Because the number of new yachts sold by Company J was always greater than the number of refurbished yachts it sold, a decrease in the former and an increase in the latter results in the two data lines coming closer together. Only the year 2001 shows the correct pattern and both of the proper changes:The number of refurbished yachts sold increased from about 6,200 to about 6,500, and the number of new yachts sold decreased from about 9,300 to about 8,800.The answer is choice (D).

Be sure you’ve identified the correct chart, the correct year, and the correct data line: Use the chart showing the number of yachts sold, the data line showing refurbished yachts, and the information for 1996.The data point for 1996 lies just below 6,000, so select choice (B). If you selected choice (A), you may have used the data line showing information for new yachts; if you selected choice (C), (D), or (E), you may have used information from the wrong year.

First, find the volume of the entire box, which equals 6 × 8 × 5 = 240. Solve for the volume of the three-dimensional triangular shape on top and subtract it from the total volume to find the volume of the shaded part.The triangular shape has known dimensions of 8 by 5.The third dimension ranges based on the length of AE, with 3 < AE < 4 because AE has to be bigger than EB.Therefore, the triangular shape’s volume falls between one-half of 8 × 5 × 3 = 60 and one-half of 8 × 5 × 4 = 80.The shaded area’s volume falls between 240 – 80 = 160 and 240 – 60 = 180. Only choice (D) works.

5.5

The volume of a cylinder = πr²h. Since the height equals the diameter: 332.75π = π(r²)(2r). Solving for r gives you 5.5 as the final answer

The distance from C to F is the diagonal of the box, so use the Super Pythagorean theorem: a² + b² + c² = d², where a, b, and c are the sides of the box and d is the diagonal.You have the length and height of the box, so use the volume formula to find the width:720 = (15)(6)w, so the width is 8. Now plug your numbers into the formula: 15² + 8² + 6² = d², so 325 = d², and d = 18.03.

The volume formula for a cube is V = s³, so a volume of 125 yields a side of 5. One face therefore has an area of 25, and the total area of 2 faces is 50. If you selected choice (C), you may have found the perimeter rather than the area. If you selected choice (B), you may have forgotten to find the total for 2 faces, and if you selected choice (A), you may have done both.

4,175

Calculate the surface area of each side of the box.Two sides are each: 29 × 37 × 2 = 1,073 square inches.Two other sides are 29 × 47 × 2 = 1,363 square inches.The last two sides are 37 × 47 × 2 = 1,739 square inches.The sum of the six sides is 4,175.

Draw a rectangular box.The longest distance between any two corners is going to be the box’s three-dimensional diagonal from a bottom corner to the top corner furthest away.You can solve this problem by using the Super Pythagorean theorem a² + b² + c² = d². 232 + 292 + 372 = 2,739 = d².The square root is a little more than 52.

Because all the edges are equal, the figure is a cube.The formula for the surface area of a cube is 6s², where s is a side of the cube. Thus, the surface area of the solid is 337.5; eliminate choice (A).The formula for the volume of a cube is s³, so the volume of the cube is 421.875; eliminate choice (B). WT is a diagonal of the cube.The formula for the diagonal of a box is a² + b² + c² = d², where a, b, and c are the sides of the box and d is the diagonal.Thus, WT is 12.99 and does not equal UT.Eliminate choice (C). VS is also a diagonal of the cube, so its length is 12.99.The only correct answer is choice (D).

704

Because the cylinder’s height is 11 and its volume is 176π, and V = πr²h, 176π = π(r²)(11), and r = 4.The diameter of the cylinder is 8.The box will need a length of 8 and a width of 8 to accommodate the base of the cylinder, and a height of 11.The volume of the smallest box will equal 8 × 8 × 11, or 704.