5 + 2 = 7\). This matches the second part of the code.
3rd letter is N: Position is 14. Add 3. \(14 + 3 = 17\). This matches the third part of the code.

The pattern is confirmed: Code = (Alphabetical Position of Letter) + (Position of Letter in the Word).

Applying the Code Logic to CAP

Now we apply the same logic to the word CAP:

C is the 1st letter of CAP and the 3rd letter of the alphabet. Its position in the word is 1.
A is the 2nd letter of CAP and the 1st letter of the alphabet. Its position in the word is 2.
P is the 3rd letter of CAP and the 16th letter of the alphabet. Its position in the word is 3.

Let's calculate the coded value for each letter in CAP:

For C (1st letter of CAP): Alphabetical position is 3. Add its position in the word (1). Code for C = \(3 + 1 = 4\).
For A (2nd letter of CAP): Alphabetical position is 1. Add its position in the word (2). Code for A = \(1 + 2 = 3\).
For P (3rd letter of CAP): Alphabetical position is 16. Add its position in the word (3). Code for P = \(16 + 3 = 19\).

Combining the coded values for C, A, and P in order, we get 4, 3, and 19.

So, the code for CAP is 4319.

Word	Letter	Alphabetical Position	Position in Word	Calculation	Coded Value
PEN	P	16	1st	\(16 + 1\)	17
	E	5	2nd	\(5 + 2\)	7
	N	14	3rd	\(14 + 3\)	17
Coded PEN: 17717
CAP	C	3	1st	\(3 + 1\)	4
	A	1	2nd	\(1 + 2\)	3
	P	16	3rd	\(16 + 3\)	19
Coded CAP: 4319

Therefore, following the same code language logic used for PEN, the word CAP is written as 4319.

Revision Table: Key Concepts

Concept	Description	Application in Problem
Coding Language	A system where words or letters are represented by numbers, symbols, or other patterns based on specific rules.	Decoding the rule for PEN=17717.
Alphabetical Position	The sequential number of a letter in the standard alphabet (A=1, B=2, ... Z=26).	Used as the base value for each letter in the code.
Positional Increment	Adding a value that depends on the position of the letter within the word being coded (e.g., 1st letter gets +1, 2nd gets +2, etc.).	The key pattern identified: add 1 for the 1st letter, 2 for the 2nd, 3 for the 3rd.

Additional Information: Types of Letter Coding

Letter coding is a common type of question in logical reasoning tests. Understanding different patterns helps solve these puzzles. Some common patterns include:

Alphabetical Position: Using the direct position (A=1, B=2) or reverse position (A=26, B=25).
Shifting: Shifting letters a fixed number of places forward or backward (e.g., A becomes C, B becomes D - a +2 shift).
Opposite Letters: Coding letters by their opposite (A is coded as Z, B as Y, etc.).
Vowel/Consonant Based: Different rules for vowels and consonants.
Patterned Increment/Decrement: Adding or subtracting values based on the letter's position in the word, as seen in this problem, or other sequences.
Substitution: Replacing letters with specific symbols or other letters according to a key.

Practicing different types of letter coding helps improve pattern recognition skills.