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Arithmetic Reasoning

This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.

commutative

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

Arithmetic Reasoning

A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 50% off." If Damon buys two shirts, each with a regular price of $39, how much will he pay for both shirts?

$58.50

By buying two shirts, Damon will save $39 x $ \frac{50}{100} $ = $ \frac{$39 x 50}{100} $ = $ \frac{$1950}{100} $ = $19.50 on the second shirt.

So, his total cost will be
$39.00 + ($39.00 - $19.50)
$39.00 + $19.50
$58.50

Word Knowledge

Clarence, an irrepressible comic, was held after cass for his buffoonery.

jocularity

Foolish behavior.

Arithmetic Reasoning

In a class of 24 students, 14 are taking German and 6 are taking Spanish. Of the students studying German or Spanish, 3 are taking both courses. How many students are not enrolled in either course?

The number of students taking German or Spanish is 14 + 6 = 20. Of that group of 20, 3 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 20 - 3 = 17 who are taking at least one language. 24 - 17 = 7 students who are not taking either language.

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.

Electronics Information

This circuit component symbol represents a(n):

DC source

Direct current flows in only one direction in a circuit, from the negative terminal of the voltage source to the positive. A common source of direct current (DC) is a battery.

Word Knowledge

The promote peace, the diplomat hosted a talk between the warring nations.

advance

To contribute to the growth or prosperity of.

Arithmetic Reasoning

What is $ \frac{28\sqrt{35}}{4\sqrt{5}} $?

7 $ \sqrt{7} $

To divide terms with radicals, divide the coefficients and radicands separately:

$ \frac{28\sqrt{35}}{4\sqrt{5}} $
$ \frac{28}{4} $ $ \sqrt{\frac{35}{5}} $
7 $ \sqrt{7} $

Shop Information

Which of the following types of saws would you use if you needed to cut the wood quickly and weren't concerned with leaving rough edges?

rip saw

Wood saws are categorized primarily by their teeth. Crosscut saws utilize knife-shaped teeth that cut across the grain of the wood while rip saws cut with the grain using chisel-shaped teeth that rip the wood cells apart as the cut is made. The kerf (slot) made by by a crosscut saw is much smoother than that made by a rip saw but a rip saw cuts much faster. Coping saws are a type of bow saw used to make detailed often curving cuts using replaceable blades with fine small teeth.

Mechanical Comprehension

If the handles of a wheelbarrow are 1.5 ft. from the wheel axle, how many pounds of force must you exert to lift the handles if it's carrying a 130 lbs. load concentrated at a point 0.5 ft. from the axle?

43.3

This problem describes a second-class lever and, for a second class lever, the effort force multiplied by the effort distance equals the resistance force multipied by the resistance distance: F_ed_e = F_rd_r. In this problem we're looking for effort force:
$ F_e = \frac{F_r d_r}{d_e} $
$ F_e = \frac{130 \times 0.5}{1.5} $
$ F_e = \frac{65.0}{1.5} $
$ F_e = 43.3 $