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Magoosh
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The numbers p and q are both positive. If p percent of 160 equals q percent of 40, then \frac{p}{q} =
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Magoosh
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$$If x^{4} = y^{16}$$, then y =
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Manhattan
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 Two circles share a center at point C, as shown to the right. Segment AC is broken up into two shorter segments, AB and BC, with dimensions shown. What is the ratio of the area of the large circle to the area of the small circle ?
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Manhattan
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If 9^{2x + 1} = 27^{2}, then x =
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Manhattan
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A recycling facility is staffed by eight floor workers and one manager. All of the floor workers are paid equal wages, but the manager is paid q times as much as a floor worker. If the manager’s wages account for\frac {1}{7} of all wages paid at the facility, what is the value of q?
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Magoosh
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(3×10^{20})·(3×10^{-5})=
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Magoosh
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If points A and B are randomly placed on the circumference of a circle with radius 2, what is the probability that the length of chord AB is greater than 2?
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({\sqrt{{7}+\sqrt{48}}+\sqrt{{7}-\sqrt{48}}})^{2}
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Working alone at their respective constant rates, machine A and machine B can fill a certain order in 3 hours and 6 hours, respectively. If the two machines work simultaneously at their respective constant rates, how many hours does it take the two machines to fill 1/2 of that order?
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In the figure above, two circles with radii equal to 10 units of length overlap such that their centres, {O}_{1} and {O}_{2}, are 16 units apart. What is the distance between the line joining the centres of the circles and the line drawn through point P parallel to the line connecting the centres?
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If {n}=\sqrt{\frac{16}{81}} what is the value of \sqrt{n}?
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To make a certain type of ale, a brewery must mix enzymes, flax, and barley in the proportion 3:5:7 by volume. What is the largest amount in cubic meters of this mixture the brewery can obtain with one cubic meter of enzymes?
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For all positive values of P,W,L and A, consider the family of rectangles having perimeter P feet, width W feet, length L feet, and area A square feet. In the first column of the table, select the expression in terms of P and W that is equivalent to A, and in the second column of the table select the expression in terms of P and W that is equivalent to L. select only two expressions, one in each column.
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PREP07 Test 2
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 If the two regions above have the same area, what is the ratio t : s ?
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PREP07 Test 2
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What is the greatest possible area of a triangular region with one vertex at the center of a circle of radius 1 and the other two vertices on the circle?
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PREP07 Test 2
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In a survey of 248 people, 156 are married, 70 are self-employed, and 25 percent of those who are married are self-employed. If a person is to be randomly selected from those surveyed, what is the probability that the person selected will be self-employed but not married?
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PREP07 Test 1
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In a certain deck of cards, each card has a positive integer written on it. In a multiplication game, a child draws a card and multiplies the integer on the card by the next larger integer. If each possible product is between 15 and 200, then the least and greatest integers on the cards could be
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PREP07 Test 1
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All of the stocks on the over-the-counter market are designated by either a 4-letter or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
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Manhattan
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On a fishing excursion, Jeannie keeps$$\frac{ 1}{4} of the fish she catches and releases the remainder of the fish back into the lake. If \frac{2}{3}$$ of the fish she keeps are trout, and 1/3 of the fish she releases are trout, what proportion of the total number of fish she catches are trout?
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(1 + \sqrt{5})(1 - \sqrt{5}) =
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