Two spies have to communicate using a secret code. they need to create exactly 30 possible precoded messages, using a single number and letter. which structure should the code have?

a.

select a number from {1, 2, 3, 4} and a vowel.

b.

select a number from {1, 2, 3, 4, 5} and a vowel.

c.

select a number from {1, 2, 3, 4, 5, 6} and a vowel.

d.

select a number from {1, 2, 3, 4, 5} and a consonant.

C. Select a number from {1, 2, 3, 4, 5, 6} and a vowel.

Step-by-step explanation:

Let's start this with a simple example: how many messages are possible using one number from {7, 9} and one letter from {a, b}. It will be 4 as 7a, 7b, 9a and  9b. This result can also come by multiplying the number of digits used and number of alphabets used - here number of digits are 2 (they are 7 and 9) and number of alphabets used are 2 (they are 'a' and 'b'). So 2 × 2 = 4.

[NOTE : In this question 7a and a7 are same]

Maximum number of options consists of vowels as letters so we will first find the number of digits needed if vowels are used as letters.

The number of vowels are 5 (they are 'a', 'e', 'i', 'o', 'u').

The number of possible precodes needed = 30

Let the number of digits needed be 'n'.

Then n × 5 = 30

∴ n = 6

Therefore the number of digits needed is 6 which is there in option C. The digits are {1, 2, 3, 4, 5, 6}

Therefore option C is the answer.