BCA Problem Solving 3

Question 1

A water tank is 1/3 full. After adding 24 gallons, it is 3/4 full. What is the total capacity of the tank?

Accepted Answer

64 gallons

Answer

(3/4 − 1/3) × C = 24; (5/12) × C = 24; C = 64 gallons.

Question 2

If f(x) = 2x² − 3x + 1, what is f(−2)?

Accepted Answer

15

Answer

f(−2) = 2(4) − 3(−2) + 1 = 8 + 6 + 1 = 15.

Question 3

A ladder 13 feet long leans against a wall. The base is 5 feet from the wall. How high up the wall does the ladder reach?

Accepted Answer

12 feet

Answer

By the Pythagorean theorem: h = √(13² − 5²) = √(169 − 25) = √144 = 12 feet.

Question 4

A prize is split among three people in the ratio 2:3:5. If the total prize is $2,000, how much does the person with the largest share receive?

Accepted Answer

$1,000

Answer

Total parts = 10; largest share = (5/10) × $2,000 = $1,000.

Question 5

Two trains start from cities 300 miles apart and travel toward each other. Train A goes 60 mph and Train B goes 90 mph. In how many hours do they meet?

Accepted Answer

2 hours

Answer

Combined speed = 150 mph; time = 300 ÷ 150 = 2 hours.

(BCA) Bergen County Academies Practice Test

(BCA) Bergen County Academies Practice Test

BCA Problem Solving 3