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Magoosh
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The numbers D, N, and P are positive integers, such that D < N, and N is not a power of any other positive integer. Is D a prime number?Statement #1: N has exactly four factors, and D is a factor of NStatement #2: $$D = (3^P) + 2$$
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Magoosh
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Is $$x^2-\frac{4}{3}x+\frac{5}{12}\lt0$$Statement #1:$$ 0 \le x$$Statement #2: x is an integer
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Magoosh
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Based on the analysis of musicologists who focused on his early manuscripts, Beethoven often created sketches of musical motifs that he would frequently make significant revisions weeks or even months later and that these preliminary ideas were included in much larger works that often underwent numerous revisions themselves.
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Magoosh
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Modern planetary science has a detailed understanding of the conditions necessary for a planet to develop life, but scientists are still unable to determine whether a given specific planet meeting all these conditions is to develop life.
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Magoosh
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Rome's great intellectual achievements laid in organizing the Empire, but Greece's had laid in mathematical and philosophical breakthroughs.
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Magoosh
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When positive integer k is divided by 6 the remainder is 3. Which of the following CANNOT be an even integer?
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Magoosh
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Which of the following is equivalent to$${2x^2+8x-24}\over{2x^2+20x-48}$$ for all values of x for which both expressions are defined?
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Magoosh
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If$$ x^2 - y^2 = 12$$ and x - y = 4, then x =
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Magoosh
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In the xy-coordinate system, line k has slope $$\frac{1}{2}$$ and passes through point (0, 5). Which of the following points cannot lie on line k?
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Magoosh
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If the areas of the 4 squares are 50, 32, 18 and 12, what is the ratio of the small shaded portion to the area of the large shaded portion?Note: Figure not drawn to scale
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Magoosh
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If the average (arithmetic mean) of 24 consecutive odd integers is 48, what is the median of the 24 numbers?
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Magoosh
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For a long time, the price of a certain console remained the same. Because of new tariffs, the price of this console increased by 50% last week, and stayed at this new level. This week, Amanda purchased the console with a 50%-off coupon. Amanda paid $240. What was the original price, before the last week's price increase?
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Magoosh
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In a certain town in Connecticut, the ratio of NY Yankees fans to NY Mets fans is 3:2, and the ratio of NY Mets fans to Boston Red Sox fans is 4:5. If there are 300 baseball fans in the town, each of whom is a fan of exactly one of those three teams, how many NY Mets fans are there in this town?
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Magoosh
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Ben is three times as old as Ron. Ed is 8 years younger than Ben. Ron is 7 years older than Ken. If the sum of the ages of all four people is 161, how many years old is Ron?
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Magoosh
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What percent of Gigacorp's 80 female employees are college graduates?(1) Gigacorp has 20 male employees.(2) 30 percent of Gigacorp's employees are college graduates.
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Magoosh
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S is a set of n consecutive positive integers. Is the mean of the set an integer?Statement #1: the range of S is an even integerStatement #2: the median of S is an integer
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Magoosh
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There are 42 students in a group. If each student is either a freshmen or a senior, how many of the students are seniors?(1) The group has more than four times as many seniors as it has freshmen.(2) The group has more than 7 freshmen.
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Magoosh
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If F is the prime factorization of N!, how many factors in F have an exponent of 1?Statement #1: 32 ≤ N ≤ 40
Statement #2: 27 ≤ N ≤ 35
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Magoosh
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What is the average (arithmetic mean) of x and y?(1) The average (arithmetic mean) of x, y and k is 7.(2) The average (arithmetic mean) of x, y and 3k is 13.
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Magoosh
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If lines k and j are in the xy–coordinate plane, is the slope of line k greater than the slope of line j?(1) The x-intercept of line k is greater than the x-intercept of line j(2) Lines k and j intersect at (7, 2)
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