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Magoosh
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 In the diagram above, angle C = 90º and AC = BC. Point M is the midpoint of AB. Arc AXB has its center at C, and passes through A and B. Arc AYB has its center at M and passes through A and B. The shaded region between the two arcs is called a "lune." What is the ratio of the area of the lune to the area of triangle ABC?
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$$\frac{1}{\frac{3}{4}-\frac{2}{3}}=$$
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$$\frac{3}{8}$$ of all students at Social High are in all three of the following clubs: Albanian, Bardic, and Checkmate. $$\frac{1}{2}$$ of all students are in Albanian, $$\frac{5}{8}$$ are in Bardic, and $$\frac{3}{4}$$ are in Checkmate. If every student is in at least one club, what fraction of the student body is in exactly 2 clubs?
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Two secretaries, Sally and Lisa, type at even but difference paces. Sally is more experienced and types 80 characters per minute. Lisa, a beginner, can type only 30 characters per minute. On one day, Lisa starts typing before Sally. At some point, both have typed the same number of characters. Then both continue typing and Sally types 800 more characters until her computer breaks down. Assuming Lisa does not take any break, how long, in hours, will it take her to finish typing the same number of characters?
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Three types of aircraft fly three different routes which lengths are related as 1:3:5. The ratio of the amount of fuel burnt over these routes in the same respective order is 5:3:1. What are the ratios of their respective fuel consumption in units of distance per one unit of fuel burnt?
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On the first day of the climb, mountaineers covered $$\frac{5}{7}$$ of the distance to the top, on the second day of the climb, they covered $$\frac{1}{5}$$ of the remaining distance. What fraction of the total climb do the mountaineers have to cover to reach the top on the third day?
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Which of the following is NOT equal to the square of an integer?
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2, 4, 6, 8, n, 3, 5, 7, 9In the list above, if n is an integer between l and 10, inclusive, then the median must be
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Which of the following ratios is most nearly equal to the ratio $$1 +\sqrt{5}$$ to 2?
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PREP07 Test 2
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240, 120, 60, 30, . . . In the sequence above, each term after the first is ½ of the preceding term. What is the least term of the sequence that is greater than 1 ?
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PREP07 Test 2
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 The figure shown represents a board with four rows of pegs, and at the bottom of the board are four cells numbered 1 to 4. Whenever the ball shown passes through the opening between two adjacent pegs in the same row, it will hit the peg directly beneath the opening. The ball then has probability 1/2 of passing through the opening immediately to the left of that peg and probability 1/2 of passing through the opening immediately to the right. What is the probability that when the ball passes through the first two pegs at the top it will end up in cell 2 ?
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PREP07 Test 2
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If two of the four expressions x + y, x + 5y, x - y, and 5x - y are chosen at random, what is the probability that their product will be of the form of $$x^2 - (by)^2$$, where b is an integer?
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PREP07 Test 2
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Which of the following is equal to the average (arithmetic mean) of $$(x + 2)^2$$ and $$(x - 2)^2$$ ?
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PREP07 Test 2
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In the infinite sequence $$a_1$$,$$a_2$$,$$a_3$$,...,$$a_n$$,..., each term after the first is equal to twice the previous term. If $$a5-a2=12$$, what is the value of a1 ?
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PREP07 Test 2
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If $$(7^\frac{3}{4})^n=7$$, what is the value of n ?
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PREP07 Test 1
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Three grades of milk are 1 percent, 2 percent, and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x + y + z gallons of a 1.5 percent grade, what is x in terms of y and z ?
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PREP07 Test 1
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 In the circle above, PQ is parallel to diameter OR, and OR has length 18. What is the length of minor arc PQ ?
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PREP07 Test 1
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Alice's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did not save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?
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PREP07 Test 1
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Which of the following is equal to the value of $${2}^{5}+{2}^{5}+{3}^{5}+{3}^{5}+{3}^{5}$$ ?
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PREP07 Test 1
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The perimeter of a certain isosceles right triangle is 16+16$$\sqrt{2}$$. What is the length of the hypotenuse of the triangle?
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