During a numerical assessment, a student is asked to calculate a final parameter N by dete… — State PSC Exam

During a numerical assessment, a student is asked to calculate a final parameter $N$ by determining three specific mathematical components:

- Component $A$ : The mathematically correct positive remainder when $-27$ is divided by $4$ .
- Component $B$ : The unit digit of the number $2^{120}$ .
- Component $C$ : The value of the arithmetic expression $8 + 12 \div 4$ .

The parameter is then calculated using the formula $N = A + B + C + 7$ . Assuming the student evaluates all components correctly, which of the following best describes the classification of the number $N$ ?

A
An odd prime number
B
An even composite number
An odd perfect squareCevap
D
An odd composite number that is not a perfect square

Cevap

The mathematically correct evaluation of the formula yields 25, which is classified as an odd perfect square.

When correctly calculated, Component A is 1, Component B is 6, and Component C is 11. Substituting these into the given formula yields

N = 1 + 6 + 11 + 7 = 25

. Because 25 is an odd number and can be expressed as

5^2

, it correctly falls under the classification of an odd perfect square.

Adım Adım Çözüm

Calculate Component A (the positive remainder of

-27 \div 4

)

A = 1

By definition of division,

-27 = 4 \times (-7) + 1

. The remainder must be a non-negative integer less than the divisor.

Calculate Component B (the unit digit of

2^{120}

)

B = 6

The unit digit of powers of 2 follows a cycle of 4 (2, 4, 8, 6). Since 120 is perfectly divisible by 4, the unit digit corresponds to the 4th position in the cycle, which is 6.

Calculate Component C (the value of

8 + 12 \div 4

)

C = 11

According to the BODMAS rule, division must be performed before addition. First,

12 \div 4 = 3

. Then,

8 + 3 = 11

Calculate the final parameter

N

using the formula

N = A + B + C + 7

N = 1 + 6 + 11 + 7 = 25

Substituting the correctly evaluated components yields

25

, which is equal to

5^2

(an odd perfect square).

Anahtar Kavram

Classification of numbers based on proper mathematical operations, modular arithmetic, and cyclicity rules.

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru