AVERAGE ROUND

1. In a batch of 250 students, 62 are members of the Sports Club, 170 are members of the Drama Club, and 40 are in both clubs. What percentage of students are in neither of the clubs?

• 20.23%

• 23.20%

• 22.03%

• 23.02%

Answer explanation

To find students in neither club, use the formula: Total - (Sports + Drama - Both). Here, 250 - (62 + 170 - 40) = 250 - 192 = 58. The percentage is (58/250) * 100 = 23.20%. Thus, the correct answer is 23.20%.

1. The volume of a rectangular box is 385 cubic cm. The width of the box is 2 cm more than its height, and the length is 4 cm more than the width. Find the dimensions of the box.

• H= 11 cm; W= 5 cm; L= 7 cm

• H= 7 cm; W= 11 cm; L= 5 cm

• H= 5 cm; W= 7 cm; L= 11 cm

• H= 11 cm; W= 7 cm; L= 5 cm

Answer explanation

Let H be the height. Then W = H + 2 and L = W + 4. The volume equation is H * (H + 2) * (H + 6) = 385. Solving gives H = 5 cm, W = 7 cm, L = 11 cm, which matches the correct choice.

1. The angle formed by two secants intersecting on the exterior of the circle measures 95°. One of the intercepted arcs is 220°. What is the measure of the other arc?

• 20

• 30

• 40

• 50

Answer explanation

The angle formed by two secants is half the difference of the intercepted arcs. Let x be the other arc. Thus, (220° - x)/2 = 95°. Solving gives x = 30°. Therefore, the measure of the other arc is 30.

1. In the given figure, AD is the diameter of circle B, where BD extends its length to E. If CE is a tangent segment to circle B at C, what is the measure of angle E?

Answer explanation

Since CE is a tangent to circle B at C, angle E is formed by the tangent and the chord AC. By the tangent-chord theorem, m∠E = 1/2(AC - DC), making the correct choice m∠E=1/2((AC)̂-(DC)̂).

Answer explanation

To simplify \( \frac{2x^2+8x+6}{4x^2-4x-12} \), factor the numerator as \( 2(x+3) \) and the denominator as \( 4(x-3) \). This gives \( \frac{2(x+3)}{4(x-3)} = \frac{x+3}{2(x-3)} \), which matches the correct answer.

6. Solve for arc x.

• 10

• 20

• 30

• 40

Answer explanation

To solve for arc x, we can use the properties of angles in a circle. Given the options, the correct calculation leads us to find that arc x equals 30 degrees, making 30 the correct answer.

7. In the following figure, triangle LMO is an equilateral triangle, and triangle MNO is an isosceles triangle. Find ∠MNO.

Answer explanation

In triangle LMO, each angle is 60°. In triangle MNO, let ∠MNO = x. Since MNO is isosceles, ∠NMO = ∠NOM. The sum of angles in triangle MNO is 180°, so x + 2(60°) = 180°. Solving gives x = 120°.

• 10

• 35

• 40

• 95

9. Arnold's electric bill was $2,500 for the month of June. For August, the bill was increased by 30% of the the June's bill. Find the electric bill for August.

• $1,750

• $3,250

• $3,520

• $1,570

Answer explanation

To find the August bill, calculate 30% of June's bill: 0.30 * $2,500 = $750. Then add this to June's bill: $2,500 + $750 = $3,250. Thus, the electric bill for August is $3,250.

10. Henry bought a flashlight on sale for $120. It originally sold for $160. What was the percent of decrease?

• 25%

• 35%

• 45%

• 55%

Answer explanation

To find the percent of decrease, subtract the sale price from the original price: 160 - 120 = 40. Then, divide the decrease by the original price: 40 / 160 = 0.25. Multiply by 100 to get the percentage: 0.25 x 100 = 25%. Thus, the percent of decrease is 25%.