Post Your Scaled Score/Percentile

[TennisBoy78]

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Looking to find out correlations between scaled scores and percentiles. From reading various scores on each subsection, a small increase in the scaled score generally means larger increases in percentile jumps.

My scores are average for the most part except for one section. Here they are:

Verbal 407 63
Biology 402 57
Reading 396 43
Quantitative 383 25
Chemistry 400 54
Composite 398 47

Although these scores are not stellar, I've seen some messages in this forum and have talked to some classmates who got a few more points (like increases from 400 to 420 on a certain subsection) whose percentile jumped to 70-80 percentile (from 50th).

What this means to me is that just a few questions on each section separates a good score from an average score.

If you please, post your scaled score and percentile for each section. Only posting your percentile does nothing for me.

Thanks for your input!

 

[RyanMaverick]

I'll post this and hope it helps you, but there really is absolutely no way to correlate scaled scores to a raw score unless you're a Harcourt statistician. You have to remember that this is all curved and with a huge number of test takers, values around the median (400) are going to be very compact. You may have gotten 80% as a raw score, but if at least half the test takers got that score or better, then you're in the 50th percentile with a 400 scaled score. You just have to outdo the competition. I also have posted my online practice test results (which I did under exam conditions) on the "I got my PCAT score" thread so that people can use it to guage their progress on the practice exam compared to the actual test. While I'm unsure whether I just performed much better on the actual exam or not, I'm pretty sure that they are nearly the same as I had the same preparation and exam strategy for both.
Hope this helps!
~Ryan

Verbal: 427 - 87%
Biology: 433 - 90%
Reading: 462 - 99%
Quant: 452 - 97%
Chem: 460 - 98%
Writing Score = 4

Composite: 447 - 99%

 

[starrfishes]

Oh my God, those individual scores look so much like mines...
Are you going to re-take the PCATs?

Just wondering...

Looking to find out correlations between scaled scores and percentiles. From reading various scores on each subsection, a small increase in the scaled score generally means larger increases in percentile jumps.

My scores are average for the most part except for one section. Here they are:

Verbal 407 63
Biology 402 57
Reading 396 43
Quantitative 383 25
Chemistry 400 54
Composite 398 47

Although these scores are not stellar, I've seen some messages in this forum and have talked to some classmates who got a few more points (like increases from 400 to 420 on a certain subsection) whose percentile jumped to 70-80 percentile (from 50th).

What this means to me is that just a few questions on each section separates a good score from an average score.

If you please, post your scaled score and percentile for each section. Only posting your percentile does nothing for me.

Thanks for your input!

 

[TennisBoy78]

Oh my God, those individual scores look so much like mines...
Are you going to re-take the PCATs?

Just wondering...

Absolutely, it is necessary. If you got similar scores, I feel that you should consider it also. I will commit a lot more time to this test, especially with math concepts. However, I feel a little jipped by my verbal and reasoning scores.

Although I don't feel as though I am the most versed person when it comes to language, the words in the verbal and passages in the reading were not difficult to comprehend, and it would be difficult to employ a way to study for this. It can be done with practice, but verbal and reading is not an exact science, so I don't know how to exactly go about it. I felt very confident that I would excel in these areas because I never made below an "A" in any English Comp or Lit class and because writing comes natural to me. But I just have to accept this and will try to find a solution somehow.

I will retake it in June, but feel that it should be the last time. If the scores do not improve to the level that the schools I am applying, I will have to have a heart to heart talk with them. If pharmacy school (or college in general) was based on SATs, PCATs, GREs alone, I would not be fit to step in the classroom the first day. But my academic record (3.7) and appeal to professors and fellow classmates should indicate that I can be successful in the long run. The PCAT is a once in a lifetime deal, unless you take it more than once. Pharmacy school, on the other hand, presents daily challenges.

This is not to say that I am off the hook for the PCAT, but that the PCAT alone should not define me or my abilities.

Good luck to you and hopefully this won't keep us from getting into Pharmacy School! Implementing a different game plan is crucial for my success but I also realize that it may still not be good enough to obtain the scores needed. However, I will make sacrifices for this because the importance of getting into Pharmacy School trumps my inner desire to discredit or invalidate the significance of the PCAT.

 

[Plion]

Absolutely, it is necessary. ood enough to obtain the scores needed. However, I will make sacrifices for this because the importance of getting into Pharmacy School trumps my inner desire to discredit or invalidate the significance of the PCAT.

Tell me, did anyone find these questions on the exam?

Math Test per some SAT book:

Question # 1 of 58
If the square root of x is greater than x, then x could be:

A. 0
B. 1/2
C. 2
D. 4

Reasoning:
Consider each possible answer:
1. square root of zero is 0 which is not greater than 0
2. square root of 1/2 is .707 which is greater than 1/2 (.5)
3. square root of 2 is 1.414 which is not greater than 2
4. square root of 4 is 2 which is not greater than 2

Question # 2 of 58
If the average (arithmetic mean) of a series of numbers is 20 and their sum is 160, how many numbers are in the series?

A. 8
B. 16
C. 32
D. 48

Reasoning:
The average is found by taking the sum of a list of numbers and dividing the sum by the number in the list. If n is the number of numbers in the series, 160 / n = 20, so n = 8 numbers.

Question # 3 of 58
The Pentagon building in Washington, D.C., is shaped like a regular pentagon. If the length of one side of the Pentagon is represented by n + 2, its perimeter would be represented by:

A. 5n + 10
B. 5n + 2
C. n + 10
D. 10n

Reasoning:
A regular pentagon has 5 sides of equal length. The perimeter would be 5(n+2) which equals 5n+10.

Question # 4 of 58
If x = 32 - 16 ÷ 2 X 4, then x =

A. 0
B. 2
C. 4
D. 8

Reasoning:
Given x = 32 - 16 ÷ 2 X 4, find the value of x by working from left to right, doing any divisions and multiplications before any additions or subtractions
x = 32 - 16 ÷ 2 X 4
x = 32 - 8 X 4
x = 32 - 32
x = 0

Question # 5 of 58
If 12x - 4y = 12, 4y - 11z = 17, and 11z - 4x = 11, what is the value of x?

A. Cannot be determined.
B. 5
C. -8
D. 8

Reasoning:
Adding the three equations gives 12x - 4x = 12 + 17 + 11.
So, 8x = 40 or x = 5.

Question # 6 of 58



A. 2[f👎]2
B. 2f👎 - [f👎]2
C. 2f👎 + [f👎]2
D. 2[f👎]2 - [f👎]4

Reasoning:



Question # 7 of 58
The measures of the angles in a triangle are in the ratio of 1:2:6. Find the number of degrees in the largest angle of the triangle.

A. 20º
B. 40º
C. 90º
D. 120º

Reasoning:
The angles of a triangle add to 180º. x + 2x + 6x = 180
9x=180
x=20
Be careful! The question asks for the LARGEST angle. Substitute:6x=6(20)=120º

Question # 8 of 58
Solve for x: x/(x+8) = 5/15

A. 3
B. 4
C. 5
D. 6

Reasoning:
Cross multiply and solve. 15x = 5(x + 8)
15x = 5x + 40
10x = 40
x = 4

Question # 9 of 58
The slope of a vertical line is:

A. 0
B. 1
C. -1
D. undefined.

Reasoning:
A vertical line has "rise" but no "run". Thus, the denominator in the rise/run formula is 0 and it is an undefined fraction.

Question # 10 of 58
The direct distance between city A and city B is 200 miles. The direct distance between city B and city C is 300 miles. Which could be the direct distance between city C and city A?

A. 50 miles.
B. 350 miles.
C. 550 miles.
D. 650 miles.

Reasoning:
Picture the three cities forming a triangle. (According to the answers, the three cities do not form a straight line.) The sides of a triangle are related in such a manner that the adding of any two sides of the triangle must give a value larger than any single side of the triangle. The value 350 is the only choice that will uphold this relationship.

Question # 11 of 58
If x(y+z)= w and x, y, z, and w are all integers, which of the following must be true?

A. x(y + z) > 0
B. xy + z = w
C. xy + xz = w
D. x, y, z and w are all positive

Reasoning:
Choice 3 shows the distributive property at work. While the other choices may or may not be true, the distributive property is always true.


Question # 12 of 58
Two-fifths of the caps in a box are red, one-fourth are blue, and the rest are green. What is the ratio of the green caps to the blue caps?

A. 7:8
B. 8:7
C. 5:7
D. 7:5

Reasoning:
Let there be y caps in the box. Then, there are 2y/5 red caps.
One-fourth of the caps are blue. So, there are y/4 blue caps.
Therefore, number of green caps = y - 2y/5 - y/4 = (20y - 8y - 5y)/20 = 7y/20.
Ratio of green caps to blue caps = (7/20) ÷ (1/4) = (7/20) x 4 = 7/5

Question # 13 of 58
Which of the following is a prime number?

A. 11
B. 9
C. 0.5
D. 6

Reasoning:
A prime number is a whole number that cannot be divided by any other whole number but itself or 1.

Question # 14 of 58
Two-fifths of the caps in a box are red, one-fourth are blue, and the rest are green. What is the ratio of the green caps to the blue caps?

A. 7:8
B. 7:5
C. 5:7
D. 5:8

Reasoning:
Let there be y caps in the box. Then, there are 2y/5 red caps.
One-fourth of the caps are blue. So, there are y/4 blue caps.
Therefore, number of green caps = y - 2y/5 - y/4 = (20y - 8y - 5y)/20 = 7y/20.
Ratio of green caps to blue caps = (7/20) ÷ (1/4) = (7/20) x 4 = 7/5 or 7:5.

Question # 15 of 58
In an Easter egg-hunt, all eggs of the same color are worth the same number of points. If one player finds 2 red eggs and 4 blue eggs for a total score of 24 points, and another player collects 3 red tokens and 2 blue tokens for a total score of 16 points, how many points is a blue token worth?

A. 2
B. 4
C. 5
D. 6

Reasoning:
We want to set up two equations here and solve for blue tokens.
2R + 4B = 24, 2R = 24 - 4B, 2R/2 = (24 - 4B)/2, R = 12 - 2B
3R + 2B = 16
substituting: 3(12 - 2B) + 2B = 16
36 -6B + 2B = 16
20 = 4B
5 = B

Question # 16 of 58
A pair of dice is rolled. A possible event is rolling a multiple of 5. What is the probability of the complement of this event?

A. 2/36
B. 12/36
C. 29/36
D. 32/36

Reasoning:
Multiples of 5: 5, 10
There are 7 ways to roll a 5 or 10.
P(multiple of 5)=7/36
P(complement)=1-7/36=29/36

Question # 17 of 58
Which of the following are true for all real numbers x, y and z?
I. x(y + z) = xy + xz
II. x + y + z = z + y + x
III. x - y - z = z - y - z

A. I only
B. II only
C. I and II only
D. I, II and III

Reasoning:
I. the distributive property is always true.
II. addition is commutative for all values.
III. subtraction is not commutative. Imagine 5-2 = 2-5. This is NOT true, since 3 does not equal -3.

Question # 18 of 58
What is the largest integer, n, for which 297/(3n) is an integer?

A. 1
B. 2
C. 3
D. 4

Reasoning:
297/3 = 99 ; 99/3 = 33 ; 33/3 = 11. So, n = 3.
Note 297/(33) = 297/27 = 11, whereas 297/(34) = 297/81 = 3.67.

Question # 19 of 58
A ladder 6 feet long leans against a wall and makes an angle of 71º with the ground. Find to the nearest tenth of a foot how high up the wall the ladder will reach.

A. 2
B. 3.5
C. 5.7
D. 6

Reasoning:
Draw a diagram. The right triangle has a hypotenuse of 6 and the angle of 71º should be placed between the ladder and the ground. Place x on the vertical side. The correct trig. function is sin 71º = x/6.


Question # 20 of 58
What is the largest prime factor of 399?

A. 7
B. 13
C. 17
D. 19

Reasoning:
Now, 399/19 = 21 = 3 x 7 (note that 21 is not a prime number).
Since 399 = 3 x 7 x 19, the largest prime factor is 19.

Question # 21 of 58
If w > x, y < z, and x > z, then which of the following must be true?

A. w > x > y > z
B. w > x > z > y
C. x > z > y > w
D. z < y < x < w

Reasoning:
The first and third statements declare:
w > x and x > z, therefore w > x > z.
The second statement says that y is less than z, therefore:
w > x > z > y.


Question # 22 of 58
lf p is a prime number greater than 5, which of the following is NOT a factor of 10p?

A. p2
B. 10p
C. 5p
D. 2p

Reasoning:
Remember that prime members are divisible only by themselves and 1. Focus here on the answer choices and see which one is not a factor of 10. Since p is a prime number, it's square cannot be a factor.


Question # 23 of 58
The image of the point (5,6) reflected in the y-axis is:

A. (6,5)
B. (-6,5)
C. (5,-6)
D. (-5,6)

Reasoning:
Draw a sketch and fold along the y-axis. Your new point is in the 2nd Quadrant. It is the same distance away from the y-axis as the original point (5,6).

Question # 24 of 58
Which of the combinations of sides and angles is insufficient for proving triangles congruent?

A. Two corresponding sides and the included angle from each triangle.
B. Two corresponding angles and the included side from each triangle.
C. Two corresponding sides and the non-included angle from each triangle.
D. Two corresponding angles and the non-included side from each triangle.

Reasoning:
SSA (or ASS) is the Donkey Theorem and is not sufficient to prove two triangles congruent.


Question # 25 of 58
If 8 and 12 each divide K without a remainder, what is the value of K?

A. 16
B. 24
C. 48
D. It cannot be determined from the information given.

Reasoning:
The best way to solve questions like this is to try choices rather than to reason it out algebraically. Now, trying our choices, B works, but so does C. If you chose A, you should review remainders. If you chose B or c, you jumped at an answer too quickly. Since more than one choice works, the answer must be D.

- PCAT Professor himself (UK)

 

[Plion]

Question # 26 of 58
Which of the following triangles are always similar?

A. Right triangles.
B. Scalene triangles.
C. Isosceles triangles.
D. Equilateral triangles.
Reasoning
The only triangle choice which guarantees TWO angles of the same size in each triangle would be the equilateral triangles where each equilateral triangle contains three 60º angles.
Question # 27 of 58
Your state issues license plates consisting of letters and numbers. There are 26 letters and the letters may be repeated. There are 10 digits and the digits may be repeated. How many possible license plates can be issued with two letters followed by three numbers?

A. 25,000
B. 67,600
C. 250,000
D. 676,000
Reasoning:
26 x 26 x 10 x 10 x 10 = 676000

Question # 28 of 58
If y = 25 - x2 and 1 &#8804; x &#8804; 5, what is the smallest possible value of y?

A. 0
B. 1
C. 5
D. 10
Reasoning:
If y = 25 - x2, the smallest possible value of y is obtained by subtracting the largest possible value of x2 from 25. Since 1 &#8804; x &#8804; 5, the largest possible value of x2 is 5<SUP.2< sup> = 25. When x2 = 25, then y = 25 - 25 = 0.


Question # 29 of 58
4,5,16,20,25,50
Two integers are "related" if they share a factor other than 1. Which of the preceding numbers is related to every number in the list above?

A. 4
B. 5
C. 6
D. 10
Reasoning:
Here we are looking for common factors. Looking closely at the answer choices we see that 2 and 5 must be factors, which leaves us with 10.

Question # 30 of 58
Solve for x: 12x = 50x -20

A. 5/9
B. 10/38
C. 10/19
D. 21/38
Reasoning:
12x = 50x - 20
Subtract 50x from each side.
-38x = -20
Divide each side by -38.
x = 20/38 = 10/19

Question # 31 of 58
The volume of a right circular cylinder with radius 10meters and height 2.5 meters is how many times the volume of a right circular cylinder with radius 2.5 meters and an height 10 meters?

A. 2
B. 3
C. 4
D. 5
Reasoning:
Remember that volume is really just area times height. In this case calculate the volume of each cylinder and set the results up as a ratio.
V = &#61520;r2h
(10)2&#61520; (2.5) = 250&#61520;
(2.5)2 &#61520; (10) = 62.5&#61520;
(250&#61520😉/(62.5&#61520😉= 4
Question # 32 of 58
If the sides of a triangle are 6, 8 and x, how many integer values of x could be the measure of the third side of the triangle?

A. 5
B. 6
C. 8
D. 11

Reasoning:
Remember that the sum of any two sides of a triangle must be larger than the third side. The third side could be as small as 3, or as large as 13, and still make this rule true. This is a total of 11 values.
Question # 33 of 58
If a and b are positive integers, a + b <1 5, and a > 5, what is the greatest possible value of a - b?

A. 1
B. 5
C. 11
D. 12
Reasoning:
We want the greatest possible value for a - b we want the greatest value for "a" and the smallest value for "b." And note these are both INTEGERS.
a = 13
b = 1
13 - 1 = 12
Question # 34 of 58
A quadratic equation has a highest power of what?

A. 2
B. 3
C. 4
D. 5
Reasoning:
A quadratic equation is an equation that has x^2 power in it. So the highest power of a quadratic equation is 2

Question # 35 of 58
Find the area of a circle whose diameter is 10. Express answer to the nearest tenth.
A. 39.2
B. 78.5
C. 314.2
D. 628.4

Reasoning:
Be Careful! This problem give the diameter (10), but the area formula requires the radius (5). Area of a circle is pi times the radius squared.
Question # 36 of 58
The grand prize for winning a contest is $20,000. After 28 percent of the prize is deducted for taxes, the winner receives the balance of the prize in annual portions of equal amounts over a 4-year period. How many dollars will the prizewinner receive each of the 4 years?

A. 1400
B. 2800
C. 3600
D. 4200
Reasoning:
First find out what the 28 percent reduction would be subtracting 28 percent from 100 percent. Then divide the balance by 4 to find the amount to be paid each of four years.
1.00 - .28 = .72
.72(20,00) = 14,400
14,400/4 = 3,600

Question # 37 of 58
Which equation is an illustration of the additive identity property?
A. (x)•(1) = x
B. x + 0 = x
C. x - x = 0
D. (x)•(1/x) = 1

Reasoning:
Zero is the additive identity. Adding zero to any number will give an answer equal to the original number.

Question # 38 of 58
The perimeter of a rectangle is 40. One of the sides is 5. Find the lengths of the other three sides.

A. 10, 10, 10
B. 5, 10, 10
C. 5, 15, 15
D. 10, 15, 15
Reasoning:
Perimeter is the distance around the outside. A rectangle has opposite sides equal. One of the other sides is 5, which leaves 30 units (from the 40 in the perimeter) to be split between the other two sides.
Question # 39 of 58
If the five digits 23456 continue to repeat as shown in the number above, what will be the digit in the 28th place to the right of the decimal point?

A. 2
B. 3
C. 4
D. 5
Reasoning:
Begin by identifying the number of digits in their pleading patterns. Then divide that number into the place your looking for in the sequence. Then see what the remainder is, and from that determine which number in the sequence falls on the remainder number. In this case there are 5 repeating digits.
28/5 = 5 remainder 3
The digit 4 lies in the third position in the sequence.

Question # 40 of 58
When the point (2,-5) is reflected in the x-axis, what are the coordinates of its image?
A. (-5,2)
B. (-2,5)
C. (2,5)
D. (5,2)

Reasoning:
Draw yourself a sketch and think of folding the point over the x-axis.

Question # 41 of 58
What is the largest of four consecutive even integers whose sum is 892?
A. 220
B. 226
C. 230
D. 232
Reasoning:
Let the largest of the four consecutive even integers be m. Then,
m + (m - 2) + (m - 4) + (m - 6) = 892 or 4m - 12 = 892.
Thus, m = 904 / 4 = 226.
The four consecutive even integers are 220, 222, 224 and 226.

Question # 42 of 58
If you multiply an inequality by a negative number, when should you reverse the inequality symbol?
A. Always.
B. Never.
C. Sometimes.
D. Only when the negative number is a fraction.
Reasoning:
Whenever you multiply (or divide) an inequality by a negative number, you MUST reverse the direction of the inequality symbol.

Question # 43 of 58
During a recent winter, the ratio of deer to foxes was 7 to 3. If there were 210 foxes, what was the number of deer?

A. 90
B. 147
C. 280
D. 490
Reasoning:
Since the ratio of deer to foxes is 7 to 3, you can represent the number of deer by 7x and the number of foxes by 3x. If there are 210 foxes, you know that 3x = 210 and x = 70. This means that the number of deer (7x) must be 7(70)=490.

Question # 44 of 58
The expression (5x+6y)-(7x-2y)+(x-2y) when simplified is:
A. -x+6y
B. x+6y
C. 13x-2y
D. 13x+10y

Reasoning:
Removing the parentheses gives
(5x+6y)-(7x-2y)+(x-2y)
5x+6y-7x+2y+x-2y
-x+6y
Question # 45 of 58
If x³ < x² < x then the value of x could be:

A. 0
B. 1
C. "1/3"
D. square root of 3

Reasoning:
For choice 3, the expression reads 1/27 < 1/9 < 1/3
Question # 46 of 58
If w,x,y, and z are all integers greater than 3, which of the following is the greatest?

A. xy+z+w
B. (x+z)y+w
C. x+z(y+w)
D. (x+w)(y+z)
Reasoning:
It's possible to solve this one by picking numbers for the variables, but it's not necessary. Since all the variables are grater than 3, multiplying any two of them together will produce a greater value than either variable alone would have. If you multiply out each answer choice and eliminate the parentheses, then you get:
A)xy+z+w
B)XY+XY+W
C)X=+zy+zw
D)xy+wy+xz+wz
A piece by piece comparison shows that choice D must have the greatest value.
Question # 47 of 58
Solve for x: (x/3) + 2 = (2x/3)
A. 2
B. 3
C. 5
D. 6
Reasoning:
(x/3) + 2 = (2x/3)
Convert 2 to fraction form.
(x/3) + (6/3) = (2x/3)
Multiply both sides by 3.
x + 6 = 2x
Subtract x from both sides.
x = 6
Question # 48 of 58
A sales item costs $350 after a 30 percent discount. What was the original cost of the item?

A. $200
B. $350
C. $500
D. $650
Reasoning:
In this case we want a 30 percent discount. So taking 30 percent from 100 percent, we're looking for 70 percent of price and solve according.
x - .3x = 350
.7x - 350
x = 350/.7 = 500

Question # 49 of 58
Your math marks decreased by 60% from the first quiz to the second quiz. If your marks in the third quiz were identical to those in the first quiz, by what percent did your marks increase from the second quiz to the third quiz?
A. 2.5
B. 1.5
C. 1.4
D. 1.1

Reasoning:
Let m be your marks in the first quiz.
Then, your marks are 0.4m in the second quiz and m in the third quiz.
Percent Increase
= (Marks in third Quiz - Marks in second quiz) x 100/Marks in second quiz
= (m - 0.4m) x 100 / 0.4m = (0.6/0.4) x 100 = 150
Question # 50 of 58
Triangle ABC is congruent to triangle DEF with segment AB congruent to segment DE. If AB = 2x + 10, and DE = 4x - 20,find the value of x.

A. 5
B. 10
C. 15
D. 60
Reasoning:
Congruent means equal. 2x+10=4x-20
30=2x
15=x

- PCAT professor himself (UK)

 

[Plion]

Question # 51 of 58
Jones has to sell a box of candy bars for a fund-raiser. Oh Monday he sold 1/3 of the total number of candy bars that came in the box, and on Tuesday he sold 3 candy bars. If his sales for these two days were 11/30 of the total number of candy bars that came in the box, how many candy bars came in the box?
A. 30
B. 54
C. 60
D. 90
Reasoning:
We determine the fraction of the amount sold, the fraction the amount remaining represents of the total, and use the three candy bars as the hard number to convert to the total.
(1/3)x + 3 = (11/30)x
(10/30)x + 3 = (11/30)x
3 = (1/30)x
90 = x

Question # 52 of 58
Chipmunk, the cow, weighs 451 kg, to the nearest Kilogram. Which weight listed cannot be the actual weight of the cow?
A. 450.6 kg
B. 451.0 kg
C. 451.4 kg
D. 451.6 kg
Reasoning:
451.6 kg. would round to 452kg to the nearest kilo.

Question # 53 of 58
The value of -3² is?

A. 9
B. 3
C. -9
D. -3

Reasoning:
Be Careful!! There are no parentheses in this problem, such as (-3)².
(-3)² = 9
but -3² = -9. The power is being applied to the 3 only.

Question # 54 of 58
In a magazine, 30 pages of the 80 pages are devoted to sports. What percent of the magazine is devoted to sports?

A. 2.70 %
B. 3.75 %
C. 27 %
D. 37.50 %
Reasoning:
Written literally: 30 = m% of 80
30 = (m/100)(80)
30 = (80m)/100
80m=3000
m=37.5
Question # 55 of 58
a = b,
8a - 5b = 27
In the system of equations above, what is the value of 5b?
A. 27/13
B. 27/5
C. 9
D. 45

Reasoning:
These are simultaneous equations where substitution is the key.
We want to solve for "b" so we want everything in terms of "b."
8b - 5b = 27
3b = 27
b = 9
5b = (5)(9) = 45
Question # 56 of 58
Solve for x: 3x/2 - 2 = 7

A. 2
B. 4
C. 6
D. 8
Reasoning:
Remember to isolate the variable. 3x/2 - 2 = 7. Multiply through by 2. 3x -4 = 14. Add 4 to both sides. 3x = 18. Multiply through by 1/3 (or divide by 3) x = 6
Question # 57 of 58
How many different 6-letter arrangements can be formed using the letters in the word ABSENT, if each letter is used only once?
A. 6
B. 36
C. 720
D. 46,656
Reasoning:
There are 6 letters which can be used to fill the first position in the new word, 5 letters to fill the second position, 4 letters to fill the third position, and so on. The answer is 6 factorial.

Question # 58 of 58
Soybean production in 1996 was 12,000 tons. If soybean production decreased thirty percent from 1996 to 1997 and increased thirty percent from 1997 to 1998, what is the soybean production, in tons, in 1998?
A. 8400
B. 10920
C. 12200
D. 13250
Reasoning:
Here we are looking for a 30 percent decrease and an increase of 30 percent from that new value. A 30 percent decrease means we want 70 percent of the value. A 30 percent increase represents 130 percent of the value. In terms of numbers:
.7(12,000) = 8,400
1.3(8,400) = 10,920

- PCAT professor himself (UK)