Admission Tests Admission Tests Certifications PCAT Questions & Answers

• Question 51:

  i3 –i3/2 =

  

  A. Option

  B. Option

  C. Option

  D. Option

  Correct Answer: D

  Simplify the expression:

  

• Question 52:

  

  =

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  Correct Answer: C

• Question 53:

  If a recipe calls for 3 parts sugar and 2 parts milk, and a total of 45 oz is made, how much milk is there?

  A. 18 oz

  B. 9 oz

  C. 27 oz

  D. 18 parts

  Correct Answer: A

  The ratio of sugar to milk is 3x : 2x. Combining these and setting the amount equal to the given total:

  5x = 45 ?gt; x = 9 Plugging this back in to find the total amount of milk: 2 ?9 = 18 oz

• Question 54:

  ln e7 = 1 - x, what is x?

  A. 6

  B. ln 7 - e

  C. -6

  D. -ln e - 7

  Correct Answer: C

  Recall that ln e7 can be rewritten as 7 ?ln e and that ln e = 1. Rewriting the original expression and solving for x:

  7 ?1 = 1 - x ?gt; x = -6

• Question 55:

  What is 0.25% of 1/3?

  A. 0.83

  B. 0.083

  C. 0.0083

  D. 0.00083

  Correct Answer: D

  Convert 0.25% to a fraction and multiply it by 1/3:

  

• Question 56:

  What are the critical points of y = 4x2 + 3x?

  A. 0

  B. -3/ 8

  C. 0 and -3/8

  D. 0 and 3/8

  Correct Answer: B

  A critical point of a function is a point where the derivative of the function is equal to 0 or is undefined. Evaluate the derivative with respect to x, set it equal to 0, and solve for x:

  0 = 8x + 3 ?gt; x = -3/8

• Question 57:

  What is the x-intercept of y = e5x + 2?

  A. 2

  B. 0

  C. ln 2

  D. no x-intercept

  Correct Answer: D

  The x-intercept is where the function crosses the x-axis and can be found by setting the function equal to 0 and solving for x:

  0 = e5x + 2 ?gt; -2 = e5x

  To isolate the variable, take the natural log of both sides; however, ln -2 is undefined, so this function does not cross the x-axis.

• Question 58:

  The following are the results of a class test:

  65, 75, 87, 86, 78, 92, 77, 81, 82, 86, 21, 91, 3

  Which of the following is the best to use to quantify the overall performance on the exam?

  A. Mean

  B. Median

  C. Mode

  D. Standard Deviation

  Correct Answer: B

  Since there are a few extreme outliers: 3 and 21, which differ from the norm, it is better to use the median, which is unaffected by outliers, rather than the mean, which is affected by outliers.

• Question 59:

  How many solutions does the equation have?

  

  A. 3

  B. 2

  C. 1

  D. 0

  Correct Answer: C

  A solution to an equation is a value that when plugged in yields a true statement. Begin by isolating the square root and squaring both sides to eliminate it:

  

  Move all of the terms to one side and factor to solve for x:

  x2 − x − 2 = 0 –andgt; (x + 1) (x − 2) = 0 –andgt; x = −1, x = 2

  Check for extraneous solutions by plugging both solutions into the original equation:

  

  –andgt; 2 ≠ 0, so x = −1 is extraneous. –andgt; 0 = 0, so x = 2 is a solution. The equation has only 1 solution.

• Question 60:

  A man went to the store and bought pencils, pens, and erasers in the ratio of 2 : 4 : 3. If he bought 6 erasers then how many items total did he buy?

  A. 9

  B. 18

  C. 12

  D. 10

  Correct Answer: B

  The ratio can be expressed as: 2x : 4x : 3x, where 3x = 6 represents the number of erasers bought. Solving for x: x = 2, and plugging this value into the ratio: 2(2) : 4(2) : 3(2) ?gt; 4 : 8 : 6. Find the total number of items purchased by combining these numbers: 4 + 8 + 6 = 18.