In a certain code language, 'WIFE' is written as '172' and 'CAT' is written as '72'. How will 'SON' be written in that language?

Question

Prepp Team · Accepted Answer

Understanding the Coding Language Pattern

The question presents a coding language where words are converted into numbers. We are given two examples: 'WIFE' is coded as '172' and 'CAT' is coded as '72'. Our task is to figure out the rule governing this conversion and apply it to find the code for the word 'SON'.

Let's analyze the given examples using the alphabetical positions of the letters (A=1, B=2, ..., Z=26).

W = 23
I = 9
F = 6
E = 5

Sum of the alphabetical positions for 'WIFE':

$ \text{Sum}_{\text{WIFE}} = 23 + 9 + 6 + 5 = 43 $

The coded value is 172. How can we get 172 from 43? Notice that 172 is $ 43 \times 4 $. The word 'WIFE' has 4 letters. This suggests a potential pattern: (Sum of alphabetical positions) multiplied by (Number of letters in the word).

Let's test this rule with the second example, 'CAT'.

C = 3
A = 1
T = 20

Sum of the alphabetical positions for 'CAT':

$ \text{Sum}_{\text{CAT}} = 3 + 1 + 20 = 24 $

The word 'CAT' has 3 letters. Applying the potential rule:

$ \text{Code}_{\text{CAT}} = \text{Sum}_{\text{CAT}} \times \text{Number of letters in CAT} $

$ \text{Code}_{\text{CAT}} = 24 \times 3 = 72 $

This matches the given code for 'CAT'. So, the rule is confirmed: the code for a word is the product of the sum of the alphabetical positions of its letters and the number of letters in the word.

Applying the Rule to Find the Code for 'SON'

Now, let's apply this rule to the word 'SON'.

S = 19
O = 15
N = 14

First, calculate the sum of the alphabetical positions for 'SON':

$ \text{Sum}_{\text{SON}} = 19 + 15 + 14 = 48 $

The word 'SON' has 3 letters.

Now, apply the rule to find the code for 'SON':

$ \text{Code}_{\text{SON}} = \text{Sum}_{\text{SON}} \times \text{Number of letters in SON} $

$ \text{Code}_{\text{SON}} = 48 \times 3 $

$ \text{Code}_{\text{SON}} = 144 $

Therefore, 'SON' will be written as '144' in that code language.

Step-by-Step Calculation

Here's a summary of the steps for finding the code for 'SON':

Assign numerical values to the letters of 'SON' based on their alphabetical position (S=19, O=15, N=14).
Calculate the sum of these numerical values: $ 19 + 15 + 14 = 48 $.
Count the number of letters in the word 'SON', which is 3.
Multiply the sum of the values by the number of letters: $ 48 \times 3 = 144 $.
The resulting number, 144, is the code for 'SON'.

Let's look at the options provided:

244
144
241
141

Our calculated code, 144, matches the second option.

Letter Positions and Calculations
Word	Letter Values	Sum of Values	Number of Letters	Calculated Code (Sum x Letters)	Given Code
WIFE	23, 9, 6, 5	43	4	$ 43 \times 4 = 172 $	172
CAT	3, 1, 20	24	3	$ 24 \times 3 = 72 $	72
SON	19, 15, 14	48	3	$ 48 \times 3 = 144 $	?

Revision Table: Key Concepts in Coding-Decoding

Coding-Decoding Methods Overview
Method Type	Description	Example Rule
Letter Coding	Letters are replaced by other letters based on a pattern (e.g., shift, reverse alphabetical order).	Each letter shifted 3 positions forward (A becomes D).
Number Coding	Words are coded into numbers based on letter positions, counts, or other arithmetic operations.	Sum of letter positions, Product of letter positions, Sum/Product multiplied by letter count.
Symbol Coding	Letters or words are coded using symbols.	A @, B #, CAT @#$
Mixed Coding	Sentences or phrases are given with their codes, and you deduce the code for individual words.	'go home' is 'na ta', 'come home' is 'sa ta' --> 'home' is 'ta'.

Additional Information on Alphabetical Values

Assigning numerical values to letters based on their position in the standard English alphabet is a common technique in coding and decoding questions.

Here are the standard values:

Alphabetical Positions (1-26)
A-E	F-J	K-O	P-T	U-Y	Z
A=1, B=2, C=3, D=4, E=5	F=6, G=7, H=8, I=9, J=10	K=11, L=12, M=13, N=14, O=15	P=16, Q=17, R=18, S=19, T=20	U=21, V=22, W=23, X=24, Y=25	Z=26

Understanding these values and being able to quickly calculate sums or apply other operations based on them is crucial for solving many coding-decoding problems in reasoning sections of competitive exams. Practice with different types of patterns, such as adding/subtracting a constant value, reversing the alphabet (A=26, B=25, etc.), or combining letter values with other word properties like the number of letters or vowels/consonants.