AMCAT Math 3 — Questions and Answers
Question 1: The ratio of boys to girls in a class is 3:4. If there are 28 girls, how many students are in the class?
- 42
- 49 (Correct answer)
- 56
- 63
Correct answer: 49
If 4 parts = 28, then 1 part = 7; total parts = 7, so total students = 7 × 7 = 49.
Question 2: A shopkeeper bought an item for $240 and sold it at a 25% profit. What was the selling price?
- $280
- $290
- $300 (Correct answer)
- $310
Correct answer: $300
Selling price = 240 × 1.25 = $300.
Question 3: What is the value of √(0.0081)?
- 0.009
- 0.09 (Correct answer)
- 0.9
- 0.81
Correct answer: 0.09
√(0.0081) = √(81/10000) = 9/100 = 0.09.
Question 4: If a car depreciates at 10% per year, what is its value after 2 years if it originally cost $20,000?
- $16,000
- $16,200 (Correct answer)
- $18,000
- $17,800
Correct answer: $16,200
Value = 20000 × (0.9)² = 20000 × 0.81 = $16,200.
Question 5: Find the HCF of 48, 72, and 96.
- 12
- 16
- 24 (Correct answer)
- 48
Correct answer: 24
Prime factorization: 48=2⁴×3, 72=2³×3², 96=2⁵×3; HCF = 2³×3 = 24.
Question 6: A pipe can fill a tank in 6 hours and another pipe can drain it in 8 hours. If both are open simultaneously, how long to fill the tank?
- 12 hours
- 16 hours
- 20 hours
- 24 hours (Correct answer)
Correct answer: 24 hours
Net rate = 1/6 - 1/8 = 4/24 - 3/24 = 1/24 per hour; tank fills in 24 hours.
Question 7: If 3 men can complete a job in 12 days, how many days will 4 men take to complete the same job?
- 6 days
- 8 days
- 9 days (Correct answer)
- 10 days
Correct answer: 9 days
Total work = 3 × 12 = 36 man-days; with 4 men: 36/4 = 9 days.
AMCAT Math 3
The ratio of boys to girls in a class is 3:4.
If there are 28 girls, how many students are in the class?