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Magoosh
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For a certain cylinder, the diameter equals the height. If every length in this cylinder is decreased by 60%, then to the nearest integer, by what percent does the volume decrease?
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Magoosh
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If n is an integer, what is the least possible value of n such that $$40,000,000 < 5^{n}$$ ?
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Magoosh
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If k is an integer and $$121 < k^{2} < 225$$, then k can have at most how many values?
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Magoosh
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$$(30^{30}) * (29^{29}) * (28^{28}) * . . . * (3^{3}) * (2^{2}) * (1^{1}) = N$$What is the highest value of K, such that $$\frac{N}{(125^{K})}$$ is an integer?
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Magoosh
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This year, a woman has a lucrative one-year position. During this year, she will give a fraction f of her salary to her husband, a private investor, to invest and they will live this year on the remainder. Through investments, her husband can turn each dollar she gives him into 1 + r, which will be deposited in a bank account. Their goal is to save & invest enough money so they can live off this money for two years following the end of the wife's position. Toward this end, they want to choose f such that the amount in the account at the end of the year is twice what they lived off this year. In terms of r, what should f be?
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Magoosh
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 In the diagram above, JKL is an equilateral triangle. Point M is the midpoint of segment JL, and M is the center of a circle that passes through points J and L. The shaded regions in the diagram indicate all the regions inside the circle that are outside the triangle. What fraction of the total area of the circle is outside the triangle?
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Magoosh
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Pump A can empty a pool in A minutes, and pump B can empty the same pool in B minutes. Pump A begins emptying the pool for 1 minute before pump B joins. Beginning from the time pump A starts, how many minutes will it take to empty the pool?
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Magoosh
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If A, B and C represent different digits in the multiplication, then A + B + C =
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Magoosh
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What is the sum of all possible solutions of the equation$$|x + 4|^{2} - 10|x + 4| = 24?$$
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Magoosh
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Fifteen points are evenly spaced on the circumference of a circle. How many combinations of three points can we pick from these 15 that do not form an equilateral triangle?
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Magoosh
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If it takes Bill 8 minutes to peel 30 potatoes, how many potatoes can he peel in one hour?
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Magoosh
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A sequence is defined by$$ s_n = (s_{n – 1} – 1)(s_{n – 2})$$ for n > 2,and it has the starting values of$$ s_1 = 2$$ and $$s_4 = 9.$$ All terms are positive. Find the value of $$s_6$$.
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Magoosh
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 In the diagram above, A & B are the centers of the two circles, each with radius r = 6, and ∠A = ∠B = 60°. What is the area of the shaded region?
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Magoosh
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How many integers between 1 and$$ 10^{21}$$ are such that the sum of their digits is 2?
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Magoosh
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If x and y are positive odd integers, then which of the following must also be an odd integer?I. $$x^{y+1}$$II. x(y+1)III. $$(y+1)^{x-1} + 1$$
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OG18 OG19 OG20 OG2022
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Between 14,000 and 8,000 B.C. the ice cap that covered northern Asia, Europe, and America began to melt, uncovering vast new areas that were to be occupied by migrating peoples moving northward.
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OG18 OG19 OG20 OG2022
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Positing an enormous volcanic explosion at the end of the Permian period would explain the presence of a buried crater, account for the presence of the element iridium (originating deep within the earth), and the presence of quartz having been shattered by high-impact shock waves.
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OG18 OG19 OG20 OG2022
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With the patience of its customers and with its network strained to the breaking point, the on-line service company announced a series of new initiatives trying to relieve the congestion that has led to at least four class-action lawsuits and thousands of complaints from frustrated customers.
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OG18 OG19 OG20 OG2022
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Among the Tsonga, a Bantu-speaking group of tribes in southeastern Africa, dance teams represent their own chief at the court of each other, providing entertainment in return for food, drink, and lodging .
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OG18 OG19 OG20 OG2022
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Political theorist: Even with the best spies, area experts, and satellite surveillance, foreign policy assessments can still lack important information. In such circumstances intuitive judgment is vital. A national leader with such judgment can make good decisions about foreign policy even when current information is incomplete, since_______ .
Which of the following, if true, most logically completes the argument?
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