PCAT PCAT Certifications PCAT-SECTION3 Questions & Answers

• Question 21:

  Solve for x: x3 64x = 0

  A. x=± 8

  B. x=± 6

  C. x=± 4

  D. x=± 2

  Correct Answer: A

  In order to solve the equationx3 64x= 0 forx, you can apply factor analysis and solve for x in each term:

  

• Question 22:

  Solve for x: x2 12 x=36

  A. 2

  B. 3

  C. 4

  D. 6

  Correct Answer: D

  The first thing to do in solving the equationx2 12x=36 forxis to rewrite the equation by adding 36 to both sides and then to express the equation in terms of factors: x2 12x+ 36 = 0 (x6) · (x 6) = 0 Solving the equation forxyieldsx= 6.

• Question 23:

  What is the range of the data set?

  A. 3.7mL

  B. 4.5mL

  C. 5.8mL

  D. 9.8mL

  Correct Answer: D

  The range or the difference between the largest and smallest values in this data set is 12.2mL2.4mL=9.8mL.

• Question 24:

  Chemistry students performed nine volume measurements of a solution during a lab and obtained the

  following results:

  {2.4mL, 3.2mL, 3.7mL, 3.7mL, 4.5mL, 6.8mL, 7.3mL, 8.1mL, 12.2mL}

  What is the mode of the data set?

  A. 3.7mL

  B. 4.5mL

  C. 5.8mL

  D. 9.8mL

  Correct Answer: A

  The mode is the measurement that is the most frequent or common value in the data set. In this example, the mode is 3.7mL, because it occurs twice, more than any of the other measurements that occur only once.

• Question 25:

  Chemistry students performed nine volume measurements of a solution during a lab and obtained the

  following results:

  {2.4mL, 3.2mL, 3.7mL, 3.7mL, 4.5mL, 6.8mL, 7.3mL, 8.1mL, 12.2mL}

  What is the median of the data set?

  A. 3.7mL

  B. 4.5mL

  C. 5.8mL

  D. 9.8mL

  Correct Answer: B

  The median is the middle or center value of the data set arranged in ascending numerical order, or 4.5mL.

• Question 26:

  Chemistry students performed nine volume measurements of a solution during a lab and obtained the

  following results:

  {2.4mL, 3.2mL, 3.7mL, 3.7mL, 4.5mL, 6.8mL, 7.3mL, 8.1mL, 12.2mL}

  What is the mean of the data set?

  A. 3.7mL

  B. 4.5mL

  C. 5.8mL

  D. 9.8mL

  Correct Answer: C

  The mean of a data set is the arithmetic average of the values of the data set or

  

• Question 27:

  What is the probability that two cards drawn from a deck of cards are of a black suit (e.g., either clubs or spades) if the first card drawn is replaced before the second card is drawn?

  A. 1352/2704

  B. 676/2704

  C. 6/2704

  D. 2/2704

  Correct Answer: B

  Because the two drawings are made from a complete deck of cards, the two events are independent of one another. You first need to determine the probability of drawing a card of twosuits from a deck of cards. Out of a total of 52 cards, there are 13 cards of any suit and 26 cards of a black suit. The probability of drawing a card of a black suit, P(A), is 26/52. Because the first card is replaced before the second drawing, the probability of drawing a card of the same suit, P(B), is also 26/52. Thus, the probability of drawing two cards of the same suit is

  

• Question 28:

  Upon rolling a pair of dice, what is the probability that the sum of the two numbers on the dice is either 7 or 12?

  A. 1/6

  B. 1/36

  C. 5/36

  D. 7/36

  Correct Answer: D

• Question 29:

  What is the probability of selecting a face card of a spade suit from two standard decks of cards?

  A. 3/52

  B. 6/52

  C. 6/104

  D. 46/104

  Correct Answer: C

  You are asked to determine the probability of randomly selecting one face card (king, queen, or jack) of a spade suit from two standard decks of cards. Because there are two decks of cards, a single card can be selected from two decks inn= 104 different ways. Since there are 3 face cards of a spade suit in one deck of cards, such a card can be drawn from the two decks ins= 6 different ways. Thus, the probability that the selected card is a face card of a spade suit is:p=s/n= 6/104

• Question 30:

  What is the probability of selecting an ace of a red suit from a standard deck of cards?

  A. 1/52

  B. 2/52

  C. 48/52

  D. 50/52

  Correct Answer: B

  To determine the probability that a randomly selected card is an ace of a red suit, you should first note that a card can be selected from a deck inn= 52 different ways. Since there are two such aces (ace of hearts and ace of diamonds), then an ace can be drawn from the deck ins= 2 different ways. Thus, the probability that the selected card is an ace is: