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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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Magoosh
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What is the sum of all possible solutions to the equation$$\sqrt{2x^{2}-x-9}=x+1$$ ?
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Magoosh
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If$$\sqrt{17+\sqrt{264}} $$ can be written in the form $$\sqrt{a}+\sqrt{b}$$ , where a and b are integers and b < a, then a - b =
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Magoosh
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For how many unique coordinate points (P, Q), such that P and Q are integers, is it true that $$P^{2} - Q^{2} =$$ 1155?
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Magoosh
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If x is an odd negative integer and y is an even integer, which of the following statements must be true?I. (3x - 2y) is oddII. $$xy^{2}$$ is an even negative integerIII. $$(y^{2} - x)$$ is an odd negative integer
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Magoosh
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How many positive integers less than 10,000 are such that the product of their digits is 210?
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Magoosh
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If ABCD is a square with area 625, and CEFD is a rhombus with area 500, then the area of the shaded region is
Note: Figure not drawn to scale
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Magoosh
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In the above diagram, the 16 points are in rows and columns, and are equally spaced in both the horizontal & vertical direction. How many triangles, of absolutely any shape, can be created from three points in this diagram? Different orientations (reflections, rotations, translations, etc.) count as different triangles.
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Magoosh
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If triangle ABC is an isosceles triangle, what is ∠ABC ?(1) ∠CAB=45°(2) ∠BCA=90°
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Magoosh
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In the United States, a jury consists either of six citizens, in a civil case, or the twelve required by a criminal case.
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Magoosh
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According to the last paragraph, planning itself may be thwarted for which of the following reasons?
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Magoosh
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If A is the initial amount put into an account, R is the annual percentage of interest written as a decimal, and the interest compounds annually, then which of the following would be an expression, in terms of A and R, for the interest accrued in three years?
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Magoosh
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Which of the following sets of numbers has the greatest standard deviation?
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Magoosh
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A drawer contains 8 socks, and 2 socks are selected at random without replacement. What is the probability that both socks are black?(1) The probability is less than 0.2 that the first sock is black.(2) The probability is more than 0.8 that the first sock is white.
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Manhattan
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If$$ [[x]] = x^{2} + 2x + 4$$, what is the value of [[3]]?
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