BCA Problem Solving 2

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?

Accepted Answer

4

Answer

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?

Accepted Answer

34

Answer

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?

Accepted Answer

3

Answer

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?

Accepted Answer

108 cm²

Answer

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?

Accepted Answer

5

Answer

Using inclusion-exclusion: 18 + 12 − 5 = 25 play at least one sport; 30 − 25 = 5 play neither.

(BCA) Bergen County Academies Practice Test