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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

Sam can do 50 ft. lb. of work in 2 minutes and 5 seconds. What would Sam have to do to increase his power output?

do the work in 2 minutes

Power is the rate of doing work or \(\frac{W}{t}\). To increase power, increase the work being done in the same amount of time or do the same amount of work in less time.

Electronics Information

Which of the following is the same for each branch of a parallel circuit?

voltage

In a parallel circuit, each load occupies a separate parallel path in the circuit and the input voltage is fully applied to each path. Unlike a series circuit where current (I) is the same at all points in the circuit, in a parallel circuit, voltage (V) is the same across each parallel branch of the circuit but current differs in each branch depending on the load (resistance) present.

Word Knowledge

Emily's smile is just a facade masking her broken heart.

mask

false or superficial appearance.

Math Knowledge

If a = 4, b = 2, c = 9, and d = 4, what is the perimeter of this quadrilateral?

Perimeter is equal to the sum of the four sides:

p = a + b + c + d
p = 4 + 2 + 9 + 4
p = 19

General Science

Which of the following describes the Earth's mantle?

primarily solid

Mantle makes up 84% of the Earth's volume and has an average thickness of approximately 1,800 miles (2,900 km). It is dense, hot, and primarily solid although in places it behaves more like a viscous fluid as the plates of the upper mantle and crust gradually "float" along its circumference.

Word Knowledge

Augment most nearly means:

enhance

To make greater.

Mechanical Comprehension

A = 5 ft., the green box weighs 50 lbs., and the blue box weighs 80 lbs. What does distance B need to be for this lever to balance?

3.13 ft.

In order for this lever to balance, the torque acting on side A must equal the torque acting on side B. Torque is weight x distance from the fulcrum which means that the following must be true for the lever to balance:

f_Ad_A = f_Bd_B

For this problem, the equation becomes:

50 lbs. x 5 ft. = 80 lbs. x d_B

d_B = \( \frac{50 \times 5 ft⋅lb}{80 lbs.} \) = \( \frac{250 ft⋅lb}{80 lbs.} \) = 3.13 ft.

Mechanical Comprehension

The force exerted on an object due to gravity is called:

weight

Mass is an intrinsic property of matter and does not vary. Weight is the force exerted on the mass of an object due to gravity and a specific case of Newton's Second Law of Motion. Replace force with weight and acceleration with acceleration due to gravity on Earth (g) and the result is the formula for weight: W = mg or, substituting for g, weight equals mass multiplied by 9.8 m/s².

General Science

Absolute zero is which of the following?

the coldest temperature possible in the universe

In contrast to the Celsius scale (measured in degrees centigrade) that fixes 0° at the freezing point of water and the Fahrenheit scale that uses 32°, the Kelvin scale fixes 0 at absolute zero (-273°C) which is the lowest temperature possible in the universe.