BCA Problem Solving 2 — Questions and Answers
Question 1: A store sells apples for $0.75 each and oranges for $0.50 each. If Maya spends exactly $5.00 buying a total of 8 fruits, how many apples did she buy?
- 2
- 3
- 4 (Correct answer)
- 5
Correct answer: 4
Let a = apples and o = oranges; 0.75a + 0.50o = 5.00 and a + o = 8, solving gives a = 4.
Question 2: A sequence follows the rule: each term is the sum of the two preceding terms (starting 2, 3, 5, 8, …). What is the 8th term?
- 21
- 34 (Correct answer)
- 55
- 13
Correct answer: 34
The sequence is 2, 3, 5, 8, 13, 21, 34, so the 8th term is 34.
Question 3: If it takes 6 workers 4 days to complete a job, how many days would it take 8 workers to complete the same job, assuming constant work rate?
- 2
- 3 (Correct answer)
- 5
- 6
Correct answer: 3
Total work = 6 × 4 = 24 worker-days; 24 ÷ 8 = 3 days.
Question 4: A rectangle's length is three times its width. If the perimeter is 48 cm, what is the area of the rectangle?
- 108 cm² (Correct answer)
- 72 cm²
- 144 cm²
- 96 cm²
Correct answer: 108 cm²
Width = 6, length = 18, so area = 6 × 18 = 108 cm².
Question 5: In a class of 30 students, 18 play soccer, 12 play basketball, and 5 play both. How many students play neither sport?
- 3
- 5 (Correct answer)
- 7
- 10
Correct answer: 5
Using inclusion-exclusion: 18 + 12 − 5 = 25 play at least one sport; 30 − 25 = 5 play neither.
Question 6: A car travels 120 miles at 40 mph, then 120 miles at 60 mph. What is the car's average speed for the entire trip?
- 48 mph (Correct answer)
- 50 mph
- 52 mph
- 54 mph
Correct answer: 48 mph
Total time = 3 + 2 = 5 hours; average speed = 240 ÷ 5 = 48 mph.
Question 7: How many distinct arrangements are there of the letters in the word 'LEVEL'?
- 30 (Correct answer)
- 60
- 120
- 20
Correct answer: 30
5! ÷ (2! × 2!) = 120 ÷ 4 = 30, accounting for two L's and two E's.
BCA Problem Solving 2
A store sells apples for $0.75 each and oranges for $0.50 each.
If Maya spends exactly $5.00 buying a total of 8 fruits, how many apples did she buy?