MATHalino
9. If a car can travel x km in y hours, how many hours
can it travel a distance of z km?
A. xy/z
C. xz/y
B. yz/x
D. xyz
Engineering Mathematics
PRE-EVALUATION TEST
10. If 8 men can cut 22 trees in a day, how many trees can
20 men cut in a day?
A. 45
C. 65
B. 75
D. 55
Basic Algebra Review Course
https://mathalino.com/node/18037
INSTRUCTION
Solve the following problems offline for about 2 hours and
40 minutes straight (averaging 4 minutes per problem).
Submit your solution by taking the Quiz in the next step
in the course outline. Answer key is provided right after
you submit all your answers. Good luck!
1. The sum and product of three distinct positive
integers are 15 and 45, respectively. What is the
smallest integer?
A. 1
C. 5
B. 9
D. 3
2. The sum of thirteen consecutive integers is zero. What
is the smallest integer?
A. -4
C. -5
B. -7
D. -6
11. Albert can do a work in 1 hour, Bryan can do it in 2
hours, and Carl can do it in 4 hours. Working together
from start, how long can they do the work?
A. 0.5455 hr
C. 0.5714 hr
B. 0.5623 hr
D. 0.6175 hr
12. Mario’s hat is four more than Alex’s hat and one-half
that of Gabriel’s hat. If the total number of hats is 24,
how many hats does Alex have?
A. 14
C. 7
B. 3
D. 16
13. The shipment of items is divided into two portions. If
the difference between the portions is one-third of
their average, what is the ratio of the larger portion to
the smaller portion?
A. 4/3
C. 7/5
B. 6/5
D. 3
3. X and Y are inversely proportional with each other.
Given that X = 15,000 when Y = 162,500. Find X
when Y = 328,400.
A. 6,567.45
C. 7,422.35
B. 7,849.56
D. 8,956.32
14. A group of musicians is composed of three drummers,
four pianists, and seven guitarists. How many ways
can a trio are formed with 1 pianist, 1 drummer, and 1
guitarist?
A. 84 ways
C. 42 ways
B. 96 ways
D. 164 ways
4. What is the value of x - y from the following linear
equations?
15. If |3t - 5| > 4, which of the following is correct?
A. 3 > t > 1/3
C. 3 < t > 1/3
B. 3 < t < 1/3
D. 3 > t < 1/3
3x + 2y = 2
6x - 5y = -32
A. -6
B. -4
16. How many ways can 6 persons be seated at a round
table if one seat is reserved for a specific person?
A. 120
C. 720
B. 24
D. 240
C. -8
D. -10
5. Solve for x2 if 481/x = 4 ´ 31/x
A. 2
C. 1
B. 4
D. 3
17. If xyz = 8 and x2z = 18, what is the value of y/x?
A. 2/3
C. 4/9
B. 9/4
D. 3/2
6. Given the following equations:
18. Find the non-zero solution to the equation 3x4 - 27x3
= 0.
A. 10
C. 15
B. 5
D. 9
ab = 1/8
Find the value of b.
A. 6
B. 12
ac = 3
bc = 6
C. 0.5
D. 0.25
7. What is the coefficient of the term involving x-3 in the
expansion of (2x + 2/x)5?
A. 320
C. 32
B. 160
D. 180
8. The polynomial x3 + 4x2 - 3x + 8 is divided by x - 5.
What is the remainder?
A. 281
C. 218
B. 812
D. 182
19. A line is divided into 12 equal parts. If the measure of
each part is a prime integer, what is the possible
length of the line?
A. 204
C. 252
B. 192
D. 324
20. Solve for D in the given partial fraction:
4𝑥 ! + 7𝑥 + 8 𝐴
𝐵
𝐶
𝐷
= +
+
+
𝑥(𝑥 + 2)"
𝑥 𝑋 + 2 (𝑥 + 2)! (𝑥 + 2)"
MATHalino
A. 1
C. 2
B. -1
D. -5
21. Two cars A and B are traveling at the speed of 30 kph
and 40 kph respectively on two different roads
making an angle of 30° with each other. Car A is
located 200 m from the intersection of the roads at
the instant car B is 400 m from the intersection. After
a lapse of 5 minutes, how far is car A from car B in
meters.
A. 1736.84
C. 1833.28
B. 1941.32
D. 2213.65
22. A and B start at the same time from two places 154 km
apart and travel toward each other. A travels 10 kph
and B 8 kph. If B stopped 1 hour on the way, in how
many hours will they meet?
A. 9 hrs
C. 7 hrs
B. 8 hrs
D. 6 hrs
23. The numbers 28, x + 2, 112, ... form a geometric
progression. What is the 10th term?
A. 13,312
C. 16,336
B. 14,336
D. 15,336
24. A jogger starts a course at a steady rate of 8 kph. Five
minutes later, a second jogger took the same course
at 10 kph. How long will it take for the second jogger
to catch the first?
A. 20 min
C. 30 min
B. 25 min
D. 15 min
25. What is the middle term in the expansion of (x2 + 3x)8.
A. 5670x12
C. 70x12
B. 5760x8
D. 270x8
26. Find k so that the expression kx2 - 3kx + 9 is a perfect
square.
A. 3
C. 6
B. 12
D. 4
27. Determine the value of ‘a’ if (x + 2) is a factor of (x3 ax2 + 7x + 10).
A. -3
C. 2
B. 3
D. -2
28. Express the following statement mathematically: 5
less than four times a certain number is 12.
A. 5 – 4x = 12
C. 5 + 4x = 12
B. 5x – 4 = 12
D. 4x – 5 = 12
29. The distance between the centers of the three circles
which are mutually tangent to each other externally
are 10, 12, and 14 units. The area of the smallest circle
is:
A. 72p
C. 64p
B. 23p
D. 16p
30. In a class experiment, a student needs 5 liters of 6%
solution. He found a 4% and a 10% solution in the
laboratory. How many liters of each solution should
he mix in order to obtain 5 liters of 6% solution?
A. 3.33 liters of 4% and 1.67 liters of 10% solution
B. 1.67 liters of 4% and 3.33 liters of 10% solution
Basic Algebra Review Course
C. 3.67 liters of 4% and 1.33 liters of 10% solution
D. 1.33 liters of 4% and 3.67 liters of 10% solution
31. How many 3-digit numbers greater than 300 can be
made out from digits 0, 1, 2, 3, 4, 5, and 6 if repetition
of digit is not allowed?
A. 210
C. 180
B. 120
D. 150
Situation 1. A manufacturer estimates that 1.5% of his
output of a small item is defective. Find the
probabilities that in a pack of 200 items:
32. None is defective.
A. 0.0498
C. 0.224
B. 0.1494
D. 0.3528
33. Two are defective.
A. 0.224
C. 0.3528
B. 0.1494
D. 0.0498
34. Three or more are defective.
A. 0.224
C. 0.1494
B. 0.0498
D. 0.3528
Situation 2. Charles’s law states that for a given mass
of gas at constant pressure the volume is directly
proportional to its thermodynamic temperature. A
gas occupies a volume of 2.25 liters at 400°K.
Determine the following:
35. The constant of proportionality,
A. 0.004625
C. 0.007215
B. 0.005125
D. 0.005625
36. The volume at 420°K
A. 2.87 liters
C. 2.12 liters
B. 2.36 liters
D. 3.15 liters
37. The temperature when the volume is 2.625 liters.
A. 467°K
C. 444°K
B. 433°K
D. 367°K
Situation 3. A tank is supplied by two pipes A and B
and emptied by a third pipe C. If the tank is empty
and all pipes are opened, the tank can be filled in 20
hours. If the tank is full and A and C are opened, the
tank can be emptied in 4 hours. If the tank is full and
B and C are opened, the tank can be emptied in 2
hours. Pipe A supplies 50 liters per minute more than
B.
38. Find the rate of pipe A in liters per minute.
A. 120
C. 110
B. 130
D. 140
39. Find the rate of pipe C in liters per minute.
A. 170
C. 150
B. 160
D. 140
40. Find the capacity of the tank in liters.
A. 12,000
C. 11,500
B. 12,500
D. 13,000
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