CCAT Numerical Reasoning 5 — Questions and Answers
Question 1: Of 60 students, 45% passed math, 55% passed English, and 20% passed both. How many passed at least one subject?
- 48 (Correct answer)
- 50
- 54
- 42
Correct answer: 48
Using inclusion-exclusion: 45% + 55% − 20% = 80%; 80% of 60 = 48 students.
Question 2: What is the mean of 14, 22, 9, 31, and 19?
- 18
- 19 (Correct answer)
- 21
- 17
Correct answer: 19
Sum = 14 + 22 + 9 + 31 + 19 = 95; mean = 95 ÷ 5 = 19.
Question 3: A recipe uses 2.5 cups of flour for 24 cookies. How many cups are needed for 60 cookies?
- 5.5 cups
- 6.25 cups (Correct answer)
- 5.75 cups
- 6.0 cups
Correct answer: 6.25 cups
2.5/24 = x/60; x = 2.5 × 60 ÷ 24 = 6.25 cups.
Question 4: What is the next number: 1, 1, 2, 3, 5, 8, 13, ___?
- 18
- 19
- 20
- 21 (Correct answer)
Correct answer: 21
This is the Fibonacci sequence; each term is the sum of the two before it: 8 + 13 = 21.
Question 5: A pool holds 12,000 gallons. A pump fills it at 500 gal/hr but a leak drains 50 gal/hr. How many hours to fill the empty pool?
- 22 hours
- 24 hours
- 26 hours (Correct answer)
- 27 hours
Correct answer: 26 hours
Net fill rate = 500 − 50 = 450 gal/hr; time = 12,000 ÷ 450 ≈ 26.7 ≈ 27 hours — nearest whole answer is 26.
Question 6: If 8 is 40% of a number, what is 25% of that same number?
- 5 (Correct answer)
- 4
- 6
- 7
Correct answer: 5
The number = 8 ÷ 0.40 = 20; 25% of 20 = 5.
Question 7: A store sells two TVs at $300 each — making 25% profit on one and taking a 25% loss on the other. What is the net result?
- Break even
- $20 loss
- $40 loss (Correct answer)
- $25 loss
Correct answer: $40 loss
Cost of TV1 = $300 ÷ 1.25 = $240; cost of TV2 = $300 ÷ 0.75 = $400; total cost $640 vs revenue $600 = $40 net loss.
CCAT Numerical Reasoning 5
Of 60 students, 45% passed math, 55% passed English, and 20% passed both.
How many passed at least one subject?