Magoosh
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If a and b are positive integers, and %$$(2^{3})(3^{4})(5^{7}) = a^{3}b$$, how many different possible values of b are there?
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Magoosh
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Given that the length of each side of a quadrilateral is a distinct integer and that the longest side is not greater than 7, how many different possible combinations of side lengths are there?
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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 x-y plane, point (p, q) is a $$\mathbf {lattice}$$ $$\mathbf {point}$$ if both p and q are integers. Circle C has a center at (–2, 1) and a radius of 6. Some points, such as the center (–2, 1), are inside the circle, but a point such as (4, 1) is $$\mathbf {on}$$ the circle but not $$\mathbf {in}$$ the circle. How many lattice points are in circle C?
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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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