PCAT PCAT Certifications PCAT Questions & Answers

• Question 1:

  One pipe can fill a tank in 30 minutes. The tank can be drained by an other pipe in 70 minutes. If both pipes are opened, how long will it take to fill the tank?

  A. 21

  B. 52.5

  C. 36

  D. 40.6

  Correct Answer: B

• Question 2:

  George can run 25 miles in the same amount of time that his brother, Alan, can run 15 miles. If George runs 3 miles per hour faster than Alan, how fast does Alan run?

  A. 10

  B. 4.5

  C. 15

  D. 7.6

  Correct Answer: B

• Question 3:

  Find:

  

  A. -2/21

  B. 10

  C. -5/3

  D. 35

  Correct Answer: A

  

• Question 4:

  255 feet of fencing is needed to enclose a rectangular-shaped back yard. If the yard is 32 feet wide, what is the length?

  A. 121 ft

  B. 36.56 ft

  C. 95.5 ft

  D. 0.521 ft

  Correct Answer: C

  The perimeter of a rectangle can be calculated by using the following equation:

  P = 2L + 2W, where P = perimeter, L = length, W = width

  P = 2L + 2W 255 = 2L + 2 ?32 255 - 64 = 2L 191 = 2L L = 95.5 ft

• Question 5:

  What is the slope of the line passing through (2, 5) and (-1, -4) points?

  A. 5

  B. 6/5

  C. 3

  D. -1/2

  Correct Answer: C

  The slope (m) of the line can be calculated by using the following equation:

  

• Question 6:

  Simplify the following:

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  Correct Answer: B

  

• Question 7:

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

  A. 2x + 3

  B. (x - 2) / 3

  C. (3x - 2) / 3

  D. -2/3

  Correct Answer: B

  f(x) = y,

  y = 3x + 2 x = 3y + 2 (replacing x an y variables) x - 2 = 3y y = f-1(x) = (x ?2) / 3

• Question 8:

  If f(x) = x2 - 2x + 12 and g(x) = (x - 1), what is the value of function f(g(x))?

  A. x3 - 4x

  B. x2 - 4x + 15

  C. x2 - 8x + 17

  D. x2 + 4x - 15

  Correct Answer: B

  To solve this problem, we have to substitute x for g(x) in f(x).

  f(g(x)) = f (x - 1) = (x - 1)2 - 2(x - 1) + 12 = x2 - 2x + 1 - 2x + 2 + 12 = x2 - 4x + 15

• Question 9:

  If -10 3x + 4 < 20, what would be the interval notation of the value of x?

  A. (-14/3, )

  B. (, 16/3)

  C. [-14/3, 16/3]

  D. [-14/3, 16/3)

  Correct Answer: D

  Subtract 4 from all parts of the inequality, and then divide everything by 3 to find out the value of x:

  -10 3x + 4 < 20 -10 - 4 3x + 4 - 4 < 20 ?4 -14 3x < 16 -14/3 x < 16/3

  Therefore, the answer in interval form should be [-14/3, 16/3).

• Question 10:

  A school has 800 students. Of these, 400 students drink milk and 300 students drink coffee. 150 students drink both milk and coffee.

  How many students drink neither milk nor coffee?

  A. 175

  B. 250

  C. 325

  D. 450

  Correct Answer: B

  De Morgan's Laws:

  1.

  (A )' = A' B'

  2.

  (A )' = A' B'

  Let A be the set of students drinking milk, then n(A) = 400.

  Let B be the set of students drinking coffee, then n(B) = 300.

  The set of students drinking both milk and coffee is A B, therefore n(A B) = 150.

  Finally, let the set of students of the school be U, therefore n(U) = 800.

  The set of students drinking neither coffee nor milk should be A' B' = (A )':

  n(A )' = n(U) - n(A )

  = n(U) - [n(A) + n(B) - n(A B) = 800 - 400 ?300 + 150 = 250