PCAT Quantitative Reasoning 3

Question 1

A right triangle has legs of length 7 and 24. What is the length of the hypotenuse?

Accepted Answer

25

Answer

Hypotenuse = √(7² + 24²) = √(49 + 576) = √625 = 25.

Question 2

Which of the following is equivalent to (x²y³)⁴ / (x³y²)?

Accepted Answer

x⁵y¹⁰

Answer

(x²y³)⁴ = x⁸y¹²; dividing by x³y² gives x⁵y¹⁰.

Question 3

What is the probability of rolling an even number on a standard six-sided die twice in a row?

Accepted Answer

1/4

Answer

P(even) = 3/6 = 1/2 each roll; combined probability = (1/2)(1/2) = 1/4.

Question 4

If 5x − 3 = 2x + 12, what is x?

Accepted Answer

5

Answer

5x − 2x = 12 + 3 → 3x = 15 → x = 5.

Question 5

A solution contains 45 mg of drug per 15 mL. What volume contains 120 mg?

Accepted Answer

40 mL

Answer

Concentration = 45/15 = 3 mg/mL; 120 mg ÷ 3 mg/mL = 40 mL.

PCAT - Pharmacy College Admission Test Practice Test