AMCAT Math 2 — Questions and Answers
Question 1: A train travels 360 km in 4 hours. If it increases its speed by 30 km/h, how long will it take to cover the same distance?
- 3 hours (Correct answer)
- 3.5 hours
- 2.5 hours
- 4 hours
Correct answer: 3 hours
Original speed = 360/4 = 90 km/h; new speed = 120 km/h; new time = 360/120 = 3 hours.
Question 2: If 2x + 3y = 12 and x - y = 1, what is the value of x?
- 2
- 3 (Correct answer)
- 4
- 5
Correct answer: 3
From x - y = 1, x = y + 1; substituting into 2(y+1) + 3y = 12 gives 5y = 10, y = 2, x = 3.
Question 3: A rectangle has a perimeter of 54 cm and its length is twice its width. What is the area of the rectangle?
- 162 cm² (Correct answer)
- 108 cm²
- 81 cm²
- 54 cm²
Correct answer: 162 cm²
2(l + w) = 54 and l = 2w gives 2(2w + w) = 54, so w = 9, l = 18; area = 18 × 9 = 162 cm².
Question 4: What is the compound interest on $5,000 at 10% per annum for 2 years, compounded annually?
- $1,000
- $1,050 (Correct answer)
- $1,100
- $1,025
Correct answer: $1,050
CI = 5000(1.1)² - 5000 = 5000(1.21) - 5000 = 6050 - 5000 = $1,050.
Question 5: The average of 5 numbers is 20. If one number is removed, the average becomes 18. What is the removed number?
- 22
- 26
- 28 (Correct answer)
- 30
Correct answer: 28
Sum of 5 numbers = 100; sum of remaining 4 = 72; removed number = 100 - 72 = 28.
Question 6: If log₂(32) = x, what is the value of x?
- 4
- 5 (Correct answer)
- 6
- 8
Correct answer: 5
2^x = 32 = 2^5, so x = 5.
Question 7: A bag contains 4 red, 5 blue, and 6 green balls. What is the probability of drawing a blue ball at random?
- 1/3
- 4/15
- 5/15 (Correct answer)
- 6/15
Correct answer: 5/15
Total balls = 15; P(blue) = 5/15 = 1/3.
AMCAT Math 2
A train travels 360 km in 4 hours.
If it increases its speed by 30 km/h, how long will it take to cover the same distance?