Number System MCQs with Answers & Explanations

Step 1: Natural numbers typically start at 1. Step 2: Whole numbers include 0, 1, 2, ... Step 3: Integers include ..., -1, 0, 1, ... Step 4: Therefore both whole numbers and integers include 0.

Step 1: Apply order of operations: exponents, then multiplication, then addition. Step 2: 2^2 = 4. Step 3: Multiply: 4*3 = 12. Step 4: Add: 6 + 12 = 18.

Step 1: (-3)^2 means the square of -3: (-3)*(-3) = 9. Step 2: -3^2 means the negative of 3^2: -(3*3) = -9. Step 3: Therefore (-3)^2 = 9 and -3^2 = -9.

Step 1: Use the negative exponent rule: a^-1 = 1/a for nonzero a. Step 2: 4^-1 = 1/4.

Step 1: The modulus gives the remainder after division. Step 2: 12 divided by 5 is 2 with remainder 2 (since 5*2 = 10, 12 - 10 = 2). Step 3: Therefore 12 mod 5 = 2.

Step 1: By convention, GCD(0, n) = n for n != 0. Step 2: Therefore GCD(0, 14) = 14. Step 3: Reason: any number divides 0, so the greatest common divisor with 14 is 14.

Step 1: A prime has exactly two distinct positive divisors. Step 2: A composite has more than two. Step 3: 0 has infinitely many divisors and does not meet either definition. Step 4: Therefore 0 is neither prime nor composite.

Step 1: Multiply fractions first: (3/4)*(2/3) = 6/12 = 1/2. Step 2: Then 1/2 of 18 = 18*(1/2) = 9.

Step 1: Divide both sides by 3: x = 18/3. Step 2: Compute 18/3 = 6.

Step 1: 0.25 = 25/100 = 1/4. Step 2: Since it can be expressed as a fraction of integers, it is rational. Step 3: It is not an integer or natural.

Step 1: Apply order of operations: multiply first. Step 2: 4*2 = 8. Step 3: Compute 15 - 8 + 3 = 7 + 3 = 10. Step 4: Therefore the correct answer is 10, so option B.

Step 1: Adding a positive to a negative moves right on the number line. Step 2: 12 - 5 = 7. Step 3: Therefore (-5) + 12 = 7.

Step 1: Subtracting 6 from -8 moves further left. Step 2: -8 - 6 = -14.

Step 1: Use exponent quotient rule: a^m / a^n = a^(m - n). Step 2: 3^4 / 3^2 = 3^(4 - 2) = 3^2. Step 3: 3^2 = 9; the simplest exponential form is 3^2.

Step 1: Raise numerator and denominator: (1^3)/(2^3) = 1/8. Step 2: Therefore (1/2)^3 = 1/8.

Step 1: 2/5 = 0.4 in decimal. Step 2: 0.4 = 0.40 when normalized to two decimal places. Step 3: 0.4 = 40% as a percentage. Step 4: All are equivalent representations.

Step 1: 7^2 = 49. Step 2: 5^2 = 25. Step 3: Subtract: 49 - 25 = 24.

Step 1: Align decimals: 0.60 + 0.15. Step 2: Add tenths and hundredths: 0.60 + 0.15 = 0.75.

Step 1: Multiply: (2/3)*45 = 2*15 = 30. Step 2: Therefore 2/3 of 45 is 30.

Step 1: The 1/2 power is the square root. Step 2: sqrt(9) = 3. Step 3: Therefore 9^(1/2) = 3.