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Magoosh	If $$6^{A} = 2, 6^{B} = 5, and 6^{Q} = 15$$, then express Q in terms of A and/or B.
Magoosh	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?
Magoosh	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?
Magoosh	A sum of money was distributed among Lyle, Bob and Chloe. First, Lyle received 4 dollars plus one-half of what remained. Next, Bob received 4 dollars plus one-third of what remained. Finally, Chloe received the remaining $32. How many dollars did Bob receive?
Magoosh	Sarah invested $38,700 in an account that paid 6.2% annual interest, compounding monthly. She left the money in this account, collecting interest for three full years. Approximately how much interest did she earn in the last month of this period?
Magoosh	If A, B and C represent different digits in the multiplication, then A + B + C =
Magoosh	Given that $$n = 10^{a} + 10^{b} + 10^{c}$$, where a, b, and c are distinct positive integers, how many different positive values of n result if n is less than 1 billion (1,000,000,000) ?
Magoosh	If a and b are integers and$$(\sqrt[3]{a}×\sqrt{b})^{6} = 500$$, then a + b could equal
Magoosh	If p and q are two different odd prime numbers such that p < q, then which of the following must be true?
Magoosh	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?
Magoosh	In the diagram above, the triangle is equilateral with a side of 2. All three circles are of equal size and all are tangent to each other and to two sides of the triangle. Which of the following is the radius of one of the circles?
Magoosh	At a certain university, 60% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women, tenured, or both, then what percent of the men are tenured?
Magoosh	$$(1\frac{4}{5})^{2}$$=
Magoosh	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?
Magoosh	There are 10 people in a room. If each person shakes hands with exactly 3 other people, what is the total number of handshakes?
Magoosh	What is the sum of all possible solutions of the equation$$\|x + 4\|^{2} - 10\|x + 4\| = 24?$$
Magoosh	When a company places a wholesale order on coffee cups with the company logo, they pay $692 for 80 cups. When Phil wants to buy just one such cup, it costs him $12.50. How much above the wholesale price per cup is he paying?
Magoosh	The average (arithmetic mean) of two numbers is 4x. If one of the numbers is y, then the value of the other number is
Magoosh	If 4x = 14 and xy = 1 then y =
Magoosh	The price of a pair of sneakers was $80 for the last six months of last year. On January first, the price increased 20%. After the price increase, an employee bought these sneakers with a 10% employee discount. What price did the employee pay?