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Arithmetic Reasoning

23 members of a bridal party need transported to a wedding reception but there are only 4 5-passenger taxis available to take them. How many will need to find other transportation?

There are 4 5-passenger taxis available so that's 4 x 5 = 20 total seats. There are 23 people needing transportation leaving 23 - 20 = 3 who will have to find other transportation.

Mechanical Comprehension

Which of the following surfaces would have the lowest coefficient of friction?

ice

Coefficient of friction (μ) represents how much two materials resist sliding across each other. Smooth surfaces like ice have low coefficients of friction while rough surfaces like concrete have high μ.

Automotive Information

The air-fuel mixture is delivered to the combustion chamber by a(n):

intake valve

The combustion chamber is located in the cylinder head and contains the combustion of the air-fuel mixture. This mixture is delivered by an intake valve and the waste gases from combustion are removed from the combustion chamber by the exhaust valve.

Word Knowledge

The nurse was worried by the patient's pallid face and shallow breathing.

pale

Lacking color.

Shop Information

Which of the following saws would you use if you're cutting wood across the grain?

crosscut saw

Wood saws are categorized by their teeth shape and the number of teeth per inch (TPI). The higher the TPI of a saw the finer the cut it will make. 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.

Arithmetic Reasoning

What is $ \frac{3}{3} $ - $ \frac{5}{5} $?

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

$ \frac{3 x 5}{3 x 5} $ - $ \frac{5 x 3}{5 x 3} $

$ \frac{15}{15} $ - $ \frac{15}{15} $

Now, because the fractions share a common denominator, you can subtract them:

$ \frac{15 - 15}{15} $ = $ \frac{0}{15} $ =

Math Knowledge

$\sqrt{80}$

If side a = 8, side b = 4, what is the length of the hypotenuse of this right triangle?

$ \sqrt{80} $

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 8² + 4²
c² = 64 + 16
c² = 80
c = $ \sqrt{80} $

Word Knowledge

Elate most nearly means:

delight

To fill with joy.

Electronics Information

Electromotive force is another name for:

voltage

Voltage (V) is the electrical potential difference between two points. Electrons will flow as current from areas of high potential (concentration of electrons) to areas of low potential. Voltage and current are directly proportional in that the higher the voltage applied to a conductor the higher the current that will result.

Mechanical Comprehension

A truck is using a rope to pull a car. Tension in the rope is greatest in which of the following places?

near the truck

Tension is a force that stretches or elongates something. When a cable or rope is used to pull an object, for example, it stretches internally as it accepts the weight that it's moving. Although tension is often treated as applying equally to all parts of a material, it's greater at the places where the material is under the most stress.