A cryptography algorithm generates a numerical verification key, V, through a specific two… — State PSC Exam

A cryptography algorithm generates a numerical verification key, $V$ , through a specific two-step mathematical process. First, it determines the value of $K$ , which is strictly defined as the positive remainder when $-26$ is divided by $7$ . Second, it calculates the final key using the expression $V = K \times (18 \div 6 \times 3)$ . Based on the fundamental classification of numbers, which of the following accurately describes the final value of $V$ ?

It is a positive, even, and composite number.Answer
B
It is a negative, odd integer.
C
It is a positive, even, and prime number.
D
It is a positive, odd, and composite number.

Answer

The final value is 18, which is uniquely classified as a positive, even, and composite number.

By applying the formal definition of the modulo operation, the positive remainder of

-26

divided by

7

is found by the equation

-26 = 7 \times (-4) + 2

, giving

K = 2

. Next, using the correct order of operations (left to right for consecutive division and multiplication), the expression evaluates to

(18 \div 6) \times 3 = 3 \times 3 = 9

. Multiplying these results yields

V = 2 \times 9 = 18

. The number 18 is classified as positive (greater than zero), even (divisible by 2), and composite (having factors other than 1 and itself).

Step-by-Step Solution

Determine the positive remainder when

-26

is divided by

7

to find the value of

K

K = 2

By the formal definition of Euclidean division, the remainder must be non-negative. We must express

-26

7 \times (-4) + 2

, which gives a valid positive remainder of

2

Evaluate the mathematical expression

18 \div 6 \times 3

following the correct order of operations.

The expression evaluates to

9

According to the BODMAS rule, division and multiplication share the same level of precedence and must be evaluated strictly from left to right. Therefore,

(18 \div 6) = 3

, and

3 \times 3 = 9

Calculate the final value of the verification key

V

and classify it.

V = 2 \times 9 = 18

. The number

18

is a positive, even, and composite number.

The number

18

is greater than zero (positive), perfectly divisible by

2

(even), and possesses divisors other than

1

and itself, such as

2, 3,

and

6

(composite).

Key Concept

Classification of Numbers and Fundamental Arithmetic Operations

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