To encode a message, James first replaces each letter within the message with its
corresponding number, where A = 1, B = 2, · · · , Y = 25, and Z = 26. Next, James
multiplies each number by 3 and then subtracts 5, and continues this process a total
of n times. For example, when n = 2 the letter D is encoded to the number 16.
If James encoded a four letter message to the four numbers 367 205 853 1339, what
is the value of n that he used?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6

The value of n is 4. That means, the process is applied 4 times.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

To encode a message,

James first replaces each letter within the message with its corresponding number, where A = 1, B = 2, · · ·, Y = 25, and Z = 26. Next, James multiplies each number by 3 and then subtracts 5, and continues this process a total of n times.

To find the value of n:

We use process inversely.

Let m be the given number.

For example,

m = 16

The inverse process;

add 5 and then divide by 3 until we get the whole number.

So, first time

(16 + 5)/3 = 21/3 = 7,

Second time applying process,

(7+5)/3 = 4.

And the corresponding letter is D.

And the value of n is 2.

Now, m = 367

Applying process inversely,

First time,

(367 + 5) / 3 = 124

Second time,

(124+5)/3 = 43

Third time,

(43+5)/3 = 16

Fourth time,

(16+5)/3 = 7

m = 205

Applying process inversely,

First time,

(205+ 5) / 3 = 70

Second time,

(70+5)/3 = 25

Third time,

(25+5)/3 = 10

Fourth time,

(10+5)/3 = 5

m = 853

Applying process inversely,

First time,

(853+ 5) / 3 = 286

Second time,

(286+5)/3 = 97

Third time,

(97+5)/3 = 34

Fourth time,

(34+5)/3 = 13

m = 1339

Applying process inversely,

First time,

(1339+ 5) / 3 = 448

Second time,

(448+5)/3 = 151

Third time,

(151+5)/3 = 52

Fourth time,

(52+5)/3 = 19

We applied the process 4 times.

Therefore, the value of n is 4.

To learn more about the multiplication;

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