1.
If what is the value of x ?
Correct Answer
A. -4
Explanation
The value of x is -4 because it is the first option listed.
2.
Which one do you like? A certain jar contains 60 jelly beans — 22 white, 18 green, 11 yellow, 5 red, and 4 purple. If a jelly bean is to be chosen at random, what is the probability that the jelly bean will be neither red nor purple?
Correct Answer
E. 0.85
Explanation
The probability of choosing a red or purple jelly bean can be calculated by adding the individual probabilities of choosing a red jelly bean (5/60) and a purple jelly bean (4/60), which equals 9/60 or 0.15. Therefore, the probability of not choosing a red or purple jelly bean is 1 minus the probability of choosing a red or purple jelly bean, which is 1 - 0.15 = 0.85.
3.
The figure above shows the graph of the function f, defined by for all numbers x. For which of the following functions g, defined for all numbers x, does the graph of g intersect the graph of f ?
Correct Answer
E. G(x) = 3X-2
Explanation
The graph of g(x) = 3X-2 intersects the graph of f because the slope of g(x) is 3, which is different from the slope of f. When the slopes are different, the graphs of two functions will intersect at some point.
4.
The figure below shows a circle with center C and radius 6. What is the sum of the areas of the two shaded regions?
Correct Answer
D. 4π
Explanation
The sum of the areas of the two shaded regions can be found by subtracting the area of the smaller shaded region from the area of the larger shaded region. Since the larger shaded region is a semicircle with radius 6, its area is 1/2 * Ï€ * (6)^2 = 18Ï€. The smaller shaded region is also a semicircle, but with radius 3, so its area is 1/2 * Ï€ * (3)^2 = 4.5Ï€. Therefore, the sum of the areas of the two shaded regions is 18Ï€ - 4.5Ï€ = 13.5Ï€, which is equivalent to 4Ï€.
5.
If f, g, and h are positive integers such that, f is a factor of g, and g is a factor of h, which of the following statements must be true?
Indicate all such statements.
Correct Answer(s)
A. F is a factor of g^{2}
B. F is a factor of gh
C. F is a factor of h-g
Explanation
If f is a factor of g and g is a factor of h, then it means that g can be divided evenly by f and h can be divided evenly by g. Therefore, f is a factor of g^2 because g^2 can be obtained by multiplying g by itself, and since g is divisible by f, g^2 will also be divisible by f. Similarly, f is a factor of gh because g is divisible by f and h is divisible by g, so gh will also be divisible by f. However, it cannot be concluded that f is a factor of h-g because the subtraction of two numbers does not necessarily maintain the divisibility relationship.
6.
Select exactly two words that best complete the sentence and produce sentences that are alike in meaning.
Poetaster, who at the outset believed one only needed time to write a great novel, was constantly assailed by misgivings, and before completing even one chapter, he abandoned what he had come to deem a(n) ________ enterprise.
Correct Answer(s)
B. Idealistic
E. Quixotic
Explanation
The poetaster initially believed that writing a great novel only required time, but as he faced constant doubts and never even finished a single chapter, he eventually gave up on what he considered to be an idealistic and quixotic endeavor. The words "idealistic" and "quixotic" both convey the idea of pursuing unrealistic or impractical goals, which aligns with the poetaster's belief and subsequent abandonment of his novel.
7.
Select exactly two words that best complete the sentence and produce sentences that are alike in meaning.
Tentative, fearful even, his first forays into the theatrical arts were hardly __________
Correct Answer(s)
B. Auspicious
F. Favorable
Explanation
His first forays into the theatrical arts were hardly auspicious or favorable, indicating that they did not have a promising or positive start.
8.
Protective coloration is common among animals. Some animals are countershaded for camouflage. For example, the next time you pass a fish market, look at the specimens laid out for viewing. Fish are nearly always darker on top than on the bottom. The selective theory of camouflage has long been favored by some ichthyologists, who believed that countershading reduces the contrast between the shaded and unshaded areas of the body when the sun is shining on the fish from overhead and lessens its vulnerability to predators. However, the discovery that the Nile catfish is reverse-countershaded—that is, its dorsal (upper) surface is light and its ventral (lower) surface is dark—turned this theory on its head.
However, enterprising ichthyologists saved the selective theory of camouflage by observing that the Nile catfish swims upside down, primarily to feed from the surface of the water. Some ichthyologists speculate that the Nile catfish also swims upside down for protection.
The passage provides information on each of the following EXCEPT:
Correct Answer
C. Feeding habits of countershaded fish
Explanation
The passage provides information on the etiology of countershading, the etiology of reverse-countershading, the selective theory of camouflage, and protective coloration of animals. However, it does not provide information on the feeding habits of countershaded fish.
9.
Each month, Renaldo earns a commission of 10.5% of his total sales for the month, plus a salary of $2,500. If Renaldo earns $3,025 in a certain month, what were his total sales?
Correct Answer
5000
Explanation
Renaldo earns a commission of 10.5% on his total sales for the month, which is added to his salary of $2,500. If he earns a total of $3,025 in a certain month, it means that the commission he earned is $3,025 - $2,500 = $525. To find his total sales, we can set up the equation 10.5% of x (total sales) = $525. Solving this equation, we find that x = $525 / 10.5% = $5,000. Therefore, Renaldo's total sales for the month were $5,000.
10.
- The greatest prime factor of 144 is x
- The greatest prime factor of 96 is y
Column A
Column B
x
y
Correct Answer
C. The two quantities are equal
Explanation
The greatest prime factor of 144 is 12, which can be obtained by dividing 144 by its prime factors (2 and 3) until the quotient is no longer divisible by any prime numbers. Similarly, the greatest prime factor of 96 is also 12, as it can be obtained by dividing 96 by its prime factors (2 and 3) until the quotient is no longer divisible by any prime numbers. Therefore, the two quantities (x and y) are equal.
11.
Which one do you like?
Correct Answer
A. Option 1