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Arithmetic Reasoning

The __________ is the smallest positive integer that is a multiple of two or more integers.

least common multiple

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

Word Knowledge

Jason, a notorious gossip, was a conduit for information about his friends.

channel

Means for transmitting or distributing.

Mechanical Comprehension

If the green box weighs 20 lbs. and is 1 ft. from the fulcrum, how far from the fulcrum would a 70 lbs. force need to be applied to balance the lever?

0.29 ft.

To balance this lever the torques at the green box and the blue arrow must be equal. Torque is weight x distance from the fulcrum so the equation for equilibrium is:

R_ad_a = R_bd_b

where a represents the green box and b the blue arrow, R is resistance (weight/force) and d is the distance from the fulcrum.

Solving for d_b, our missing value, and plugging in our variables yields:

d_b = \( \frac{R_ad_a}{R_b} \) = \( \frac{20 lbs. \times 1 ft.}{70 lbs.} \) = \( \frac{20 ft⋅lb}{70 lbs.} \) = 0.29 ft.

Mechanical Comprehension

How much work can a 1 hp engine do in 3 seconds?

1650 ft⋅lb

Horsepower (hp) is a common measure of power output for complex machines. By definition, a 1 hp machine does 550 ft⋅lb of work in 1 second: 1 hp = 550 ft⋅lb/s. Substituting the variables for this problem gives us:
\( W = 1 hp \times 550 \frac{ft⋅lb}{s} \times 3s = 1650 ft⋅lb \)

Math Knowledge

A(n) __________ is to a parallelogram as a square is to a rectangle.

rhombus

A rhombus is a parallelogram with four equal-length sides. A square is a rectangle with four equal-length sides.

Mechanical Comprehension

Which class of lever is used to increase force on an object in the same direction as the force is applied?

second

A second-class lever is used to increase force on an object in the same direction as the force is applied. This lever requires a smaller force to lift a larger load but the force must be applied over a greater distance. The fulcrum is placed at one end of the lever and mechanical advantage increases as the object being lifted is moved closer to the fulcrum or the length of the lever is increased. An example of a second-class lever is a wheelbarrow.

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?

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.

Math Knowledge

Solve 3b + 2b = 9b - 9y + 8 for b in terms of y.

1\(\frac{5}{6}\)y - 1\(\frac{1}{3}\)

To solve this equation, isolate the variable for which you are solving (b) on one side of the equation and put everything else on the other side.

3b + 2y = 9b - 9y + 8
3b = 9b - 9y + 8 - 2y
3b - 9b = -9y + 8 - 2y
-6b = -11y + 8
b = \( \frac{-11y + 8}{-6} \)
b = \( \frac{-11y}{-6} \) + \( \frac{8}{-6} \)
b = 1\(\frac{5}{6}\)y - 1\(\frac{1}{3}\)

Word Knowledge

Regurgitate most nearly means:

spew

To pour out or throw back.

General Science

Which of the following is not one of the outer planets?

Venus

In contrast to the solid terrestrial planets, the outer planets (Jupiter, Saturn, Uranus, and Neptune) consist of hydrogen and helium gas and water.