what is the probability of consecutively pulling two more orange blocks without replacement from a bag containing 3 orange blocks 5 green blocks and 4

ATI TEAS 7

Math Practice TEAS Test

1. What is the probability of consecutively pulling two more orange blocks, without replacement, from a bag containing 3 orange blocks, 5 green blocks, and 4 purple blocks?

A. 3/12
B. 3/55
C. 2/10
D. 1/3

Correct answer: B

Rationale: To calculate the probability of consecutively pulling two more orange blocks without replacement, we first determine the probability of pulling an orange block on the first draw, which is 3/12 (3 orange blocks out of 12 total blocks). After removing one orange block, there are only 11 blocks left, so the probability of pulling another orange block on the second draw is 2/11. To find the combined probability, we multiply the probabilities together: (3/12) * (2/11) = 6/132 = 3/55. Therefore, the correct answer is B. Choice A (3/12) incorrectly simplifies the probability before calculating the second draw. Choice C (2/10) does not consider the specific number of orange blocks in the bag. Choice D (1/3) does not account for the reduced number of blocks after the first draw.

2. A driver drove 305 miles at 65 mph, stopped for 15 minutes, then drove another 162 miles at 80 mph. How long was the trip?

A. 6.44 hours
B. 6.69 hours
C. 6.97 hours
D. 5.97 hours

Correct answer: B

Rationale: To find the total trip duration, calculate the driving time for each segment and add the stop time. The driving time for the first segment is 305 miles ÷ 65 mph = 4.69 hours. The driving time for the second segment is 162 miles ÷ 80 mph = 2.025 hours. Adding the 15-minute stop (0.25 hours) gives a total time of 4.69 hours + 2.025 hours + 0.25 hours = 6.965 hours, which is closest to 6.69 hours (Choice B). Option A is incorrect as it miscalculates the total duration. Option C is incorrect as it overestimates the total duration. Option D is incorrect as it underestimates the total duration.

3. What is the solution to 4 x 7 + (25 – 21)²?

A. 512
B. 36
C. 44
D. 22

Correct answer: C

Rationale: To find the solution, first solve the expression inside the parentheses: 25 - 21 = 4. Then, square the result from the parentheses: 4² = 16. Next, perform the multiplication: 4 x 7 = 28. Finally, add the results: 28 + 16 = 44. Therefore, the correct answer is 44. Choice A (512), Choice B (36), and Choice D (22) are incorrect as they do not follow the correct order of operations for solving the given mathematical expression.

4. If you have a rectangle with a width of 5 inches and a length of 10 inches and scale it by a factor of 2, what will the new perimeter be?

A. 30 inches
B. 40 inches
C. 60 inches
D. 50 inches

Correct answer: C

Rationale: When a rectangle is scaled by a factor of 2, both the length and width are multiplied by 2. The new dimensions become width = 5 * 2 = 10 inches and length = 10 * 2 = 20 inches. Therefore, the new perimeter is calculated as 2 * (10 + 20) = 60 inches. Choice A, B, and D are incorrect as they do not reflect the correct calculation based on scaling the dimensions of the rectangle.

5. What is the result of dividing 8 by 4?

A. 2
B. 4
C. 6
D. 8

Correct answer: A

Rationale: To find the result of dividing 8 by 4, we divide 8 by 4, which equals 2. Choice B (4) is incorrect because it is the divisor, not the result of the division. Choice C (6) is incorrect as it is not the correct quotient. Choice D (8) is incorrect as it is the dividend, not the result of the division.