Crossover Aptitude Test Math 5 — Questions and Answers
Question 1: A tank is 1/4 full. After adding 30 gallons it is 3/4 full. What is the tank's total capacity?
- 50 gallons
- 60 gallons (Correct answer)
- 70 gallons
- 80 gallons
Correct answer: 60 gallons
3/4 - 1/4 = 1/2 of the tank equals 30 gallons, so capacity = 60 gallons.
Question 2: The probability of rain on any day is 0.3. What is the probability it does NOT rain on two consecutive days?
- 0.49 (Correct answer)
- 0.42
- 0.09
- 0.51
Correct answer: 0.49
P(no rain each day) = 0.7; P(no rain both days) = 0.7 × 0.7 = 0.49.
Question 3: Simplify: √75 + √27
- 5√3
- 8√3 (Correct answer)
- 10√3
- 6√3
Correct answer: 8√3
√75 = 5√3 and √27 = 3√3; sum = 8√3.
Question 4: A circle has a circumference of 20π. What is its area?
- 100π (Correct answer)
- 40π
- 400π
- 10π
Correct answer: 100π
2πr = 20π gives r = 10; Area = π(10)² = 100π.
Question 5: Which inequality holds true when x = 3?
- 2x + 1 < 5
- x² < 8
- x² > 8 (Correct answer)
- x/2 > 2
Correct answer: x² > 8
x² = 9 > 8 is true; the other options evaluate to false when x = 3.
Question 6: What is the greatest common factor (GCF) of 48, 72, and 120?
- 12
- 24 (Correct answer)
- 6
- 36
Correct answer: 24
48 = 2⁴×3, 72 = 2³×3², 120 = 2³×3×5; GCF = 2³×3 = 24.
Question 7: Worker A finishes a job in 6 hours; Worker B finishes it in 4 hours. How long do they take working together?
- 2.4 hours (Correct answer)
- 2.8 hours
- 3 hours
- 5 hours
Correct answer: 2.4 hours
Combined rate = 1/6 + 1/4 = 5/12 job/hr; time = 12/5 = 2.4 hours.
Crossover Aptitude Test Math 5
A tank is 1/4 full.
After adding 30 gallons it is 3/4 full.
What is the tank's total capacity?