MPT Problem Solving 5

Question 1

A boat travels 24 miles upstream in 3 hours and returns downstream in 2 hours. What is the speed of the current?

Accepted Answer

2 mph

Answer

Upstream speed = 8 mph, downstream = 12 mph; current = (12−8)/2 = 2 mph.

Question 2

A coin is flipped and a standard die is rolled. What is the probability of getting heads and a number greater than 4?

Accepted Answer

1/6

Answer

P(heads) = 1/2; P(>4) = 2/6 = 1/3; combined = 1/2 × 1/3 = 1/6.

Question 3

A piece of wire 60 cm long is bent into a rectangle whose length is twice its width. What is the length?

Accepted Answer

20 cm

Answer

2(l+w) = 60 and l = 2w → 2(2w+w) = 60 → 6w = 60 → w = 10, l = 20.

Question 4

An investment grows from $500 to $605 in one year. What is the annual interest rate?

Accepted Answer

21%

Answer

Rate = (605 − 500)/500 = 105/500 = 0.21 = 21%.

Question 5

If x + y = 10 and x − y = 4, what is the value of x²− y²?

Accepted Answer

40

Answer

x² − y² = (x+y)(x−y) = 10 × 4 = 40.

(MPT) UCF Math Placement Test Practice Test