Three mathematical values, X, Y, and Z, are defined below: - X = \frac{22}{7} - \pi - Y = … — State PSC Exam

Three mathematical values, $X$ , $Y$ , and $Z$ , are defined below:

- $X = \frac{22}{7} - \pi$
- $Y = \text{The positive remainder obtained when } -23 \text{ is divided by } 6$
- $Z = 2 + 18 \div 3 \times 2$

Based on the fundamental properties of numbers, which of the following statements correctly classifies all three values?

Value $X$ is an irrational number, $Y$ is neither prime nor composite, and $Z$ is an even composite number.Cevap
B
Value $X$ is an irrational number, $Y$ is neither prime nor composite, and $Z$ is an odd prime number.
C
Value $X$ is an irrational number, $Y$ is an odd prime number, and $Z$ is an even composite number.
D
Value $X$ is a rational number, $Y$ is neither prime nor composite, and $Z$ is an even composite number.

Cevap

Value

X

is an irrational number,

Y

is neither prime nor composite, and

Z

is an even composite number.

First,

X

is the difference between a rational number (

22/7

) and an irrational number (

\pi

), which results in a non-zero irrational number. Second, applying the division algorithm (

a = bq + r

where

0 \le r < b

), we evaluate

-23 = 6 \times (-4) + 1

. Thus, the positive remainder

Y

is 1, which is uniquely defined as a natural number that is neither prime nor composite. Finally, evaluating

Z

requires applying BODMAS rules from left to right for multiplication and division:

18 \div 3 = 6

, then

6 \times 2 = 12

, and

2 + 12 = 14

. The result 14 is an even composite number.

Adım Adım Çözüm

Evaluate and classify the value of

X = \frac{22}{7} - \pi

X

is a non-zero irrational number.

Since

22/7

is a rational approximation and not strictly equal to the irrational number

\pi

, their difference yields a non-zero irrational number.

Determine the true positive remainder of

-23 \div 6

to find

Y

Y = 1

, which is neither prime nor composite.

Using the division algorithm (

a = bq + r

where

0 \le r < b

), we write

-23 = 6 \times (-4) + 1

. The positive remainder is 1, a natural number defined as neither prime nor composite.

Calculate

Z = 2 + 18 \div 3 \times 2

using proper operational precedence.

Z = 14

, which is an even composite number.

According to BODMAS, division and multiplication are evaluated strictly from left to right before addition. Thus,

18 \div 3 = 6

, followed by

6 \times 2 = 12

, and finally

2 + 12 = 14

Anahtar Kavram

Classification of Real Numbers, Modulo Arithmetic, and Order of Operations

Soru

Cevap

Adım Adım Çözüm

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