PLUMBING ARITHMETIC 1

Lisa is 16 years younger than kathy. If the sum of their ages is 30, how old is lisa?

To find Lisa's age, let Kathy's age be represented as X. Then Lisa's age is X - 16. The equation is X + (X - 16) = 30. Solving for X gives Kathy's age as 23 and Lisa's age as 7.

LCM of two prime numbers x and y is 161. Given that x > y, what is the value of 3y-x?

a. -2

b. 2

c. -3

d. 7

To find the value of 3y - x, first determine the prime factors of 161, which are 7 and 23. Let x = 23 and y = 7. Therefore, 3y - x = 3(7) - 23 = 21 - 23 = -2.

Calc:

Press 161 > equals>shift+pfact

What is the travel length of a plastic pipe 4” in diameter if the offset angle is 11.25 degrees and the offset length is 60cm?

a. 2m

b. 3m

c. 4m

d. 5m

b. 3m (use sohcahtoa)

An algebraic expression consisting of three terms.

a. trigonometric ratio

b. trigonometric function

c. trihedral angle

d. trinomial

d. trinomial

This refers to the horizontal axis.

a. Origin

b. Asymptote

c. Abscissa

d. ordinate

c. Abscissa

What property does this equation fall: (6+10)+3 = 6+ (10+3)

a. Commutative property

b. Associative property

c. Identity property

d. Transitive property

b. Associative property

A number used to designate objects or quantities

a. Abstract number

b. Ordinal number

c. Concrete number

d. Amicable number

c. Concrete number

Simplify (3+i²)(1+i²)

a. 1

b. 0

c. 2

d. 3

b. 0

Note. Use mode 2

Simplify i^46738305

a. i

b. -i

c. 0

d. 1

Answer: a. i

Divide the last 2 digits by 4

0.25= i

0.50= i²

0.75= 1³

1.00= i⁴

In a data set 1,14,5,29,38,23,23, 7,18, identify the median.

a. 38

b. 23

c. 29

d. 18

Answer: d. 18

If x<y and y<15, what is the greatest possible integer value of x+y?

a. 27

b. 28

c. 29

d. 30

Answer: c. 29

Memorize

The angle in which the line of sight to the object makes with the horizontal which is above the eye of the observer is called______.

a. Bearing

b. Azimuth

c. Angle of elevation

d. Angle of depression

Answer: c. Angle of elevation

Convert MMMMMDCCCXCIV

a. 4884

b. 5784

c. 5984

d. 5894

Answer: d. 5894

What is the value of x in the equation 3x-15-6=0?

a. 7

b. 8

c. 9

d. -9

Answer: a. 7

The roots of the quadratic equation are 1/3 and -3/2. What is the equation?

a. 6x² + 5x + 3 = 0

b. 6x² - 7x - 3 = 0

c. 6x² + 7x - 3 = 0

d. 6x² - 7x + 3 = 0

Answer: c. 6x² + 7x - 3 = 0

10^-15 is equal to?

a. 1 micro

b. 1 pico

c. femto

d. nano

Answer: c. femto

1 nautical mile is equal to ______.

a. 5280 feet

b. 6080 feet

c. 3240 feet

d. 5040 feet

Answer: b. 6080 feet or 1.85km

Note:

5280 feet or 1.61km is Statute mile

¾ + 12/5 + 5/17 =?

a. 1171/340

b. 561/140

c. 1861/644

d. 4573/1420

Answer: a. 1171/340

In how many ways can 6 children be arranged in a line?

a. 720

b. 480

c. 240

d. 640

Answer: a. 720

In how many ways can a group of 7 be placed in a circular table such that a couple always sit with each other?

a. 720

b. 480

c. 240

d. 640

Answer: c. 240

Sol.

Circular permutation formula: (n-1)!

(n-1)! x 2!

5! x 2!

=240

A jar contains 10 red marbles, 8 green marbles, 2 blue marbles, and 2 yellow marbles. What is the probability of selecting red and then blue marble without replacement?

a. 3.25%

b. 10.56%'

c. 4.33%

d. 9.18%

Answer: c. 4.33%

Find the probability of getting a king and then queen if they are drawn from a pack with replacement.

a. 0.59%

b. 15.38%

c. 6.90%

d. 0.60%

Answer: a. 0.59%

Find the 34th term of the arithmetic sequence with the initial term of 6 and a common difference of 4.

a. 252

b. 138

c. 624

d. 236

Answer: b. 138

Find the sum of all odd numbers from 0 to 61.

a. 698

b. 961

c. 896

d. 1031

Answer: b. 961

Find the 20th term of the geometric sequence with the 1st term as 4 and a common ration of 4.

a. 1099511627776

b. 10485765246

c. 360

d. 60

Answer: a. 1099511627776

In what order in the arithmetic series is 5060 with the 6th term 20 and the 8th term 32?

a. 737

b. 848

c. 352

d. 846

Answer: d. 846

A regular tank has 5m length, 2.5m width, and 2m height. What is the maximum volume it can hold?

a. 2500 liters

b. 250000 liters

c. 6605.01 gal

d. 8828 cu. ft

Answer: c. 6605.01 gal

Note:

1cu m = 1000 liters

1 liter = 3.785 gal

Convert 853 gallons to cubuc inches.

a. 7023×10²

b. 202.82×10²

c. 197.043×10³

d. 588.79×10³

Answer: c. 197.043×10³

Note:

1 gal = 231 cu. in.

How many times in a day do the hands of the clock overlap?

a. 48

b. 22

c. 24

d. 44

Answer: b. 22

Find the degree in between the hands of a clock at 3:40pm.

a. 165

b. 135

c. 140

d. 130

Answer: d. 130

Formula:

11M-60H / 2

In how many minutes after 1am will the hands of the clock be opposite to each other?

a. 16.61

b. 38.18

c. 38.83

d. 16.18

Answer: b. 38.18

How many liters of a 70% alcohol solution must be added to 50 liters of a 40% alcohol solution to produce a 50% alcohol solution?

a. 45 liters

b. 25 liters

c. 60 liters

d. 30 liters

Answer: b. 25 liters

5400 L of a water containing 18% salt is to be made by mixing water containing 12% salt with another batch of water containing 20% salt. How much of the water with 20% salt is needed?

a. 4050 liters

b. 826 liters

c. 1350 liters

d. 2038 liters

Answer: a. 4050 liters

It takes 5 hours for worker A to plan seeds, 4 hours for worker B, and 2 hours for worker C. How many hours will it take for them to plant seeds if they work together?

a. 4.9 hours

b. 2.2 hours

c. 3.2 hours

d. 1.05 hours

Answer: d. 1.05 hours

A tank should be filled in 20 hours. If pipe A inlet can fill the tank in 7 hours, and pipe B outlet can flow the water out of the tank in 5 hours, how many hours should pipe C inlet be able to fill the tank?

a. 4.33 hours

b. 7.33 hours

c. 9.33 hours

d. 6.33 hours

Answer: c. 9.33 hours

A construction job site can be done by 30 workingmen in 120 days. How long will it take for 10 working men to get the job done?

a. 240 days

b. 360 days

c. 540 days

d. 270 days

Answer: b. 360 days

A father said to his son, “I was as old as you when you are at the present at the time of your birth.” If the Father’s age is 38 years now, the son’s age five years back was:

a. 14

b. 19

c. 33

d. 38

Answer: a. 14

Mary is 24 years old. Mary was twice as old as Ana was when Mary was as old as Ana is now.

a. 12

b. 14

c. 16

d. 18

Answer: c. 16

Three years ago, Levi was five times as old as Eren. In two years, Levi will be three times as old as Eren. Find the sum of their current ages.

a. 36

b. 32

c. 28

d. 20

Answer: a.36

Simplify (3-2x+2x²) - (4x-5+3x²)

a. -x²+6x+8

b. 2x²+5x-7

c. -x²-6x+8

d. -x²+2x+8

Answer: c. -x²-6x+8

Identify x and y

4x+7y=26

2x-3y=12

a. 8/13;2/13

b. 3/16;28/189

c. 82/30;24/90

d. 1/3;34/20

Answer: a. 8/13;2/13

Note: Use mode 5-1

Find the remainder when the polynomial 5x²-25x-1 is divided by x-3?

a. -67

b. -211

c. -64

d. -31

Answer: d. -31

Solution:

equate x-3

x=3

Substitute then input to calc

Find the 3rd term in the binomial expansion(2x-3)⁵

a. -180x⁴

b. 180x³

c. 720x³

d. 240x⁴

Answer: c. 720x³

Find the constant term in the expansion of (x²-1/x)⁹

a. 83

b. 84

c. 82

d. 85

Answer: b. 84

One number is 5 less than the other. If their sum is 135, what are the numbers?

a. 70,75

b. 80,55

c. 70,65

d. 75,60

Answer: c. 70,65

The denominator of a certain fraction is three more than twice the numerator. If 7 is added to both terms of the fraction, the resulting fraction is 3/5. Find the original fraction.

a. 5/11

b. 13/5

c. 3/5

d. 5/13

Answer: d. 5/13

The width of a rectangle is 3/8 its length. If its perimeter is 114, what is its area?

a. 536.36

b. 41.45

c. 644.35

d. 52.85

Answer: c. 644.35

Find the root mean square of 7,9,40,12

a. 1702

b. 16.99

c. 22.52

d. 21.64

Answer: d. 21.64

If 3 cats kill 3 rats in 3 minutes, how long will it take 100 cats to kill 100 rats?

a. 100 minutes

b. 3 minutes

c. 10 minutes

d. 300 minutes

Answer: b. 3 minutes

Determine the x and y intercept of the equation 2x+y-2=0

a. 2 and 4

b. -1 and 2

c. 1 and 2

d. 2 and 2

Answer: c. 1 and 2

Find the slope of the line that passes through points(-1,2)(3,10).

a. 4

b. 2

c. 5

d. 3

Answer: b.2

Find the distance of the point (-3,5) from the line 4x-3y-26=0

a. 14.52

b. 10.60

c. 12.06

d. 7.63

Answer: b. 10.60

6200 mils is equivalent to _____

a. 360°

b. 349°

c. 4.68 rad

d. 1,018 rad

Answer: b. 349°

How many sides does a regular polygon have with one interior angle of 120 degrees?

a. 4

b. 5

c. 6

d. 7

Answer: c. 6

In a right triangle, calculate the opposite of 40 degrees with a hypotenuse of 8cm.

a. 5.1

b. 6.1

c. 7.1

d. 8.1

Answer: a. 5.1

What is the derivative of cosine?

a. cos(x)

b. sin(x)

c. -sin(x)

d. sin²(x)

Answer: c. -sin(x)

Solve for x in 3sec(x)-6=0.

a. π/3 ; 4π/2

b. π/2 ; π/3

c. π/4 ; 3π/2

d. π/3 ; 5π/3

Answer: d. π/3 ; 5π/3

Note;

Use calc

Rad function

Get the area of a triangle with sides 40m, 50m, 70m.

a. 592 m²

b. 980 m²

c. 670 m²

d. 360 m²

Answer: b. 980 m²

How many edges does an octahedron have?

a. 4

b. 12

c. 40

d. 20

Answer: b. 12

How many diagonals are there in a polygon with 30 sides?

a. 205

b. 310

c. 405

d. 250

Answer: c. 405

Get the area of a triangle with sides 22cm and 26cm and an interior angle of 53 degrees between them?

a. 252.85 cm²

b. 232.60 cm²

c. 242.53 cm²

d. 228.40 cm²

Answer: d. 228.40 cm²

Find the area of a regular pentagon whose one side is 83cm and the apothem is 57.12cm.

a. 11057 cm²

b. 8197 cm²

c. 1289 cm²

d. 11852 cm²

Answer: d. 11852 cm²

Get the area of a pentagon with the perimeter of 90cm.

a. 784.40

b. 557.40

c. 784.50

d. 589.80

Answer: b. 557.40

A hexagon is inscribed in a circle with a radius of 4cm. Calculate the area of the hexagon.

a. 65.47 sqcm

b. 47.67 sqcm

c. 50.88 sqcm

d. 41.56 sqcm

Answer: d. 41.56 sqcm

In triangle ABC, BC= 58m, AB= 60m, and angle A= 60 degrees, identify side b.

a. 52.68

b. 55.77

c. 52.68

d. 56.38

Answer: b. 55.77

A cylinder is 5ft long and 34 inches in diameter. What is the volume in gallons?

a. 125.80 gal

b. 235.25 gal

c. 893.43 gal

d. 273.56 gal

Answer: b. 235.25 gal

What is the radius of the circle whose area is equal to that of a trapezoidal cross section whose two parallel sides are 2.50 meters and 1.80 meters respectively and the distance between them is 1.50 meters?

a. 39.89 inches

b. 1.013 ft

c. 4.022 m

d. 30.13 inches

Answer: a. 39.89 inches

Locus of point which moves so that the sum of the distances from two fixed points (foci) is constant and is equal to the length of major axis.

a. Circle

b. parabola

c. ellipse

d. hyperbola

Answer: c. ellipse

A horizontal cylindrical tank 150 cm long and 60 cm wide is filled up to the depth of 48cm. Find the volume of water in this tank.

a. 363730 cm³

b. 353769 cm³

c. 326320 cm³

d. 367230 cm³

Answer: a. 363730 cm³

Find the volume of a sphere with a diameter of 6 inches.

a. 113.10

b. 37.70

c. 116.52

d. 34.30

Answer: a. 113.10

1 ft = _____psi

a. 2.31

b. 0.433

c. 6.895

d. 4.184

Answer: b. 0.433

Unit of capacitance is _____.

a. Farad

b. Ohm

c. Mho

d. Hertz

Answer: a. Farad

1 BTU = ____kjoule

a. 231

b. 0.29

c. 1.055

d. 4.184

Answer: c. 1.055

In trigonometry one revolution is equal to, except_______.

a. 400 grad

b. 6400 mils

c. 360 degrees

d. Pi radian

Answer: d. Pi radian

What is the lateral edge of a square pyramid with one side 25” and apex height of 52”?

a. 53.48”

b. 62.49”

c. 54.92”

d. 69.43”

Answer: c. 54.92”