Crossover Aptitude Test Numerical Reasoning: Word Problems 5 — Questions and Answers
Question 1: A flight covers 2,800 miles. For the first half of the distance, the plane averages 560 mph. For the second half, it averages 700 mph. What is the average speed for the entire trip?
- 615 mph
- 622 mph (Correct answer)
- 630 mph
- 640 mph
Correct answer: 622 mph
Time for first 1,400 miles = 1,400÷560 = 2.5 hr; second = 1,400÷700 = 2 hr; avg speed = 2,800÷4.5 ≈ 622 mph.
Question 2: A box contains red and blue marbles in a 3:5 ratio. If there are 24 red marbles, how many marbles are there in total?
- 40
- 56
- 64 (Correct answer)
- 72
Correct answer: 64
If 3 parts = 24, then 1 part = 8; total parts = 3 + 5 = 8; total marbles = 8 × 8 = 64.
Question 3: A contractor charges $50 per hour plus a $200 flat fee for any job. If a customer's total bill is $650, how many hours did the contractor work?
- 7 hours
- 8 hours
- 9 hours (Correct answer)
- 10 hours
Correct answer: 9 hours
Hourly portion = $650 − $200 = $450; hours = $450 ÷ $50 = 9 hours.
Question 4: A school has 840 students and the student-to-teacher ratio is 28:1. If 30 more students enroll and the ratio must stay the same, how many additional teachers are needed?
- 1 (Correct answer)
- 2
- 3
- 4
Correct answer: 1
New enrollment = 870; new teachers needed = 870 ÷ 28 ≈ 31.07, so 32 total vs. current 30 — actually 840÷28 = 30 teachers; 870÷28 ≈ 31.07 → 31 teachers needed, so 1 additional.
Question 5: A salesman sold 3 products at $120 each and 5 products at $85 each. He receives a 10% commission on total sales. What is his commission?
- $54.50
- $78.50 (Correct answer)
- $61.50
- $71.50
Correct answer: $78.50
Total sales = 3×$120 + 5×$85 = $360 + $425 = $785; commission = 10% × $785 = $78.50.
Question 6: Water costs $0.004 per gallon. A household uses 8,500 gallons per month. What is their monthly water bill?
- $28.00
- $32.00
- $34.00 (Correct answer)
- $36.00
Correct answer: $34.00
Bill = 8,500 × $0.004 = $34.00.
Question 7: A store buys a TV for $400 and sells it at a 35% markup. Later, the store discounts the retail price by 10%. What is the final selling price?
- $486.00 (Correct answer)
- $504.00
- $520.00
- $540.00
Correct answer: $486.00
Retail price = $400 × 1.35 = $540; final price after 10% discount = $540 × 0.90 = $486.
Crossover Aptitude Test Numerical Reasoning: Word Problems 5
A flight covers 2,800 miles.
For the first half of the distance, the plane averages 560 mph.
For the second half, it averages 700 mph.
What is the average speed for the entire trip?