Answer: C 1179

Explanation:

The problem requires us to compute the difference between 3202 and 2023. Let’s perform the subtraction step-by-step:

• Write the numbers vertically, aligning the digits by place value:

                  3202
                - 2023
                

• Subtract starting from the rightmost column (units place):
  • Units: \( 2 – 3 \). Since 2 is less than 3, borrow 10 from the tens place. The tens place is 0, so borrow from the hundreds place (2), reducing it to 1 and making the tens place 10. Now, \( 12 – 3 = 9 \).
  • Tens: After borrowing, tens place is \( 10 – 2 = 8 \).
  • Hundreds: After borrowing, hundreds place is \( 1 – 0 = 1 \).
  • Thousands: \( 3 – 2 = 1 \).
• Result:

                  3202
                - 2023
                ------
                  1179
                

Thus, \( 3202 – 2023 = 1179 \).

Verification: \( 2023 + 1179 = 3202 \) (Units: \( 3 + 9 = 12 \), carry 1; Tens: \( 2 + 7 + 1 = 10 \), carry 1; Hundreds: \( 0 + 1 + 1 = 2 \); Thousands: \( 2 + 1 = 3 \)).

Official Solution: \( 3202 – 2023 = 1179 \).

Correct answer: C: 1179.

Answer: C \( \frac{7}{12} \)

Explanation:

To add \( \frac{1}{4} + \frac{1}{3} \), we need a common denominator. The denominators are 4 and 3, and their least common multiple (LCM) is 12.

• Convert \( \frac{1}{4} \) to have denominator 12: \( \frac{1}{4} \times \frac{3}{3} = \frac{3}{12} \).
• Convert \( \frac{1}{3} \) to have denominator 12: \( \frac{1}{3} \times \frac{4}{4} = \frac{4}{12} \).
• Add the fractions: \( \frac{3}{12} + \frac{4}{12} = \frac{3 + 4}{12} = \frac{7}{12} \).

Since 7 and 12 have no common factors, \( \frac{7}{12} \) is in its simplest form.

Verification: Decimal approximation: \( \frac{1}{4} = 0.25 \), \( \frac{1}{3} \approx 0.333 \), \( 0.25 + 0.333 \approx 0.583 \), and \( \frac{7}{12} \approx 0.583 \), which matches.

Official Solution: \( \frac{1}{4} + \frac{1}{3} = \frac{3}{12} + \frac{4}{12} = \frac{7}{12} \).

Correct answer: C: \( \frac{7}{12} \).

Answer: C 420

Explanation:

We need to compute \( 20 \times 21 \). Let’s break it down:

• Express 21 as \( 20 + 1 \).
• Then, \( 20 \times 21 = 20 \times (20 + 1) = 20 \times 20 + 20 \times 1 \).
• Calculate: \( 20 \times 20 = 400 \), \( 20 \times 1 = 20 \).
• Add: \( 400 + 20 = 420 \).

Alternatively, direct multiplication:

              20
            × 21
            ----
              20 (20 × 1)
             400 (20 × 20)
            ----
             420
            

Verification: Check nearby values: \( 20 \times 20 = 400 \), \( 20 \times 22 = 440 \), so \( 20 \times 21 = 420 \) fits logically.

Official Solution: \( 20 \times 21 = 420 \).

Correct answer: C: 420.

Answer: B 12

Explanation:

To find 15% of 80, convert the percentage to a decimal and multiply:

• 15% = \( \frac{15}{100} = 0.15 \).
• \( 0.15 \times 80 = 12 \).

Alternatively: 10% of 80 is 8, 5% of 80 is 4 (half of 10%), so 15% = 10% + 5% = 8 + 4 = 12.

Verification: \( 12 \div 80 = 0.15 = 15\% \).

Official Solution: 15% of 80 = 12.

Correct answer: B: 12.

Answer: D 72

Explanation:

Calculate the expression step-by-step:

• \( 2^3 = 2 \times 2 \times 2 = 8 \).
• \( 3^2 = 3 \times 3 = 9 \).
• \( 8 \times 9 = 72 \).

Verification: Break it down: \( 8 \times 9 = 72 \) (e.g., \( 8 \times 10 = 80 \), \( 80 – 8 = 72 \)).

Official Solution: \( 2^3 \times 3^2 = 8 \times 9 = 72 \).

Correct answer: D: 72.

Answer: D 150

Explanation:

Convert hours to minutes (1 hour = 60 minutes):

• 2 hours = \( 2 \times 60 = 120 \) minutes.
• 0.5 hours = \( 0.5 \times 60 = 30 \) minutes.
• Total = \( 120 + 30 = 150 \) minutes.

Verification: \( 150 \div 60 = 2.5 \) hours.

Official Solution: \( 2.5 \times 60 = 150 \).

Correct answer: D: 150.

Answer:</

Answer: C 16 cm

Explanation:

For a square with area 16 cm²:

• Area = side², so side = \( \sqrt{16} = 4 \) cm.
• Perimeter = 4 × side = \( 4 \times 4 = 16 \) cm.

Verification: If perimeter = 16 cm, each side = \( 16 \div 4 = 4 \) cm, and area = \( 4^2 = 16 \) cm².

Official Solution: Side = \( \sqrt{16} = 4 \) cm, perimeter = \( 4 \times 4 = 16 \) cm.

Correct answer: C: 16 cm.

Answer: B 14

Explanation:

Examine the sequence: 2, 5, 8, 11.

• Differences: \( 5 – 2 = 3 \), \( 8 – 5 = 3 \), \( 11 – 8 = 3 \).
• The sequence increases by 3 each time.
• Next term: \( 11 + 3 = 14 \).

Verification: Pattern continues: 2, 5, 8, 11, 14 (differences all 3).

Official Solution: Each term increases by 3, so 11 + 3 = 14.

Correct answer: B: 14.

Answer: A 0.48

Explanation:

Multiply the decimals:

• \( 0.6 \times 0.8 = \frac{6}{10} \times \frac{8}{10} = \frac{48}{100} = 0.48 \).

Alternatively: \( 6 \times 8 = 48 \), then adjust for two decimal places: \( 0.48 \).

Verification: \( 0.48 \div 0.8 = 0.6 \), \( 0.48 \div 0.6 = 0.8 \).

Official Solution: \( 0.6 \times 0.8 = 0.48 \).

Correct answer: A: 0.48.

Answer: B \( \frac{9}{10} \)

Explanation:

Divide fractions by multiplying by the reciprocal:

• \( \frac{3}{5} \div \frac{2}{3} = \frac{3}{5} \times \frac{3}{2} \).
• \( \frac{3 \times 3}{5 \times 2} = \frac{9}{10} \).

Verification: \( \frac{9}{10} \times \frac{2}{3} = \frac{18}{30} = \frac{3}{5} \).

Official Solution: \( \frac{3}{5} \div \frac{2}{3} = \frac{3}{5} \times \frac{3}{2} = \frac{9}{10} \).

Correct answer: B: \( \frac{9}{10} \).

Answer: B 60 cm²

Explanation:

Area of a rectangle = length × width:

• Length = 12 cm, width = 5 cm.
• \( 12 \times 5 = 60 \) cm².

Verification: Perimeter = \( 2 \times (12 + 5) = 34 \) cm, but area is simply \( 12 \times 5 = 60 \).

Official Solution: \( 12 \times 5 = 60 \) cm².

Correct answer: B: 60 cm².

Answer: D 30

Explanation:

Find the least common multiple (LCM) of 2, 3, and 5:

• Prime factors: 2, 3, 5 (all distinct).
• LCM = \( 2 \times 3 \times 5 = 30 \).

Check: 30 ÷ 2 = 15, 30 ÷ 3 = 10, 30 ÷ 5 = 6 (all integers).

Smaller numbers fail: 10 (not divisible by 3), 15 (not divisible by 2), 20 (not divisible by 3).

Official Solution: LCM of 2, 3, 5 = 30.

Correct answer: D: 30.

Answer: C 10

Explanation:

Subtracting a negative is the same as adding the positive:

• \( 7 – (-3) = 7 + 3 = 10 \).

Verification: On a number line, start at 7, move 3 units right (adding 3), reach 10.

Official Solution: \( 7 – (-3) = 7 + 3 = 10 \).

Correct answer: C: 10.

Answer: D Right-angled

Explanation:

Check the angles:

• Sum: \( 30° + 60° + 90° = 180° \) (valid triangle).
• 90° indicates a right angle.

No sides are specified, but the presence of a 90° angle defines it as right-angled. (Note: It’s also a 30-60-90 triangle, a special right triangle, but “right-angled” is sufficient.)

Verification: Equilateral (all equal), isosceles (two equal), scalene (all different), obtuse (>90°) don’t fit.

Official Solution: The triangle has a 90° angle, so it is right-angled.

Correct answer: D: Right-angled.

Answer: B 16

Explanation:

Calculate using the difference of squares:

• \( 5^2 = 25 \), \( 3^2 = 9 \).
• \( 25 – 9 = 16 \).

Or: \( 5^2 – 3^2 = (5 – 3)(5 + 3) = 2 \times 8 = 16 \).

Verification: \( 25 – 9 = 16 \).

Official Solution: \( 5^2 – 3^2 = 25 – 9 = 16 \).

Correct answer: B: 16.

Answer: B 60 km/h

Explanation:

Average speed = total distance ÷ total time:

• Distance = 120 km, time = 2 hours.
• \( 120 \div 2 = 60 \) km/h.

Verification: \( 60 \times 2 = 120 \) km.

Official Solution: \( 120 \div 2 = 60 \) km/h.

Correct answer: B: 60 km/h.

Answer: B 9

Explanation:

Follow the order of operations (brackets first):

• \( 3 + 4 = 7 \).
• \( 2 \times 7 = 14 \).
• \( 14 – 5 = 9 \).

Verification: \( 2 \times 7 – 5 = 14 – 5 = 9 \).

Official Solution: \( 2 \times (3 + 4) – 5 = 2 \times 7 – 5 = 9 \).

Correct answer: B: 9.

Answer: C 78.5 cm²

Explanation:

Area of a circle = \( \pi r^2 \), where radius = diameter ÷ 2:

• Diameter = 10 cm, radius = \( 10 \div 2 = 5 \) cm.
• \( \pi \approx 3.14 \), so \( 3.14 \times 5^2 = 3.14 \times 25 = 78.5 \) cm².

Verification: Circumference = \( 2 \pi r = 2 \times 3.14 \times 5 = 31.4 \) cm, but area is \( 78.5 \).

Official Solution: \( \pi \times (5)^2 = 3.14 \times 25 = 78.5 \) cm².

Correct answer: C: 78.5 cm².

Answer: B 10

Explanation:

Order of operations (brackets first):

• \( 4 + 6 = 10 \).
• \( 100 \div 10 = 10 \).

Verification: \( 10 \times 10 = 100 \).

Official Solution: \( 100 \div (4 + 6) = 100 \div 10 = 10 \).

Correct answer: B: 10.

Answer: C 540°

Explanation:

Sum of interior angles of a polygon = \( (n – 2) \times 180° \), where \( n \) is the number of sides:

• Pentagon has 5 sides, so \( n = 5 \).
• \( (5 – 2) \times 180° = 3 \times 180° = 540° \).

Verification: Triangle = 180°, quadrilateral = 360°, pentagon = 540° (pattern: +180° per side).

Official Solution: \( (5 – 2) \times 180° = 540° \).

Correct answer: C: 540°.

Answer: A 6

Explanation:

Let the number be \( x \). Then:

• \( 2x + 5 = 17 \).
• Subtract 5: \( 2x = 17 – 5 = 12 \).
• Divide by 2: \( x = 12 \div 2 = 6 \).

Verification: \( 2 \times 6 + 5 = 12 + 5 = 17 \).

Official Solution: \( 2x + 5 = 17 \), so \( x = 6 \).

Correct answer: A: 6.

Answer: C 27 cm³

Explanation:

Volume of a cube = edge length³:

• Edge length = 3 cm.
• \( 3^3 = 3 \times 3 \times 3 = 27 \) cm³.

Verification: Surface area = \( 6 \times 3^2 = 54 \) cm², but volume = 27 cm³.

Official Solution: \( 3 \times 3 \times orsch= 27 \) cm³.

Correct answer: C: 27 cm³.

Answer: B 18

Explanation:

Calculate each part:

• \( \frac{1}{2} \) of 24 = \( \frac{1}{2} \times 24 = 12 \).
• \( \frac{1}{3} \) of 18 = \( \frac{1}{3} \times 18 = 6 \).
• Total = \( 12 + 6 = 18 \).

Verification: \( 12 + 6 = 18 \).

Official Solution: \( \frac{1}{2} \times 24 + \frac{1}{3} \times 18 = 12 + 6 = 18 \).

Correct answer: B: 18.

Answer: A \( \frac{1}{4} \)

Explanation:

Probability = favorable outcomes ÷ total outcomes:

• Total marbles = \( 3 + 4 + 5 = 12 \).
• Red marbles = 3.
• Probability = \( \frac{3}{12} = \frac{1}{4} \).

Verification: \( \frac{1}{4} = 0.25 \), and 3 out of 12 is 25%.

Official Solution: \( \frac{3}{12} = \frac{1}{4} \).

Correct answer: A: \( \frac{1}{4} \).

Answer: D 33

Explanation:

Let the integers be \( n \), \( n + 1 \), \( n + 2 \). Then:

• \( n + (n + 1) + (n + 2) = 96 \).
• \( 3n + 3 = 96 \).
• \( 3n = 93 \), \( n = 31 \).
• Integers: 31, 32, 33. Largest = 33.

Alternatively: Average = \( 96 \div 3 = 32 \), so numbers are 31, 32, 33.

Verification: \( 31 + 32 + 33 = 96 \).

Official Solution: \( 3n + 3 = 96 \), \( n = 31 \), largest = 33.

Correct answer: D: 33.