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Sample Practice Test Questions

Arithmetic Reasoning

What is \( \frac{4}{6} \) ÷ \( \frac{4}{8} \)?

1\(\frac{1}{3}\)

To divide fractions, invert the second fraction and then multiply:

\( \frac{4}{6} \) ÷ \( \frac{4}{8} \) = \( \frac{4}{6} \) x \( \frac{8}{4} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{4}{6} \) x \( \frac{8}{4} \) = \( \frac{4 x 8}{6 x 4} \) = \( \frac{32}{24} \) = 1\(\frac{1}{3}\)

Word Knowledge
Trevor decided to freeze the surplus chili for next week's tailgate party.
surfeit
Excess.
Math Knowledge
4\( \sqrt{2} \)

If the area of this square is 16, what is the length of one of the diagonals?

4\( \sqrt{2} \)

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s2

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{16} \) = 4

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c2 = a2 + b2
c2 = 42 + 42
c2 = 32
c = \( \sqrt{32} \) = \( \sqrt{16 x 2} \) = \( \sqrt{16} \) \( \sqrt{2} \)
c = 4\( \sqrt{2} \)

Arithmetic Reasoning

If all of a roofing company's 6 workers are required to staff 3 roofing crews, how many workers need to be added during the busy season in order to send 7 complete crews out on jobs?

8

In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 6 workers at the company now and that's enough to staff 3 crews so there are \( \frac{6}{3} \) = 2 workers on a crew. 7 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 7 x 2 = 14 total workers to staff the crews during the busy season. The company already employs 6 workers so they need to add 14 - 6 = 8 new staff for the busy season.

Automotive Information

The piston moves downward in the cylinder creating a vacuum that pulls an air-fuel mix into the combustion chamber. This describes which engine stroke?

intake

The four-stroke piston cycle of internal combustion engines starts with the piston at top of the cylinder head (top dead center or TDC) during the intake stroke. The piston moves downward in the cylinder creating a vacuum that pulls an air-fuel mix into the combustion chamber through the now open intake valve.

General Science

An element in the physical state of __________ maintains a constant volume and shape.

solid

An element in a solid state has atoms or molecules that are constricted and do not move freely. Solids maintain a constant volume and shape and exist at a lower temperature than liquids or gases.

Mechanical Comprehension

On Earth, acceleration due to gravity (g) is approximately __________. 

9.8 m/s2

Newton's Law of Univeral Gravitation defines the general formula for the attraction of gravity between two objects:  \(\vec{F_{g}} = { Gm_{1}m_{2} \over r^2}\) . In the specific case of an object falling toward Earth, the acceleration due to gravity (g) is approximately 9.8 m/s2

Automotive Information

Modern car engines are cooled by:

liquid

Modern car engines are cooled by liquid which circulates through the engine block and cylinder heads absorbing excess heat. This liquid is made up of half water and half antifreeze (commonly, ethylene glycol) which both keeps the water from freezing at low temperatures and raises its boiling point making heat transfer more efficient.

General Science

Tough fibrous cords of connective tissue that connect muscles to the skeleton are called:

tendons

Tough fibrous cords of connective tissue called tendons connect muscles to the skeleton while another type of connective tissue called ligaments connect bones to other bones at joints (elbow, knee, fingers, spinal column).

Word Knowledge
Abate most nearly means:
subside
Become less in amount or intensity.