there are 15 yellow and 35 orange balls in a basket how many more yellow balls must be added to make the yellow balls 65

HESI A2

HESI A2 Math Practice Exam

1. How many more yellow balls must be added to the basket to make the yellow balls constitute 65% of the total number of balls?

A. 35
B. 50
C. 65
D. 70

Correct answer: B

Rationale: To find the total number of balls needed to make the yellow balls 65% of the total, let x be the total number of balls required. Initially, there are 15 yellow balls. The total number of balls would be 15 + x after adding more yellow balls. The equation to represent this is: (15 + x) / (15 + x) = 0.65 (since the yellow balls need to constitute 65% of the total). Solving this equation gives x = 50, indicating that 50 more yellow balls need to be added to the basket to reach the desired percentage. Choice A, C, and D are incorrect as they do not accurately represent the additional yellow balls needed to achieve the specified percentage.

2. Subtract 6 1/2 - 2 2/3.

A. 4 1/6
B. 3 1/3
C. 3 5/6
D. 4 1/3

Correct answer: A

Rationale: To subtract mixed numbers, find a common denominator. Converting 6 1/2 to 6 3/6 and 2 2/3 to 2 4/6, the calculation becomes 6 3/6 - 2 4/6 = 4 1/6. Therefore, the correct answer is A. Choice B (3 1/3) is incorrect as the correct result is not an improper fraction. Choice C (3 5/6) is incorrect as it does not represent the result of the subtraction. Choice D (4 1/3) is incorrect as it does not match the correct calculation.

3. What is 25% of 200?

A. 50
B. 60
C. 25
D. 30

Correct answer: A

Rationale: To find 25% of a number, you multiply the number by 0.25. So, to calculate 25% of 200, you do 0.25 Ã— 200 = 50. Therefore, the correct answer is A. Choice B (60) is incorrect as it is the result of calculating 30% of 200. Choice C (25) is incorrect as it represents 12.5% of 200. Choice D (30) is incorrect as it is the result of calculating 15% of 200.

4. The length of a rectangle is twice its width, and its area is equal to the area of a square with 12 cm sides. What will be the perimeter of the rectangle to the nearest whole number?

A. 36 cm
B. 46 cm
C. 51 cm
D. 56 cm

Correct answer: A

Rationale: Let the width of the rectangle be x cm, and its length be 2x cm. The area of the rectangle is 2x * x = 2xÂ², and the area of the square is 12Â² = 144 cmÂ². Setting the areas equal gives 2xÂ² = 144. Solving for x gives x = 6. Thus, the width is 6 cm, and the length is 12 cm. The perimeter is 2(6 + 12) = 36 cm. Therefore, the correct answer is 36 cm. Choice B, 46 cm, is incorrect because it does not match the calculated perimeter. Choices C and D are also incorrect as they do not reflect the correct calculation of the rectangle's perimeter.