Crossover Aptitude Test Numerical Reasoning: Word Problems 5

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?

Accepted Answer

622 mph

Answer

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?

Accepted Answer

64

Answer

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?

Accepted Answer

9 hours

Answer

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?

Accepted Answer

1

Answer

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?

Accepted Answer

$78.50

Answer

Total sales = 3×$120 + 5×$85 = $360 + $425 = $785; commission = 10% × $785 = $78.50.

Crossover Aptitude Test Practice Test

Crossover Aptitude Test Practice Test

Crossover Aptitude Test Numerical Reasoning: Word Problems 5