diff --git "a/all/mathqa_geometry.json" "b/all/mathqa_geometry.json" new file mode 100644--- /dev/null +++ "b/all/mathqa_geometry.json" @@ -0,0 +1,27410 @@ +{ + "Source": "https://arxiv.org/pdf/2108.07732.pdf", + "Categories": [ + { + "Math complexity": 5, + "Language complexity": 7, + "Domain knowledge complexity": 4 + } + ], + "Instances": [ + { + "Input": "the perimeter of an equilateral triangle is 60 . if one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 45 , then how long is the base of isosceles triangle ?", + "Output Program": [ + "n0 = 60.0\nn1 = 45.0\nt0 = n0 / 3.0\nt1 = n1 - t0\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a small table has a length of 12 inches and a breadth of b inches . cubes are placed on the surface of the table so as to cover the entire surface . the maximum side of such cubes is found to be 4 inches . also , a few such tables are arranged to form a square . the minimum length of side possible for such a square is 80 inches . find b .", + "Output Program": [ + "import math\nn0 = 12.0\nn1 = 4.0\nn2 = 80.0\nt0 = n2 / n1\nt1 = n0**min(2.0, 5)\nt2 = t0**min(2.0, 5)\nt3 = t2 - t1\nanswer = math.sqrt(max(0, t3))\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a right triangle is inscribed in a circle . the legs of the triangle have lengths 6 and 8 . what is the diameter of the circle ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 8.0\nt0 = n0**min(2.0, 5)\nt1 = n1**min(2.0, 5)\nt2 = t0 + t1\nanswer = math.sqrt(max(0, t2))\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "four equal circles are described about the four corners of a square so that each touches two of the others . if a side of the square is 14 cm , then the area enclosed between the circumferences of the circles is :", + "Output Program": [ + "import math\nn0 = 14.0\nt0 = n0 / 2.0\nt1 = n0**2\nt2 = math.pi * t0**2\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "42.06195997410015" + ], + "split": "train" + }, + { + "Input": "george ' s car calls for 8 ounces of oil for each cylinder used . his car ' s engine has 6 cylinders . if 16 ounces of oil has already been put into the engine used , then how many additional ounces of oil are needed ?", + "Output Program": [ + "n0 = 8.0\nn1 = 6.0\nn2 = 16.0\nt0 = n0 * n1\nanswer = t0 - n2\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "what is the area of square field whose side of length 13 m ?", + "Output Program": [ + "n0 = 13.0\n\nanswer = n0**2\nprint(answer)" + ], + "Output Answer": [ + "169" + ], + "split": "train" + }, + { + "Input": "the number 219 can be written as sum of the squares of 3 different positive integers . what is the sum of these 3 different integers ?", + "Output Program": [ + "import math\nn0 = 219.0\nn1 = 3.0\nn2 = 3.0\nt0 = n0 / 2.0\nt1 = math.sqrt(max(0, t0))\nanswer = t1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "20.92844953645635" + ], + "split": "train" + }, + { + "Input": "eight cubes , each with a volume of 512 cm ^ 3 , are joined to form one large cube . what is the surface area of the large cube ?", + "Output Program": [ + "n0 = 512.0\nn1 = 3.0\nt0 = 2.0 * 4.0\nt1 = n0 * t0\nt2 = t1**(1 / 3)\nanswer = 6 * t2**2 # surface of a cube\nprint(answer)" + ], + "Output Answer": [ + "1535.9999999999995" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is twice its breadth . if its lengthis decreased by 5 cm & breadth is increased by 5 cm , the area of the rectangle is increased by 75 sq . cm . what is the length of the rectangle ?", + "Output Program": [ + "n0 = 5.0\nn1 = 5.0\nn2 = 75.0\nt0 = n0 * n0\nt1 = n0 * 2.0\nt2 = n2 + t0\nt3 = t1 - n0\nt4 = t2 / t3\nanswer = t4 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "a cube of edge 12 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 15 cm , find the rise in water level ?", + "Output Program": [ + "n0 = 12.0\nn1 = 20.0\nn2 = 15.0\nt0 = n1 * n2\nt1 = n0**3\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "5.76" + ], + "split": "train" + }, + { + "Input": "a rectangular floor that measures 24 meters by 64 meters is to be covered with carpet squares that each measure 8 meters by 8 meters . if the carpet squares cost $ 24 apiece , what is the total cost for the number of carpet squares needed to cover the floor ?", + "Output Program": [ + "n0 = 24.0\nn1 = 64.0\nn2 = 8.0\nn3 = 8.0\nn4 = 24.0\n\nanswer = n0 * n0\nprint(answer)" + ], + "Output Answer": [ + "576" + ], + "split": "train" + }, + { + "Input": "a rectangular lawn of dimensions 80 m * 40 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?", + "Output Program": [ + "n0 = 80.0\nn1 = 40.0\nn2 = 10.0\nn3 = 3.0\nt0 = n0 + n1\nt1 = t0 - n2\nt2 = n2 * t1\nanswer = n3 * t2\nprint(answer)" + ], + "Output Answer": [ + "3300" + ], + "split": "train" + }, + { + "Input": "can c and can \u0432 are both right circular cylinders . the radius of can c is twice the radius of can b , while the height of can c is half the height of can b . if it costs $ 4.00 to fill half of can b with a certain brand of gasoline , how much would it cost to completely fill can c with the same brand of gasoline ?", + "Output Program": [ + "n0 = 4.0\nt0 = n0 * 2.0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a cubical block of metal weighs 8 pounds . how much will another cube of the same metal weigh if its sides are twice as long ?", + "Output Program": [ + "n0 = 8.0\nt0 = 2.0 * 4.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "the area of a rhombus is equal to the area of a square whose side length is 8 cm . if one of the diagonals is 16 cm what is the length of other diagonal ?", + "Output Program": [ + "n0 = 8.0\nn1 = 16.0\nt0 = n0**2\nt1 = t0 * 2.0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "cuboid volume and base area are 144 m ^ 3 and 18 m ^ 3 respectively . find the height of a cuboid ?", + "Output Program": [ + "n0 = 144.0\nn1 = 3.0\nn2 = 18.0\nn3 = 3.0\n\nanswer = n0 / n2\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a cubical block of metal weighs 4 pounds . how much will another cube of the same metal weigh if its sides are twice as long ?", + "Output Program": [ + "n0 = 4.0\nt0 = 2.0 * 4.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "if the length of the sides of two cubes are in the ratio 4 : 1 , what is the ratio of their total surface area ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\n\nanswer = n0 * n0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a rectangular grass field is 85 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?", + "Output Program": [ + "n0 = 85.0\nn1 = 55.0\nn2 = 2.5\nn3 = 2.0\nt0 = n2 * n3\nt1 = n0 * n1 # area of rectangle\nt2 = n0 + t0\nt3 = n1 + t0\nt4 = t2 * t3 # area of rectangle\nt5 = t4 - t1\nanswer = n3 * t5\nprint(answer)" + ], + "Output Answer": [ + "1450" + ], + "split": "train" + }, + { + "Input": "the diagonal of a rhombus are 25 m and 50 m . its area is :", + "Output Program": [ + "n0 = 25.0\nn1 = 50.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "625" + ], + "split": "train" + }, + { + "Input": "the diameter of a cylindrical tin is 14 cm and height is 5 cm . find the volume of the cylinder ?", + "Output Program": [ + "import math\nn0 = 14.0\nn1 = 5.0\nt0 = n0 / 2.0\nt1 = math.pi * t0**2 * n1\nanswer = t1 / 3.141592653589793\nprint(answer)" + ], + "Output Answer": [ + "245" + ], + "split": "train" + }, + { + "Input": "the water level in a rectangular swimming pool measuring 40 feet by 25 feet is to be lowered by 6 inches . how many gallons of water must be removed ? ( 1 cu ft = 7.5 gallons )", + "Output Program": [ + "n0 = 40.0\nn1 = 25.0\nn2 = 6.0\nn3 = 1.0\nn4 = 7.5\nt0 = 10.0 + 2.0\nt1 = n2 / t0\nt2 = n0 * n1 * t1\nanswer = n4 * t2\nprint(answer)" + ], + "Output Answer": [ + "3750" + ], + "split": "train" + }, + { + "Input": "the volume of a cube is 1728 cc . find its surface .", + "Output Program": [ + "n0 = 1728.0\nt0 = n0**(1 / 3)\nanswer = 6 * t0**2 # surface of a cube\nprint(answer)" + ], + "Output Answer": [ + "863.9999999999997" + ], + "split": "train" + }, + { + "Input": "the length of rectangle is thrice its breadth and its perimeter is 40 m , find the area of the rectangle ?", + "Output Program": [ + "n0 = 40.0\nt0 = 2.0 * 3.0\nt1 = 1.0 * 2.0\nt2 = t0 + t1\nt3 = n0 / t2\nt4 = t3 * 3.0\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "a 25 cm wide path is to be made around a circular garden having a diameter of 4 meters . approximate area of the path is square meters is ?", + "Output Program": [ + "import math\nn0 = 25.0\nn1 = 4.0\nt0 = n1 / 2.0\nt1 = n0 / 100.0\nt2 = t0 + t1\nt3 = math.pi * t0**2\nt4 = math.pi * t2**2\nanswer = t4 - t3\nprint(answer)" + ], + "Output Answer": [ + "3.3379421944391545" + ], + "split": "train" + }, + { + "Input": "a circular swimming pool is surrounded by a concrete wall 4 ft wide . if the area of the concrete wall surrounding the pool is 11 / 25 that of the pool , then the radius of the pool is ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 11.0\nn2 = 25.0\nt0 = n1 / n2\nt1 = n0 * 2.0\nt2 = n0**min(2.0, 5)\nt3 = t0 * n0\nt4 = t1**min(2.0, 5)\nt5 = t3 * t2\nt6 = t5 + t4\nt7 = math.sqrt(max(0, t6))\nt8 = t1 + t7\nt9 = t8 / t0\nanswer = t9 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a certain rectangular crate measures 12 feet by 16 feet by 18 feet . a cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces . what should the radius of the tank be if it is to be of the largest possible volume ?", + "Output Program": [ + "import math\nn0 = 12.0\nn1 = 16.0\nn2 = 18.0\nt0 = n1 / 2.0\nt1 = n0 * 3.141592653589793\nt2 = math.pi * t0**2 * n0\nt3 = t2 / t1\nanswer = math.sqrt(max(0, t3))\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular plot is 10 mtr more than its width . the cost of fencing the plot along its perimeter at the rate of rs . 6.5 mtr is rs . 910 . the perimeter of the plot is ?", + "Output Program": [ + "n0 = 10.0\nn1 = 6.5\nn2 = 910.0\nt0 = n2 / n1\nt1 = t0 / 2.0\nt2 = t1 - n0\nt3 = t2 / 2.0\nt4 = t3 + n0\nt5 = t4 + t3\nanswer = t5 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "train" + }, + { + "Input": "what will be the ratio between the area of a rectangle and the area of a triangle with one of the sides of rectangle as base and a vertex on the opposite side of rectangle .", + "Output Program": [ + "t0 = 1.0 * 1.0 # area of rectangle\nt1 = t0 * t0 / 2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a man walking at the rate of 6 km per hour crosses a square field diagonally in 9 seconds the area of the field is", + "Output Program": [ + "n0 = 6.0\nn1 = 9.0\nt0 = n0 * 1000.0\nt1 = 10.0 * 360.0\nt2 = t0 / t1\nt3 = n1 * t2\nt4 = t3**min(2.0, 5)\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "112.5" + ], + "split": "train" + }, + { + "Input": "the area of a triangle is with base 4 m and height 5 m ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the side of a square is increased by 25 % then how much % does its area increases ?", + "Output Program": [ + "n0 = 25.0\nt0 = n0 + 100.0\nt1 = 100.0**2\nt2 = t0**2\nt3 = t2 - t1\nt4 = t3 * 100.0\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "56.25" + ], + "split": "train" + }, + { + "Input": "hall is 15 m long and 12 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , the volume of the hall is :", + "Output Program": [ + "n0 = 15.0\nn1 = 12.0\nt0 = n0 + n1\nt1 = n0 * n1\nt2 = t1 * 2.0\nt3 = t0 * 2.0\nt4 = t2 / t3\nanswer = t4 * t1\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "train" + }, + { + "Input": "abcd is a square . f and e are the midpoints of sides ad and cd , respectively . the area of triangle fed is 2 square inches . what is the area of square abcd ( in square inches ) ?", + "Output Program": [ + "n0 = 2.0\nt0 = n0 * 2.0\nanswer = t0 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 972 sq m , then what is the breadth of the rectangular plot ?", + "Output Program": [ + "import math\nn0 = 972.0\nt0 = n0 / 3.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "if the radius of a circle is increased by 12 % , then the area of the circle", + "Output Program": [ + "n0 = 12.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = t1**min(2.0, 5)\nt3 = t2 - 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25.44000000000002" + ], + "split": "train" + }, + { + "Input": "in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 7 , 0 ) , ( 0 , - 3.5 ) , ( - 7 , 0 ) ?", + "Output Program": [ + "n0 = 0.0\nn1 = 3.5\nn2 = 7.0\nn3 = 0.0\nn4 = 0.0\nn5 = 3.5\nn6 = 7.0\nn7 = 0.0\nt0 = n2 * 2.0\nt1 = n1 * 2.0\nanswer = t0 * t1 / 2\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "train" + }, + { + "Input": "the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 6 cm each . the radius of the sphere is", + "Output Program": [ + "import math\nn0 = 6.0\nt0 = n0 / 2.0\nt1 = 4.0 * 3.141592653589793\nt2 = n0 * t0\nt3 = t2 * 3.141592653589793\nt4 = t3 * 2.0\nt5 = t4 / t1\nanswer = math.sqrt(max(0, t5))\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the area of a triangle is with base 8 m and height 4 m ?", + "Output Program": [ + "n0 = 8.0\nn1 = 4.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a rectangular garden is to be twice as long as it is wide . if 900 yards of fencing , including the gate , will completely enclose the garden , what will be the length of the garden , in yards ?", + "Output Program": [ + "n0 = 900.0\nt0 = 1.0 + 2.0\nt1 = t0 * 2.0\nt2 = n0 / t1\nanswer = t2 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "if each edge of a cube is doubled , then its volume :", + "Output Program": [ + "\nanswer = 2.0**min(3.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 10 inches tall . carmen places her sculpture on a base that is 4 inches tall . how tall are the sculpture andbase together ?", + "Output Program": [ + "n0 = 2.0\nn1 = 10.0\nn2 = 4.0\nt0 = n0 + n1\nt1 = n0 * t0\nt2 = t1 + 10.0\nt3 = n2 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "3.1666666666666665" + ], + "split": "train" + }, + { + "Input": "if the space diagonal of cube c is 5 inches long , what is the length , in inches , of the diagonal of the base of cube c ?", + "Output Program": [ + "n0 = 5.0\n\nanswer = n0 * 1.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if the height of a cone is increased by 190 % then its volume is increased by ?", + "Output Program": [ + "n0 = 190.0\n\nanswer = n0 * 1.0 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "190" + ], + "split": "train" + }, + { + "Input": "the parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )", + "Output Program": [ + "import math\nn0 = 16.0\nn1 = 14.0\nt0 = 2 * (n0 + n1) # perimetere of rectangle\nt1 = t0 / 4. # square edge given perimeter\nt2 = t1 / 2.0\nt3 = 2 * math.pi * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "23.561944901923447" + ], + "split": "train" + }, + { + "Input": "you buy a piece of land with an area of \u00e2 \u02c6 \u0161 625 , how long is one side of the land plot ?", + "Output Program": [ + "import math\nn0 = 625.0\n\nanswer = math.sqrt(max(0, n0))\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "a rectangular box 60 m long and 40 m wide has two concrete crossroads running in the middle of the box and rest of the box has been used as a lawn . the area of the lawn is 2109 sq . m . what is the width of the road ?", + "Output Program": [ + "import math\nn0 = 60.0\nn1 = 40.0\nn2 = 2109.0\nt0 = n0 * n1\nt1 = 100.0**min(2.0, 5)\nt2 = t0 - n2\nt3 = t2 * 4.0\nt4 = t1 - t3\nt5 = math.sqrt(max(0, t4))\nt6 = 100.0 - t5\nanswer = t6 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "in the xy - plane , a triangle has vertices ( 0,0 ) , ( 4,0 ) and ( 4,10 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ?", + "Output Program": [ + "n0 = 0.0\nn1 = 0.0\nn2 = 4.0\nn3 = 0.0\nn4 = 4.0\nn5 = 10.0\nn6 = 0.0\nt0 = n0 + 10.0\nanswer = 4.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "train" + }, + { + "Input": "right triangle pqr is the base of the prism in the figure above . if pq = pr = \u00e2 \u02c6 \u0161 14 and the height of the prism is 8 , what is the volume of the prism ?", + "Output Program": [ + "import math\nn0 = 14.0\nn1 = 8.0\nt0 = math.sqrt(max(0, n0))\nt1 = t0 * t0 / 2\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "three table runners have a combined area of 224 square inches . by overlapping the runners to cover 80 % of a table of area 175 square inches , the area that is covered by exactly two layers of runner is 24 square inches . what is the area of the table that is covered with three layers of runner ?", + "Output Program": [ + "n0 = 224.0\nn1 = 80.0\nn2 = 175.0\nn3 = 24.0\nt0 = n1 / 100.0\nt1 = n0 - n3\nt2 = n2 * t0\nt3 = t1 - t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "tough and tricky questions : number properties . what is the smallest positive integer x such that 1512 x is the cube of a positive integer ?", + "Output Program": [ + "n0 = 1512.0\nt0 = n0 / 2.0\nt1 = t0 / 2.0\nt2 = t1 / 2.0\nt3 = t2 / 3.0\nt4 = t3 / 3.0\nt5 = t4 / 3.0\nanswer = t5**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "train" + }, + { + "Input": "find the area of a parallelogram with base 24 cm and height 16 cm .", + "Output Program": [ + "n0 = 24.0\nn1 = 16.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "384" + ], + "split": "train" + }, + { + "Input": "the diagonal of a rectangle is 41 cm and its area is 20 sq . cm . the perimeter of the rectangle must be :", + "Output Program": [ + "import math\nn0 = 41.0\nn1 = 20.0\nt0 = n1 * 2.0\nt1 = n0 + t0\nt2 = math.sqrt(max(0, t1))\nanswer = t2 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "the diagonals of a rhombus are 11 cm and 20 cm . find its area ?", + "Output Program": [ + "n0 = 11.0\nn1 = 20.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "110" + ], + "split": "train" + }, + { + "Input": "a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 5 m , the volume of the box ( in m 3 ) is :", + "Output Program": [ + "n0 = 48.0\nn1 = 36.0\nn2 = 5.0\nn3 = 3.0\nt0 = n2 * 2.0\nt1 = n0 - t0\nt2 = n1 - t0\nanswer = n2 * t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "4940" + ], + "split": "train" + }, + { + "Input": "a rectangular lawn of dimensions 80 m * 60 m has two roads each 15 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?", + "Output Program": [ + "n0 = 80.0\nn1 = 60.0\nn2 = 15.0\nn3 = 3.0\nt0 = n0 + n1\nt1 = t0 - n2\nt2 = n2 * t1\nanswer = n3 * t2\nprint(answer)" + ], + "Output Answer": [ + "5625" + ], + "split": "train" + }, + { + "Input": "what is the area of square field whose side of length 8 m ?", + "Output Program": [ + "n0 = 8.0\n\nanswer = n0**2\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "each of the 39 points is placed either inside or on the surface of a perfect sphere . if 72 % or fewer of the points touch the surface , what is the maximum number of segments which , if connected from those points to form chords , could be the diameter of the sphere ?", + "Output Program": [ + "n0 = 39.0\nn1 = 72.0\nt0 = n1 / 100.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "14.04" + ], + "split": "train" + }, + { + "Input": "a square mirror has exactly half the area of the rectangular wall on which it is hung . if each side of the mirror is 24 inches and the width of the wall is 42 inches , what is the length of the wall , in inches ?", + "Output Program": [ + "n0 = 24.0\nn1 = 42.0\nt0 = n0**2\nt1 = t0 * 2.0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "27.428571428571427" + ], + "split": "train" + }, + { + "Input": "in a certain parallelogram the degree measure of one angle exceeds that of the other by 10 what is the degree measure of the smaller angle ?", + "Output Program": [ + "n0 = 10.0\nt0 = 3600.0 / 10.0\nt1 = n0 * 2.0\nt2 = t0 - t1\nanswer = t2 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "85" + ], + "split": "train" + }, + { + "Input": "what is the area of square field whose side of length 7 m ?", + "Output Program": [ + "n0 = 7.0\n\nanswer = n0**2\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "train" + }, + { + "Input": "16 meters of wire is available to fence off a flower bed in the form of a circular sector . what must the radius of the circle in meters be , if we wish to have a flower bed with the greatest possible surface area ?", + "Output Program": [ + "n0 = 16.0\n\nanswer = n0 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "if each side of a rectangle is increased by 100 % , by what % the area increases ?", + "Output Program": [ + "n0 = 100.0\nt0 = n0 / 100.0\nt1 = t0 * 2.0\nt2 = t1**min(2.0, 5)\nt3 = t2 - 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "if the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm , a square with the same area as the original rectangle would result . find the perimeter of the original rectangle ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nt0 = n0 + n1\nt1 = n0 * n1\nt2 = n1 * t0\nt3 = t2 - t1\nt4 = t0 + t3\nt5 = t4 + t3\nanswer = t5 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a square carpet with an area 169 m 2 must have 2 metres cut - off one of its edges in order to be a perfect fit for a rectangular room . what is the area of rectangular room ?", + "Output Program": [ + "import math\nn0 = 169.0\nn1 = 2.0\nn2 = 2.0\nt0 = math.sqrt(max(0, n0))\nt1 = t0 - 2.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "143" + ], + "split": "train" + }, + { + "Input": "the edge of a cube is 5 a cm . find its surface ?", + "Output Program": [ + "n0 = 5.0\n\nanswer = 6 * n0**2 # surface of a cube\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "a ring x of diameter 16 inches is placed inside another ring y of diameter of 18 inches . how much fraction of the ring x surface is not covered by the ring y ?", + "Output Program": [ + "import math\nn0 = 16.0\nn1 = 18.0\nt0 = n1 / 2.0\nt1 = n0 / 2.0\nt2 = math.pi * t0**2\nt3 = math.pi * t1**2\nt4 = t2 - t3\nanswer = t4 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.2098765432098765" + ], + "split": "train" + }, + { + "Input": "the area of a triangle is with base 4.5 m and height 6 m ?", + "Output Program": [ + "n0 = 4.5\nn1 = 6.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "13.5" + ], + "split": "train" + }, + { + "Input": "cubes with each side one inch long are glued together to form a larger cube . the larger cube ' s face is painted with red color and the entire assembly is taken apart . 24 small cubes are found with no paints on them . how many of unit cubes have at least one face that is painted red ?", + "Output Program": [ + "n0 = 24.0\nt0 = 1.0 + 3.0\nt1 = t0 + 1.0\nt2 = t1**min(3.0, 5)\nanswer = t2 - n0\nprint(answer)" + ], + "Output Answer": [ + "101" + ], + "split": "train" + }, + { + "Input": "if the sum of a number and its square is 240 , what is the number ?", + "Output Program": [ + "import math\nn0 = 240.0\nt0 = math.sqrt(max(0, n0))\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "the diagonals of a rhombus are 30 cm and 12 cm . find its area ?", + "Output Program": [ + "n0 = 30.0\nn1 = 12.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "train" + }, + { + "Input": "two equilateral triangle of side 12 cm are placed one on top another , such a 6 pionted star is formed if the six vertices lie on a circle what is the area of the circle not enclosed by the star ?", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 2.0\nn3 = 19.0\nt0 = n0 * n1\nt1 = n2 * t0\nt2 = t1 / n2\nanswer = t2 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "33" + ], + "split": "train" + }, + { + "Input": "paper charge is rs . 60 per kg . how much expenditure would be there to cover a cube of edge 10 m with a paper , if one kg of paper covers 20 sq . m . area ?", + "Output Program": [ + "n0 = 60.0\nn1 = 10.0\nn2 = 20.0\nt0 = n0 / n1\nt1 = n1 * n1\nt2 = t0 * t1\nt3 = t2 / n2\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "1800" + ], + "split": "train" + }, + { + "Input": "rectangle a has sides a and b , and rectangle b has sides c and d . if a / c = b / d = 2 / 5 , what is the ratio of rectangle a \u2019 s area to rectangle b \u2019 s area ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nt0 = n0**min(2.0, 5)\nt1 = n1**min(2.0, 5)\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.16" + ], + "split": "train" + }, + { + "Input": "find the curved surface area , if the radius of a cone is 28 m and slant height is 30 m ?", + "Output Program": [ + "n0 = 28.0\nn1 = 30.0\nt0 = n0 * n1\nanswer = t0 * 3.141592653589793\nprint(answer)" + ], + "Output Answer": [ + "2638.9378290154264" + ], + "split": "train" + }, + { + "Input": "three table runners have a combined area of 220 square inches . by overlapping the runners to cover 80 % of a table of area 175 square inches , the area that is covered by exactly two layers of runner is 24 square inches . what is the area of the table that is covered with three layers of runner ?", + "Output Program": [ + "n0 = 220.0\nn1 = 80.0\nn2 = 175.0\nn3 = 24.0\nt0 = n1 / 100.0\nt1 = n0 - n3\nt2 = n2 * t0\nt3 = t1 - t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "an isosceles triangle with sides 13 13 10 and there is a circle inscribed it . find the radius of circle ?", + "Output Program": [ + "import math\nn0 = 13.0\nn1 = 13.0\nn2 = 10.0\nt0 = (lambda s, a, b, c: math.sqrt(max(0, s * (s - a) * (s - b) * (s - c))))((n0 + n0 + n2) / 2, n0, n0, n2) # Heron's formula\nt1 = n0 + n0 + n2 # perimeter of a triangle\nt2 = t0 * 2.0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "3.3333333333333335" + ], + "split": "train" + }, + { + "Input": "the diagonals of a rhombus are 10 cm and 15 cm . find its area ?", + "Output Program": [ + "n0 = 10.0\nn1 = 15.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "a rectangular floor is covered by a rug except for a strip 3 meters wide along each of the four edge . if the floor is 12 meters by 10 meters , what is the area of the rug in square meters ?", + "Output Program": [ + "n0 = 3.0\nn1 = 12.0\nn2 = 10.0\nt0 = n0 * 2.0\nt1 = n1 - t0\nt2 = n2 - t0\nanswer = t1 * t2 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "the area of a square field is 576 km 2 . how long will it take for a horse to run around at the speed of 12 km / h ?", + "Output Program": [ + "import math\nn0 = 576.0\nn1 = 2.0\nn2 = 12.0\nt0 = math.sqrt(max(0, n0))\nt1 = t0 * 4.0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm ?", + "Output Program": [ + "n0 = 25.0\nn1 = 30.0\nt0 = 10.0 * 2.0\nt1 = t0 * 2.0\nanswer = n1 * t1 / 2\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "train" + }, + { + "Input": "in a parallelogram , the length of one diagonal and the perpendicular dropped on that diagonal are 30 and 20 metres respectively . find its area", + "Output Program": [ + "n0 = 30.0\nn1 = 20.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "train" + }, + { + "Input": "find the area of the quadrilateral of one of its diagonals is 24 cm and its off sets 9 cm and 6 cm ?", + "Output Program": [ + "n0 = 24.0\nn1 = 9.0\nn2 = 6.0\nt0 = n1 + n2\nt1 = 1.0 / 2.0\nt2 = t0 * t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "train" + }, + { + "Input": "what is the measure of the angle e made by the diagonals of the any adjacent sides of a cube .", + "Output Program": [ + "\nanswer = 180.0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "a rectangular photograph is surrounded by a border that is 2 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 4 inches wide on each side , the total area would have been ( m + 94 ) square inches . what is the perimeter of the photograph , in inches ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 94.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nt2 = t0**min(2.0, 5)\nt3 = t1**min(2.0, 5)\nt4 = t2 - t3\nt5 = n2 - t4\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "23" + ], + "split": "train" + }, + { + "Input": "the area of a rectangular field is equal to 300 square meters . its perimeter is equal to 70 meters . find the width of this rectangle .", + "Output Program": [ + "import math\nn0 = 300.0\nn1 = 70.0\nt0 = n1 / 2.0\nt1 = n0 * 4.0\nt2 = t0 * t0\nt3 = t2 - t1\nt4 = math.sqrt(max(0, t3))\nt5 = t0 - t4\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "in a rectangular coordinate system , what is the area of a rectangle whose vertices have the coordinates ( - 7 , 1 ) , ( 1 , 1 ) , ( 1 , - 6 ) and ( - 7 , - 6 ) ?", + "Output Program": [ + "n0 = 7.0\nn1 = 1.0\nn2 = 1.0\nn3 = 1.0\nn4 = 1.0\nn5 = 6.0\nn6 = 7.0\nn7 = 6.0\nt0 = n0 + n1\nt1 = n1 + n5\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "a lady grows cauliflower in her garden that is in the shape of a square . each cauliflower takes 1 square foot of area in her garden . this year , she has increased her output by 223 cauliflower when compared to last year . the shape of the area used for growing the cauliflower has remained a square in both these years . how many cauliflowers did she produce this year ?", + "Output Program": [ + "n0 = 1.0\nn1 = 223.0\nt0 = n1 - n0\nt1 = t0 / 2.0\nt2 = t1**min(2.0, 5)\nanswer = n1 + t2\nprint(answer)" + ], + "Output Answer": [ + "12544" + ], + "split": "train" + }, + { + "Input": "if ( 20 ) \u00b2 is subtracted from the square of a number , the answer so obtained is 4321 . what is the number ?", + "Output Program": [ + "import math\nn0 = 20.0\nn1 = 4321.0\nt0 = 10.0 * 2.0\nt1 = t0**min(2.0, 5)\nt2 = n1 + t1\nanswer = math.sqrt(max(0, t2))\nprint(answer)" + ], + "Output Answer": [ + "68.70953354520753" + ], + "split": "train" + }, + { + "Input": "the content of several smaller cylinders ( 3 meter diameter and 6 meter height ) were to be emptied into a larger cylinder ( 20 meter diameter and 10 meter height ) , how many smaller cylinders will fill up the larger cylinder ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 6.0\nn2 = 20.0\nn3 = 10.0\nt0 = n2 / 2.0\nt1 = n0 / 2.0\nt2 = math.pi * t0**2 * n3\nt3 = math.pi * t1**2 * n1\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "74.07407407407408" + ], + "split": "train" + }, + { + "Input": "a semicircle has a radius of 9 . what is the approximate perimeter of the semicircle ?", + "Output Program": [ + "import math\nn0 = 9.0\nt0 = 2 * math.pi * n0\nt1 = n0 * 2.0\nt2 = t0 / 2.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "46.27433388230814" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is 4 times its width . if the width of the rectangle is 5 inches , what is the rectangle ' s area , in square inches ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nt0 = n0 * n1\nanswer = n1 * t0 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "in a rectangular coordinate system , what is the area of a rectangle whose vertices have the coordinates ( - 5 , 1 ) , ( 1 , 1 ) , ( 1 , - 4 ) and ( - 5 , - 4 ) ?", + "Output Program": [ + "n0 = 5.0\nn1 = 1.0\nn2 = 1.0\nn3 = 1.0\nn4 = 1.0\nn5 = 4.0\nn6 = 5.0\nn7 = 4.0\nt0 = n0 + n1\nt1 = n1 + n5\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "what is the perimeter , in meters , of a rectangular garden 8 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide ?", + "Output Program": [ + "n0 = 8.0\nn1 = 16.0\nn2 = 12.0\nt0 = n1 * n2 # area of rectangle\nt1 = t0 / n0\nanswer = 2 * (n0 + t1) # perimetere of rectangle\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "let the sides of a rectangular prism are consecutive multiples of 5 . which among the following could be the base area", + "Output Program": [ + "n0 = 5.0\nt0 = n0 * 3.0\nt1 = t0 * 2.0\nanswer = t1 * t0\nprint(answer)" + ], + "Output Answer": [ + "450" + ], + "split": "train" + }, + { + "Input": "a rectangular tiled patio is composed of 30 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 30 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?", + "Output Program": [ + "import math\nn0 = 30.0\nn1 = 2.0\nn2 = 4.0\nn3 = 30.0\nt0 = n0 * n1\nt1 = -n2\nt2 = n2**min(n1, 5)\nt3 = n2 * t0\nt4 = t3 + t2\nt5 = math.sqrt(max(0, t4))\nt6 = t1 + t5\nt7 = t6 / n1\nanswer = n0 / t7\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the dimensions of a rectangular solid are 6 inches , 5 inches , and 8 inches . if a cube , a side of which is equal to one of the dimensions of the rectangular solid , is placed entirely within thespherejust large enough to hold the cube , what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 2.0\nn3 = 1.0\nn4 = 10.0\nn5 = 35.0\nn6 = 4.0\nn7 = 3.0\nn8 = 5.0\nn9 = 3.0\nt0 = n4 + n8\nt1 = n4 * n6\nt2 = t1 / n1\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "if the length of a rectangle is increased by 20 % and the breadth is reduced by 20 % , what will be the effect on its area ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = 1.0 - t0\nt3 = t1 * t2\nt4 = 1.0 - t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "4.0000000000000036" + ], + "split": "train" + }, + { + "Input": "an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 50 cm , find the sum of the perimeters of all the triangles .", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 3.0\nn3 = 2.0\nn4 = 1.0\nn5 = 50.0\nt0 = n5 + n5 + n5 # perimeter of a triangle\nanswer = t0 + t0\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "three walls have wallpaper covering a combined area of 300 square meters . by overlapping the wallpaper to cover a wall with an area of 180 square meters , the area that is covered by exactly two layers of wallpaper is 40 square meters . what is the area that is covered with three layers of wallpaper ?", + "Output Program": [ + "n0 = 300.0\nn1 = 180.0\nn2 = 40.0\nt0 = n0 - n1\nt1 = t0 - n2\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "find the area of the quadrilateral of one of its diagonals is 26 cm and its off sets 9 cm and 6 cm ?", + "Output Program": [ + "n0 = 26.0\nn1 = 9.0\nn2 = 6.0\nt0 = n1 + n2\nt1 = 1.0 / 2.0\nt2 = t0 * t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "195" + ], + "split": "train" + }, + { + "Input": "a rectangular garden is to be twice as long as it is wide . if 240 yards of fencing , including the gate , will completely enclose the garden , what will be the length of the garden , in yards ?", + "Output Program": [ + "n0 = 240.0\nt0 = 1.0 + 2.0\nt1 = t0 * 2.0\nt2 = n0 / t1\nanswer = t2 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "the diagonals of a rhombus are 14 cm and 18 cm . find its area ?", + "Output Program": [ + "n0 = 14.0\nn1 = 18.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "126" + ], + "split": "train" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 650 sq . feet , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 20.0\nn1 = 650.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "85" + ], + "split": "train" + }, + { + "Input": "the second angle of a triangle is double the first ( 110 ) . the third angle is 40 less than the first ( 15 ) . find the first angle .", + "Output Program": [ + "n0 = 110.0\nn1 = 40.0\nn2 = 15.0\n\nanswer = n1 + n2\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "train" + }, + { + "Input": "how many diagonals does a polygon with 17 sides have , if one of its vertices does not connect to any diagonal ?", + "Output Program": [ + "n0 = 17.0\nt0 = n0 - 1.0\nt1 = t0 - 3.0\nt2 = t0 * t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "104" + ], + "split": "train" + }, + { + "Input": "if the radius of the sphere is 14 m . then its total surface area is", + "Output Program": [ + "import math\nn0 = 14.0\n\nanswer = 4 * math.pi * n0**2\nprint(answer)" + ], + "Output Answer": [ + "2463.0086404143976" + ], + "split": "train" + }, + { + "Input": "a volume of 10996 l water is in a container of sphere . how many hemisphere of volume 4 l each will be required to transfer all the water into the small hemispheres ?", + "Output Program": [ + "n0 = 10996.0\nn1 = 4.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "2749" + ], + "split": "train" + }, + { + "Input": "the area of rectangular field of length 90 meters and breadth 80 meters is equal to the area of a square plot . what will be the length of the diagonal of the square plot ?", + "Output Program": [ + "import math\nn0 = 90.0\nn1 = 80.0\nt0 = n0 * n1 # area of rectangle\nt1 = math.sqrt(t0) # square edge given area\nanswer = math.sqrt(t1**2 + t1**2)\nprint(answer)" + ], + "Output Answer": [ + "120.00000000000001" + ], + "split": "train" + }, + { + "Input": "the parameter of a square is equal to the perimeter of a rectangle of length 22 cm and breadth 16 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )", + "Output Program": [ + "import math\nn0 = 22.0\nn1 = 16.0\nt0 = 2 * (n0 + n1) # perimetere of rectangle\nt1 = t0 / 4. # square edge given perimeter\nt2 = t1 / 2.0\nt3 = 2 * math.pi * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "29.845130209103033" + ], + "split": "train" + }, + { + "Input": "the base of a triangle is 15 cm and height is 12 cm . the height of another triangle of double the area having the base 20 cm is :", + "Output Program": [ + "n0 = 15.0\nn1 = 12.0\nn2 = 20.0\nt0 = n0 * n1 / 2\nt1 = t0 * 2.0\nt2 = t1 * 2.0\nanswer = t2 / n2\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "rectangular tile each of size 20 cm by 30 cm must be laid horizontally on a rectangular floor of size 100 cm by 150 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :", + "Output Program": [ + "n0 = 20.0\nn1 = 30.0\nn2 = 100.0\nn3 = 150.0\nt0 = n2 * n3\nt1 = n0 * n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular field is 7 / 5 its width . if the perimeter of the field is 336 meters , what is the width of the field ?", + "Output Program": [ + "n0 = 7.0\nn1 = 5.0\nn2 = 336.0\nt0 = n0 / n1\nt1 = t0 + t0\nt2 = t1 + 2.0\nanswer = n2 / t2\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "the mass of 1 cubic meter of a substance is 200 kg under certain conditions . what is the volume in cubic centimeters of 1 gram of this substance under these conditions ? ( 1 kg = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )", + "Output Program": [ + "n0 = 1.0\nn1 = 200.0\nn2 = 1.0\nn3 = 1.0\nn4 = 1000.0\nn5 = 1.0\nn6 = 1.0\nn7 = 0.0\nt0 = 1000.0 * 1000.0\nt1 = n1 * 1000.0\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 8 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 8.0\nn1 = 680.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "178" + ], + "split": "train" + }, + { + "Input": "smita was making a cube with dimensions 5 * 5 * 5 using 1 * 1 * 1 cubes . what is the number of cubes needed to make a hollow cube looking of the same shape ?", + "Output Program": [ + "n0 = 5.0\nn1 = 5.0\nn2 = 5.0\nn3 = 1.0\nn4 = 1.0\nn5 = 1.0\nt0 = n0**3\nt1 = 3.0**3\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "98" + ], + "split": "train" + }, + { + "Input": "find the area of the quadrilateral of one of its diagonals is 15 cm and its off sets 6 cm and 4 cm ?", + "Output Program": [ + "n0 = 15.0\nn1 = 6.0\nn2 = 4.0\nt0 = n1 + n2\nt1 = 1.0 / 2.0\nt2 = t0 * t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "a cubical block of metal weighs 6 pounds . how much will another cube of the same metal weigh if its sides are twice as long ?", + "Output Program": [ + "n0 = 6.0\nt0 = 2.0 * 4.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "if the volume of two cubes are in the ratio 64 : 1 , the ratio of their edges is :", + "Output Program": [ + "n0 = 64.0\nn1 = 1.0\n\nanswer = n0**(1 / 3)\nprint(answer)" + ], + "Output Answer": [ + "3.9999999999999996" + ], + "split": "train" + }, + { + "Input": "four horses are tethered at four corners of a square plot of side 63 metres so that they just can not reach one another . the area left ungrazed is :", + "Output Program": [ + "n0 = 63.0\nt0 = n0 / 2.0\nt1 = n0 * n0\nt2 = 0.25 * 4.0\nt3 = t2 * 3.141592653589793\nt4 = t0 * t3\nt5 = t0 * t4\nanswer = t1 - t5\nprint(answer)" + ], + "Output Answer": [ + "851.7546894755278" + ], + "split": "train" + }, + { + "Input": "a cubic object 3 ' ' x 3 ' ' x 3 ' ' is painted blue on all the outside surfaces , including the top and bottom . if the cube is cut into 27 cubes of 1 ' ' x 1 ' ' x 1 ' ' , how many 1 ' ' cubes do have any painted surfaces ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nn2 = 3.0\nn3 = 27.0\nn4 = 1.0\nn5 = 1.0\nn6 = 1.0\nn7 = 1.0\n\nanswer = n3 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "rectangle a has sides a and b , and rectangle b has sides c and d . if a / c = b / d = 3 / 5 , what is the ratio of rectangle a \u2019 s area to rectangle b \u2019 s area ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nt0 = n0**min(2.0, 5)\nt1 = n1**min(2.0, 5)\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.36" + ], + "split": "train" + }, + { + "Input": "the area of a square field is 4802 m ( power ) 2 the length of its diagonal is :", + "Output Program": [ + "import math\nn0 = 4802.0\nn1 = 2.0\nt0 = math.sqrt(max(0, n0))\nt1 = math.sqrt(max(0, n1))\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "98.00000000000001" + ], + "split": "train" + }, + { + "Input": "the area of the house of a hall is 20 m 2 that of a longer wall 10 m 2 and of the shorter wall 8 m 2 , find the edge of the new cube ?", + "Output Program": [ + "n0 = 20.0\nn1 = 2.0\nn2 = 10.0\nn3 = 2.0\nn4 = 8.0\nn5 = 2.0\nt0 = n0 * n2\nt1 = n1 * t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "find the surface area of a 8 cm x 4 cm x 2 cm brick .", + "Output Program": [ + "n0 = 8.0\nn1 = 4.0\nn2 = 2.0\n\nanswer = 2 * (n0 * n1 + n0 * n2 + n1 * n2) # surface of a rectangular prism\nprint(answer)" + ], + "Output Answer": [ + "112" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is reduced by 22 % . by what % would the width have to be increased to maintainthe original area ?", + "Output Program": [ + "n0 = 22.0\nt0 = 100.0 - n0\nt1 = t0 / 100.0\nt2 = 1.0 - t1\nt3 = t2 / t1\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "28.2051282051282" + ], + "split": "train" + }, + { + "Input": "if the difference between the length and breadth of a rectangle is 23 m and its perimeter is 226 m , what is its area ?", + "Output Program": [ + "n0 = 23.0\nn1 = 226.0\nt0 = n0 * 2.0\nt1 = n1 - t0\nt2 = t1 / 4.0\nt3 = n0 + t2\nanswer = t3 * t2 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "3060" + ], + "split": "train" + }, + { + "Input": "frank the fencemaker needs to fence in a rectangular yard . he fences in the entire yard , except for one full side of the yard , which equals 40 feet . the yard has an area of 320 square feet . how many feet offence does frank use ?", + "Output Program": [ + "n0 = 40.0\nn1 = 320.0\nt0 = n1 / n0\nt1 = t0 + t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "the floor of a rectangular room is 15 m long and 12 m wide . the room is surrounded by a verandah of width 2 m on all its sides . the area of the verandah is :", + "Output Program": [ + "n0 = 15.0\nn1 = 12.0\nn2 = 2.0\nt0 = n2 * 2.0\nt1 = n0 * n1 # area of rectangle\nt2 = n0 + t0\nt3 = n1 + t0\nt4 = t2 * t3 # area of rectangle\nanswer = t4 - t1\nprint(answer)" + ], + "Output Answer": [ + "124" + ], + "split": "train" + }, + { + "Input": "the side of a rhombus is 20 m and length of one of its diagonals is 16 m . the area of the rhombus is ?", + "Output Program": [ + "import math\nn0 = 20.0\nn1 = 16.0\nt0 = n0 * 2.0\nt1 = n1**min(2.0, 5)\nt2 = t0**min(2.0, 5)\nt3 = t2 - t1\nt4 = math.sqrt(max(0, t3))\nt5 = n1 * t4\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "293.28484447717375" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is halved , while its breadth is tripled . whatis the % change in area ?", + "Output Program": [ + "t0 = 1.0 / 2.0\nt1 = t0 * 3.0\nt2 = t1 - 1.0\nt3 = t2 / 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a metallic sheet is of rectangular shape with dimensions 50 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is :", + "Output Program": [ + "n0 = 50.0\nn1 = 36.0\nn2 = 8.0\nn3 = 3.0\nt0 = n2 * 2.0\nt1 = n0 - t0\nt2 = n1 - t0\nanswer = n2 * t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "5440" + ], + "split": "train" + }, + { + "Input": "the size of a television screen is given as the length of the screen ' s diagonal . if the screens were flat , then the area of a square 21 - inch screen would be how many square inches greater than the area of a square 17 - inch screen ?", + "Output Program": [ + "n0 = 21.0\nn1 = 17.0\nt0 = n0**min(2.0, 5)\nt1 = n1**min(2.0, 5)\nt2 = t0 - t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "76" + ], + "split": "train" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 10 feet uncovered . if the area of the field is 600 sq . ft , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 10.0\nn1 = 600.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "130" + ], + "split": "train" + }, + { + "Input": "how many cubes of edge 2 dm can be cut out of a meter cube ?", + "Output Program": [ + "n0 = 2.0\nt0 = 10.0**3\nt1 = n0**3\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "a snooker tournament charges $ 40.00 for vip seats and $ 10.00 for general admission ( \u201c regular \u201d seats ) . on a certain night , a total of 320 tickets were sold , for a total cost of $ 7,500 . how many fewer tickets were sold that night for vip seats than for general admission seats ?", + "Output Program": [ + "n0 = 40.0\nn1 = 10.0\nn2 = 320.0\nn3 = 7500.0\nt0 = 3.0 + 4.0\nt1 = 2.0 + 3.0\nt2 = n1 * n2\nt3 = t0 * 1000.0\nt4 = t1 * 100.0\nt5 = t1 * t1\nt6 = t3 + t4\nt7 = t6 - t2\nt8 = t7 / t5\nanswer = n2 - t8\nprint(answer)" + ], + "Output Answer": [ + "148" + ], + "split": "train" + }, + { + "Input": "the area of sector of a circle whose radius is 12 metro and whose angle at the center is 39 \u00b0 is ?", + "Output Program": [ + "n0 = 12.0\nn1 = 39.0\nt0 = 3.0 + 4.0\nt1 = 3600.0 / 10.0\nt2 = 10.0 * 2.0\nt3 = n0**min(2.0, 5)\nt4 = t2 + 2.0\nt5 = n1 / t1\nt6 = t4 / t0\nt7 = t6 * t3\nanswer = t5 * t7\nprint(answer)" + ], + "Output Answer": [ + "49.02857142857143" + ], + "split": "train" + }, + { + "Input": "30 square stone slabs of equal size were needed to cover a floor area of 67.5 sq . m . find the length of each stone slab ?", + "Output Program": [ + "import math\nn0 = 30.0\nn1 = 67.5\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "a gardener changed the size of his rectangle shaped garden by increasing it ' s length by 40 % & decreasing is ' s width by 20 % . find area of new garden .", + "Output Program": [ + "n0 = 40.0\nn1 = 20.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nt2 = t0 / 100.0\nt3 = t1 / 100.0\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "1.1199999999999999" + ], + "split": "train" + }, + { + "Input": "in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 11 , 0 ) , ( 0 , - 3.5 ) , ( - 11 , 0 ) ?", + "Output Program": [ + "n0 = 0.0\nn1 = 3.5\nn2 = 11.0\nn3 = 0.0\nn4 = 0.0\nn5 = 3.5\nn6 = 11.0\nn7 = 0.0\nt0 = n2 * 2.0\nt1 = n1 * 2.0\nanswer = t0 * t1 / 2\nprint(answer)" + ], + "Output Answer": [ + "77" + ], + "split": "train" + }, + { + "Input": "the area of a triangle is with base 8.4 m and height 5.8 m ?", + "Output Program": [ + "n0 = 8.4\nn1 = 5.8\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "24.36" + ], + "split": "train" + }, + { + "Input": "the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 2 of the area of the field . what is the length of the field ?", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 1.0\nn2 = 2.0\nt0 = 1 / 2.0\nt1 = n0**2\nt2 = n2 * t1\nt3 = t2 / t0\nanswer = math.sqrt(max(0, t3))\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "what will be the cost of building a fence around a square plot with area equal to 36 sq ft , if the price per foot of building the fence is rs . 58 ?", + "Output Program": [ + "import math\nn0 = 36.0\nn1 = 58.0\nt0 = math.sqrt(max(0, n0))\nt1 = 4 * t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "1392" + ], + "split": "train" + }, + { + "Input": "a goat is tied to one corner of a square plot of side 12 m by a rope 7 m long . find the area it can graze ?", + "Output Program": [ + "import math\nn0 = 12.0\nn1 = 7.0\nt0 = math.pi * n1**2\nanswer = t0 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "38.48451000647496" + ], + "split": "train" + }, + { + "Input": "the cube root of . 000343 is", + "Output Program": [ + "n0 = 343.0\nt0 = n0 / 1000.0\nt1 = 1.0 / 3.0\nt2 = t0 / 1000.0\nanswer = t2**min(t1, 5)\nprint(answer)" + ], + "Output Answer": [ + "0.07" + ], + "split": "train" + }, + { + "Input": "how many pieces can a square pizza be cut into by making 4 linear cuts ?", + "Output Program": [ + "n0 = 4.0\nt0 = n0 * 3.0\nanswer = t0 - 1.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "a rectangular swimming pool is 10 feet by 12 feet . a deck that has uniform width surrounds the pool . the total area of the pool and deck is 360 square feet . what is the width of the deck ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 12.0\nn2 = 360.0\nt0 = n0 * n1 # area of rectangle\nt1 = n1 - 1.0\nt2 = t1**min(2.0, 5)\nt3 = n2 - t0\nt4 = t2 + t3\nt5 = math.sqrt(max(0, t4))\nt6 = t5 - t1\nanswer = t6 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?", + "Output Program": [ + "n0 = 25.0\nn1 = 15.0\nn2 = 12.0\nn3 = 5.0\nn4 = 6.0\nn5 = 3.0\nn6 = 4.0\nn7 = 3.0\nt0 = n0 + n1\nt1 = n2 * 2.0\nt2 = n4 * n5\nt3 = n5 * n6\nt4 = t0 * t1\nt5 = n5 * t3\nt6 = t4 - t2\nt7 = t6 - t5\nanswer = n3 * t7\nprint(answer)" + ], + "Output Answer": [ + "4530" + ], + "split": "train" + }, + { + "Input": "two cylinders are of the same height . their radii are in the ratio 1 : 3 . if the volume of the first cylinder is 40 cc . find the volume of the second cylinder ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 40.0\nt0 = n1 * n1\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "the volume of a cube is 3375 cc . find its surface .", + "Output Program": [ + "n0 = 3375.0\nt0 = n0**(1 / 3)\nanswer = 6 * t0**2 # surface of a cube\nprint(answer)" + ], + "Output Answer": [ + "1349.9999999999995" + ], + "split": "train" + }, + { + "Input": "a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 13 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?", + "Output Program": [ + "import math\nn0 = 13.0\nn1 = 1200.0\nn2 = 2.0\nn3 = 30.0\nt0 = n1 / n3\nt1 = n3**min(n2, 5)\nt2 = n3 + t0\nt3 = t0**min(n2, 5)\nt4 = t1 + t3\nt5 = math.sqrt(max(0, t4))\nt6 = t2 + t5\nanswer = n0 * t6\nprint(answer)" + ], + "Output Answer": [ + "1560" + ], + "split": "train" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 50 sq . feet , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 20.0\nn1 = 50.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "the diagonal of a rhombus are 65 m and 60 m . its area is :", + "Output Program": [ + "n0 = 65.0\nn1 = 60.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "1950" + ], + "split": "train" + }, + { + "Input": "find the perimeter of a triangle with sides measuring 5 centimeters , 20 centimeters and 30 centimeters .", + "Output Program": [ + "n0 = 5.0\nn1 = 20.0\nn2 = 30.0\n\nanswer = n0 + n1 + n2 # perimeter of a triangle\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "train" + }, + { + "Input": "if the height of a cone is increased by 130 % then its volume is increased by ?", + "Output Program": [ + "n0 = 130.0\n\nanswer = n0 * 1.0 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "130" + ], + "split": "train" + }, + { + "Input": "a cube of edge 17 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 15 cm , find the rise in water level ?", + "Output Program": [ + "n0 = 17.0\nn1 = 20.0\nn2 = 15.0\nt0 = n1 * n2\nt1 = n0**3\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "16.376666666666665" + ], + "split": "train" + }, + { + "Input": "a box measuring 49 inches long by 42 inches wide by 14 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?", + "Output Program": [ + "n0 = 49.0\nn1 = 42.0\nn2 = 14.0\nt0 = n2 / 2.0\nt1 = n0 * n1\nt2 = n2 * t1\nt3 = t0**3\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "the height of cylinder is 14 cm and its diameter is 10 cm . the volume of the cylinder is :", + "Output Program": [ + "import math\nn0 = 14.0\nn1 = 10.0\nt0 = n1 / 2.0\nanswer = math.pi * t0**2 * n0\nprint(answer)" + ], + "Output Answer": [ + "1099.5574287564277" + ], + "split": "train" + }, + { + "Input": "the volume of a cube is 343 cc . find its surface .", + "Output Program": [ + "n0 = 343.0\nt0 = n0**(1 / 3)\nanswer = 6 * t0**2 # surface of a cube\nprint(answer)" + ], + "Output Answer": [ + "293.9999999999999" + ], + "split": "train" + }, + { + "Input": "you buy a piece of land with an area of \u00e2 \u02c6 \u0161 1024 , how long is one side of the land plot ?", + "Output Program": [ + "import math\nn0 = 1024.0\n\nanswer = math.sqrt(max(0, n0))\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular plot is 10 mtr more than its width . the cost of fencing the plot along its perimeter at the rate of rs . 6.5 mtr is rs . 2210 . the perimeter of the plot is ?", + "Output Program": [ + "n0 = 10.0\nn1 = 6.5\nn2 = 2210.0\nt0 = n2 / n1\nt1 = t0 / 2.0\nt2 = t1 - n0\nt3 = t2 / 2.0\nt4 = t3 + n0\nt5 = t4 + t3\nanswer = t5 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "340" + ], + "split": "train" + }, + { + "Input": "if a rectangular billboard has an area of 104 square feet and a perimeter of 42 feet , what is the length of each of the shorter sides ?", + "Output Program": [ + "import math\nn0 = 104.0\nn1 = 42.0\nt0 = n1 / 2.0\nt1 = n0 * 4.0\nt2 = t0**min(2.0, 5)\nt3 = t2 - t1\nt4 = math.sqrt(max(0, t3))\nt5 = t0 - t4\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "what is the sum of the squares of the first 20 natural numbers ( 1 to 20 ) ?", + "Output Program": [ + "n0 = 20.0\nn1 = 1.0\nn2 = 20.0\nt0 = n0 + n1\nt1 = n0 * 2.0\nt2 = 2.0 * 3.0\nt3 = n1 + t1\nt4 = n0 * t0\nt5 = t3 * t4\nanswer = t5 / t2\nprint(answer)" + ], + "Output Answer": [ + "2870" + ], + "split": "train" + }, + { + "Input": "an error 2 % in excess is made while measuring the side of asquare . the % of error in the calculated area of the square is ?", + "Output Program": [ + "n0 = 2.0\nt0 = n0 + 100.0\nt1 = 100.0**2\nt2 = t0**2\nt3 = t2 - t1\nt4 = t3 * 100.0\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "4.04" + ], + "split": "train" + }, + { + "Input": "the area of a triangle is with base 4 m and height 8 m ?", + "Output Program": [ + "n0 = 4.0\nn1 = 8.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a trainer is standing in one corner of a square ground of side 25 m . his voice can be heard upto 140 m . find the area of the ground in which his voice can be heard ?", + "Output Program": [ + "import math\nn0 = 25.0\nn1 = 140.0\nt0 = math.pi * n1**2\nanswer = t0 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "15393.804002589986" + ], + "split": "train" + }, + { + "Input": "in a rectangular coordinate system , what is the area of a rectangle whose vertices have the coordinates ( - 3 , 1 ) , ( 1 , 1 ) , ( 1 , - 2 ) and ( - 3 , - 2 ) ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nn2 = 1.0\nn3 = 1.0\nn4 = 1.0\nn5 = 2.0\nn6 = 3.0\nn7 = 2.0\nt0 = n0 + n1\nt1 = n1 + n5\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the perimeter of one face of a cube is 32 cm . its volume will be :", + "Output Program": [ + "n0 = 32.0\nt0 = n0 / 4. # square edge given perimeter\nanswer = t0**3\nprint(answer)" + ], + "Output Answer": [ + "512" + ], + "split": "train" + }, + { + "Input": "if paint costs $ 3.20 per quart , and a quart covers 10 square feet , how much will it cost to paint the outside of a cube 10 feet on each edge ?", + "Output Program": [ + "n0 = 3.2\nn1 = 10.0\nn2 = 10.0\nt0 = n0 / n1\nt1 = 6 * n2**2 # surface of a cube\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "192" + ], + "split": "train" + }, + { + "Input": "in a rectangular coordinate system , what is the area of a triangle whose vertices have the coordinates ( - 1 , 0 ) , ( 7 , 4 ) , and ( 7 , - 4 ) ?", + "Output Program": [ + "n0 = 1.0\nn1 = 0.0\nn2 = 7.0\nn3 = 4.0\nn4 = 7.0\nn5 = 4.0\nt0 = n0 + n2\nt1 = n3 * t0 / 2\nanswer = t1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "in a new housing development , trees are to be planted along the sidewalk of a certain street . each tree takes up one square foot of sidewalk space , and there are to be 10 feet between each tree . how many trees can be planted if the road is 166 feet long ?", + "Output Program": [ + "n0 = 10.0\nn1 = 166.0\nt0 = n0 + 1.0\nt1 = n1 - 1.0\nt2 = t1 / t0\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many l cubes are painted on only 2 faces ?", + "Output Program": [ + "n0 = 27.0\nn1 = 2.0\nt0 = 1.0 / 3.0\nt1 = n0**min(t0, 5)\nanswer = t1 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "if the sides of a triangle are 78 cm , 72 cm and 30 cm , what is its area ?", + "Output Program": [ + "n0 = 78.0\nn1 = 72.0\nn2 = 30.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "1080" + ], + "split": "train" + }, + { + "Input": "the slant height of a cone is 22 cm and radius of the base is 7 cm , find the curved surface of the cone ?", + "Output Program": [ + "n0 = 22.0\nn1 = 7.0\nt0 = n1 * 3.141592653589793\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "483.80526865282815" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular plot is 10 mtr more than its width . the cost of fencing the plot along its perimeter at the rate of rs . 6.5 mtr is rs . 1170 . the perimeter of the plot is ?", + "Output Program": [ + "n0 = 10.0\nn1 = 6.5\nn2 = 1170.0\nt0 = n2 / n1\nt1 = t0 / 2.0\nt2 = t1 - n0\nt3 = t2 / 2.0\nt4 = t3 + n0\nt5 = t4 + t3\nanswer = t5 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "train" + }, + { + "Input": "there are two circles of different radii . the are of a square is 784 sq cm and its side is twice the radius of the larger circle . the radius of the larger circle is 7 - third that of the smaller circle . find the circumference of the smaller circle .", + "Output Program": [ + "import math\nn0 = 784.0\nt0 = 3.0 + 4.0\nt1 = math.sqrt(n0) # square edge given area\nt2 = t1 / 2.0\nt3 = t0 / 3.0\nt4 = t2 / t3\nanswer = t4 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "if the diameter of circle r is 80 % of the diameter of circle s , the area of circle r is what percent of the area of circle s ?", + "Output Program": [ + "import math\nn0 = 80.0\nt0 = math.pi * n0**2\nt1 = math.pi * 100.0**2\nt2 = t0 * 100.0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "find the perimeter and area of a square of side 9 cm .", + "Output Program": [ + "n0 = 9.0\n\nanswer = n0**2\nprint(answer)" + ], + "Output Answer": [ + "81" + ], + "split": "train" + }, + { + "Input": "some students are standing in a circle in which 6 th and the 16 th student are standing opposite to each other . find how many students were present there .", + "Output Program": [ + "n0 = 6.0\nn1 = 16.0\nt0 = n1 - n0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 3025 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?", + "Output Program": [ + "import math\nn0 = 3025.0\nn1 = 10.0\nt0 = n1 / 2.0\nt1 = math.sqrt(max(0, n0))\nt2 = t1 / t0\nt3 = t2 * 2.0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "220" + ], + "split": "train" + }, + { + "Input": "how much space , in cubic units , is left vacant when maximum number of 4 x 4 x 4 cubes are fitted in a rectangular box measuring 10 x 12 x 16 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nn2 = 4.0\nn3 = 10.0\nn4 = 12.0\nn5 = 16.0\nt0 = n4 * n5\nt1 = n0 * 2.0\nt2 = n3 - t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "384" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1600 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?", + "Output Program": [ + "import math\nn0 = 1600.0\nn1 = 10.0\nt0 = n1 / 2.0\nt1 = math.sqrt(max(0, n0))\nt2 = t1 / t0\nt3 = t2 * 2.0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "160" + ], + "split": "train" + }, + { + "Input": "the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 98 of the area of the field . what is the length of the field ?", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 1.0\nn2 = 98.0\nt0 = 1 / 2.0\nt1 = n0**2\nt2 = n2 * t1\nt3 = t2 / t0\nanswer = math.sqrt(max(0, t3))\nprint(answer)" + ], + "Output Answer": [ + "112" + ], + "split": "train" + }, + { + "Input": "a rectangular courtyard 3.78 meters long 5.25 meters wide is to be paved exactly with square tiles , all of the same size . what is the largest size of the tile which could be used for the purpose ?", + "Output Program": [ + "n0 = 3.78\nn1 = 5.25\nt0 = n0 * 100.0\nt1 = t0 / 2.0\nt2 = t1 / 3.0\nt3 = t2 / 3.0\nt4 = t3 / 3.0\nt5 = t3 / t4\nanswer = t5 * t4\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "a lady builds 10 cm length , 13 cm width , and 5 cm height box using 5 cubic cm cubes . what is the minimum number of cubes required to build the box ?", + "Output Program": [ + "n0 = 10.0\nn1 = 13.0\nn2 = 5.0\nn3 = 5.0\nt0 = n0 * n1\nt1 = n2 * t0\nanswer = t1 / n3\nprint(answer)" + ], + "Output Answer": [ + "130" + ], + "split": "train" + }, + { + "Input": "if the area of a square with sides of length 8 centimeters is equal to the area of a rectangle with a width of 4 centimeters , what is the length of the rectangle , in centimeters ?", + "Output Program": [ + "n0 = 8.0\nn1 = 4.0\nt0 = n0**min(2.0, 5)\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a clockwise rotation around point z ( that is , a rotation in the direction of the arrow ) transforms the shaded quadrilateral to the unshaded quadrilateral . the angle of rotation is approximately", + "Output Program": [ + "t0 = 3600.0 / 10.0\nt1 = t0 / 4.0\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "270" + ], + "split": "train" + }, + { + "Input": "what is the area of square field whose side of length 14 m ?", + "Output Program": [ + "n0 = 14.0\n\nanswer = n0**2\nprint(answer)" + ], + "Output Answer": [ + "196" + ], + "split": "train" + }, + { + "Input": "of the two square fields , the area of the one is 1 hectare , while anothe one is broader by 1 % . there differences in area is :", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 1.0\nt0 = 10.0 * 1000.0\nt1 = math.sqrt(max(0, t0))\nt2 = n0 + t1\nt3 = t2**2\nanswer = t3 - t0\nprint(answer)" + ], + "Output Answer": [ + "201" + ], + "split": "train" + }, + { + "Input": "there is a rectangular prism made of 1 in cubes that has been covered in tin foil . there are exactly 128 cubes that are not touching any tin foil on any of their sides . if the width of the figure created by these 128 cubes is twice the length and twice the height , what is the measure q in inches of the width of the foil covered prism ?", + "Output Program": [ + "n0 = 1.0\nn1 = 128.0\nn2 = 128.0\nt0 = 1 / 3.0\nt1 = n0 * 2.0\nt2 = n0 * t1\nt3 = n1 / t2\nt4 = t3**min(t0, 5)\nt5 = t1 * t4\nanswer = t5 + t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 60 cents . how many cents does a solution of 1 liter of spirit and 2 liters of water cost ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 60.0\nn3 = 1.0\nn4 = 2.0\nt0 = n0 + n4\nt1 = n0 / t0\nt2 = n2 * t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "the diagonals of a rhombus are 14 cm and 20 cm . find its area ?", + "Output Program": [ + "n0 = 14.0\nn1 = 20.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "train" + }, + { + "Input": "the volume of a cube is 1331 cc . find its surface .", + "Output Program": [ + "n0 = 1331.0\nt0 = n0**(1 / 3)\nanswer = 6 * t0**2 # surface of a cube\nprint(answer)" + ], + "Output Answer": [ + "725.9999999999998" + ], + "split": "train" + }, + { + "Input": "a football field is 9600 square yards . if 1200 pounds of fertilizer are spread evenly across the entire field , how many pounds of fertilizer were spread over an area of the field totaling 5600 square yards ?", + "Output Program": [ + "n0 = 9600.0\nn1 = 1200.0\nn2 = 5600.0\nt0 = n1 / n0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "700" + ], + "split": "train" + }, + { + "Input": "the perimeter of one face of a cube is 20 cm . its volume will be :", + "Output Program": [ + "n0 = 20.0\nt0 = n0 / 4. # square edge given perimeter\nanswer = t0**3\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "a square mirror has exactly half the area of the rectangular wall on which it is hung . if each side of the mirror is 18 inches and the width of the wall is 32 inches , what is the length of the wall , in inches ?", + "Output Program": [ + "n0 = 18.0\nn1 = 32.0\nt0 = n0**2\nt1 = t0 * 2.0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "20.25" + ], + "split": "train" + }, + { + "Input": "what will be the cost of building a fence around a square plot with area equal to 144 sq ft , if the price per foot of building the fence is rs . 58 ?", + "Output Program": [ + "import math\nn0 = 144.0\nn1 = 58.0\nt0 = math.sqrt(max(0, n0))\nt1 = 4 * t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "2784" + ], + "split": "train" + }, + { + "Input": "the roof of an apartment building is rectangular and its length is 4 times longer than its width . if the area of the roof is 900 feet squared , what is the difference between the length and the width of the roof ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 900.0\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * 4.0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "the surface area of a sphere is 4 \u03c0 r 2 , where r is the radius of the sphere . if the area of the base of a hemisphere is 3 , what is the surface area q of that hemisphere ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 3.0\nt0 = n2 / 3.141592653589793\nt1 = n0 * 3.141592653589793\nt2 = t0 * t1\nt3 = t0 * 3.141592653589793\nt4 = t2 / n1\nanswer = t4 + t3\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "in right triangle abc , ac is the hypotenuse . if ac is 50 and ab + bc = 70 , what is the area of the triangle abc ?", + "Output Program": [ + "import math\nn0 = 50.0\nn1 = 70.0\nt0 = 10.0 * 3.0\nt1 = 10.0 * 4.0\nanswer = (lambda s, a, b, c: math.sqrt(max(0, s * (s - a) * (s - b) * (s - c))))((n0 + t0 + t1) / 2, n0, t0, t1) # Heron's formula\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "train" + }, + { + "Input": "cubes with each side one inch long are glued together to form a larger cube . the larger cube ' s face is painted with red color and the entire assembly is taken apart . 22 small cubes are found with no paints on them . how many of unit cubes have at least one face that is painted red ?", + "Output Program": [ + "n0 = 22.0\nt0 = 1.0 + 3.0\nt1 = t0 + 1.0\nt2 = t1**min(3.0, 5)\nanswer = t2 - n0\nprint(answer)" + ], + "Output Answer": [ + "103" + ], + "split": "train" + }, + { + "Input": "if the sides of a triangle are 30 cm , 28 cm and 10 cm , what is its area ?", + "Output Program": [ + "n0 = 30.0\nn1 = 28.0\nn2 = 10.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "train" + }, + { + "Input": "if the side length of square b is sqrt ( 3 ) times that of square a , the area of square b is how many times the area of square a ?", + "Output Program": [ + "import math\nn0 = 3.0\nt0 = math.sqrt(max(0, n0))\nanswer = t0**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "2.9999999999999996" + ], + "split": "train" + }, + { + "Input": "one side of a rectangular field is 15 m and one of its diagonal is 17 m . find the area of the field .", + "Output Program": [ + "import math\nn0 = 15.0\nn1 = 17.0\nt0 = n1**min(2.0, 5)\nt1 = n0**min(2.0, 5)\nt2 = t0 - t1\nt3 = math.sqrt(max(0, t2))\nanswer = n0 * t3 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "if a rectangular billboard has an area of 120 square feet and a perimeter of 46 feet , what is the length of each of the shorter sides ?", + "Output Program": [ + "import math\nn0 = 120.0\nn1 = 46.0\nt0 = n1 / 2.0\nt1 = n0 * 4.0\nt2 = t0**min(2.0, 5)\nt3 = t2 - t1\nt4 = math.sqrt(max(0, t3))\nt5 = t0 - t4\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a park square in shape has a 3 metre wide road inside it running along its sides . the area occupied by the road is 1764 square metres . what is the perimeter along the outer edge of the road ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1764.0\nt0 = n0 * 2.0\nt1 = t0 * 2.0\nt2 = t0**min(2.0, 5)\nt3 = n1 + t2\nt4 = t3 / t1\nanswer = t4 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "train" + }, + { + "Input": "the diagonals of a rhombus are 12 cm and 10 cm . find its area ?", + "Output Program": [ + "n0 = 12.0\nn1 = 10.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "the radius of a cylinder is 12 m , height 21 m . the lateral surface area of the cylinder is :", + "Output Program": [ + "import math\nn0 = 12.0\nn1 = 21.0\nt0 = 2 * math.pi * n0\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "1583.3626974092558" + ], + "split": "train" + }, + { + "Input": "a cylinder with base radius of 8 cm and height of 2 cm is melted to form a cone of height 6 cm . the radius of the cone will be :", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 2.0\nn2 = 6.0\nt0 = math.pi * n0**2 * n1\nt1 = t0 * 3.0\nt2 = t1 / n2\nt3 = t2 / 3.141592653589793\nanswer = math.sqrt(max(0, t3))\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "if the sides of a rectangle are increased by 15 % , what is the percentage increase in the area ?", + "Output Program": [ + "n0 = 15.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = t1**min(2.0, 5)\nt3 = t2 - 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "32.24999999999998" + ], + "split": "train" + }, + { + "Input": "in the xy - plane , a triangle has vertices ( 00 ) , ( 40 ) and ( 410 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ?", + "Output Program": [ + "n0 = 0.0\nn1 = 0.0\nn2 = 4.0\nn3 = 0.0\nn4 = 4.0\nn5 = 10.0\nn6 = 0.0\nt0 = n0 + 10.0\nanswer = 4.0 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "train" + }, + { + "Input": "a rectangular floor is covered by a rug except for a strip 4 meters wide along each of the four edge . if the floor is 25 meters by 20 meters , what is the area of the rug in square meters ?", + "Output Program": [ + "n0 = 4.0\nn1 = 25.0\nn2 = 20.0\nt0 = n0 * 2.0\nt1 = n1 - t0\nt2 = n2 - t0\nanswer = t1 * t2 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "204" + ], + "split": "train" + }, + { + "Input": "the percentage increase in the area of rectangle , if each of its side is increased by 20 % is ?", + "Output Program": [ + "n0 = 20.0\nt0 = n0 + 100.0\nt1 = t0 / 100.0\nt2 = t1 * t1\nt3 = t2 - 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "43.99999999999999" + ], + "split": "train" + }, + { + "Input": "a cube is painted such that one pair of surfaces is painted brown and the other pair of surfaces is painted orange . the cube is cut in to 64 small cubes of equal size . find how many cubes have both the color brown and orange ?", + "Output Program": [ + "n0 = 64.0\nt0 = n0 / 2.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the length of each side of square a is increased by 100 percent to make square b . if the length of the side of square b is increased by 80 percent to make square c , by what percent is the area of square c greater than the sum of the areas of squares a and b ?", + "Output Program": [ + "n0 = 100.0\nn1 = 80.0\nt0 = n0 / n0\nt1 = t0 + 1.0\nt2 = n1 * t1\nt3 = t1**2\nt4 = t3 + 1.0\nt5 = t2 / n0\nt6 = t1 + t5\nt7 = t6**2\nt8 = t7 - 1.0\nt9 = t8 - 4.0\nt10 = t9 / t4\nanswer = n0 * t10\nprint(answer)" + ], + "Output Answer": [ + "159.20000000000002" + ], + "split": "train" + }, + { + "Input": "you buy a piece of land with an area of \u00e2 \u02c6 \u0161 400 , how long is one side of the land plot ?", + "Output Program": [ + "import math\nn0 = 400.0\n\nanswer = math.sqrt(max(0, n0))\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the floor of a rectangular room is 19 m long and 12 m wide . the room is surrounded by a veranda of width 2 m on all its sides . the area of the veranda is :", + "Output Program": [ + "n0 = 19.0\nn1 = 12.0\nn2 = 2.0\nt0 = n2 * n2\nt1 = n0 * n1 # area of rectangle\nt2 = n0 + t0\nt3 = n1 + t0\nt4 = t2 * t3 # area of rectangle\nanswer = t4 - t1\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "train" + }, + { + "Input": "find the area of circle whose diameter is 8 m .", + "Output Program": [ + "import math\nn0 = 8.0\nt0 = n0 / 2.0\nanswer = math.pi * t0**2\nprint(answer)" + ], + "Output Answer": [ + "50.26548245743669" + ], + "split": "train" + }, + { + "Input": "right triangle abc is the base of the prism in the figure above . if ab = ac = \u221a 2 and the height of the prism is 3 , what is the volume of the prism ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 3.0\nt0 = math.sqrt(max(0, n0))\nt1 = n1 * t0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "3.0000000000000004" + ], + "split": "train" + }, + { + "Input": "what is the area of square field whose side of length 10 m ?", + "Output Program": [ + "n0 = 10.0\n\nanswer = n0**2\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 6 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?", + "Output Program": [ + "n0 = 25.0\nn1 = 15.0\nn2 = 12.0\nn3 = 6.0\nn4 = 6.0\nn5 = 3.0\nn6 = 4.0\nn7 = 3.0\nt0 = n0 + n1\nt1 = n2 * 2.0\nt2 = n4 * n5\nt3 = n5 * n6\nt4 = t0 * t1\nt5 = n5 * t3\nt6 = t4 - t2\nt7 = t6 - t5\nanswer = n3 * t7\nprint(answer)" + ], + "Output Answer": [ + "5436" + ], + "split": "train" + }, + { + "Input": "a rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn . if the area of the lawn is 2109 sq . m , then what is the width of the road ?", + "Output Program": [ + "import math\nn0 = 60.0\nn1 = 40.0\nn2 = 2109.0\nt0 = n0 + n1\nt1 = 1.0 * 4.0\nt2 = n0 * n1\nt3 = 1.0 * 2.0\nt4 = 100.0**min(2.0, 5)\nt5 = -t0\nt6 = t2 - n2\nt7 = t1 * t6\nt8 = -t5\nt9 = t4 - t7\nt10 = math.sqrt(max(0, t9))\nt11 = t8 - t10\nanswer = t11 / t3\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the radius of the two circular fields is in the ratio 3 : 10 the area of the first field is what percent less than the area of the second ?", + "Output Program": [ + "n0 = 3.0\nn1 = 10.0\nt0 = n1**min(2.0, 5)\nt1 = n0**min(2.0, 5)\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "91" + ], + "split": "train" + }, + { + "Input": "if the sides of a triangle are 39 cm , 32 cm and 10 cm , what is its area ?", + "Output Program": [ + "n0 = 39.0\nn1 = 32.0\nn2 = 10.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "160" + ], + "split": "train" + }, + { + "Input": "find the area of a parallelogram with base 12 cm and height 10 cm ?", + "Output Program": [ + "n0 = 12.0\nn1 = 10.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "a rectangular mat has an area of 120 sq . metres and perimeter of 46 m . the length of its diagonal is :", + "Output Program": [ + "import math\nn0 = 120.0\nn1 = 46.0\nt0 = n1 / 2.0\nt1 = n0 * 2.0\nt2 = t0**min(2.0, 5)\nt3 = t2 - t1\nanswer = math.sqrt(max(0, t3))\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "a lady grows cabbage in her garden that is in the shape of a square . each cabbage takes 1 square foot of area in her garden . this year , she has increased her output by 127 cabbages when compared to last year . the shape of the area used for growing the cabbage has remained a square in both these years . how many cabbages did she produce this year ?", + "Output Program": [ + "n0 = 1.0\nn1 = 127.0\nt0 = n1 - n0\nt1 = t0 / 2.0\nt2 = n0 + t1\nanswer = t2**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "4096" + ], + "split": "train" + }, + { + "Input": "the circumferences of two circles are 528 meters and 704 meters . find the difference between the areas of the larger and the smaller circles ?", + "Output Program": [ + "import math\nn0 = 528.0\nn1 = 704.0\nt0 = 2.0 * 3.141592653589793\nt1 = n1 / t0\nt2 = n0 / t0\nt3 = math.pi * t1**2\nt4 = math.pi * t2**2\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "17254.942310250928" + ], + "split": "train" + }, + { + "Input": "if the volume of two cubes are in the ratio 125 : 1 , the ratio of their edges is :", + "Output Program": [ + "n0 = 125.0\nn1 = 1.0\n\nanswer = n0**(1 / 3)\nprint(answer)" + ], + "Output Answer": [ + "4.999999999999999" + ], + "split": "train" + }, + { + "Input": "if the sides of a triangle are 28 cm , 26 cm and 12 cm , what is its area ?", + "Output Program": [ + "n0 = 28.0\nn1 = 26.0\nn2 = 12.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "156" + ], + "split": "train" + }, + { + "Input": "a rectangular tiled patio is composed of 160 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 160 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?", + "Output Program": [ + "import math\nn0 = 160.0\nn1 = 2.0\nn2 = 4.0\nn3 = 160.0\nt0 = n0 * n1\nt1 = -n2\nt2 = n2**min(n1, 5)\nt3 = n2 * t0\nt4 = t3 + t2\nt5 = math.sqrt(max(0, t4))\nt6 = t1 + t5\nt7 = t6 / n1\nanswer = n0 / t7\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "what is the radius of the incircle of the triangle whose sides measure 5 , 12 and 13 units ?", + "Output Program": [ + "n0 = 5.0\nn1 = 12.0\nn2 = 13.0\nt0 = n0 + n1\nt1 = n0 * n1\nt2 = n2 + t0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a rectangular wall is covered entirely with two kinds of decorative tiles : regular and jumbo . 1 / 3 of the tiles are jumbo tiles , which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles . if regular tiles cover 60 square feet of the wall , and no tiles overlap , what is the area of the entire wall ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 60.0\nt0 = n2 * 3.0\nt1 = t0 / 2.0\nt2 = n1 * t1\nanswer = n2 + t2\nprint(answer)" + ], + "Output Answer": [ + "330" + ], + "split": "train" + }, + { + "Input": "a volume of 10940 l water is in a container of sphere . how many hemisphere of volume 4 l each will be required to transfer all the water into the small hemispheres ?", + "Output Program": [ + "n0 = 10940.0\nn1 = 4.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "2735" + ], + "split": "train" + }, + { + "Input": "the radius of a cone is 10 m , height 21 m . the volume of the cone is :", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 21.0\n\nanswer = math.pi * n0**2 * n1 / 3\nprint(answer)" + ], + "Output Answer": [ + "2199.114857512855" + ], + "split": "train" + }, + { + "Input": "2.2 cubic dm of lead is to be drawn into a cylindrical wire 0.50 cm diameter . find the length of the wire in meters .", + "Output Program": [ + "import math\nn0 = 2.2\nn1 = 0.5\nt0 = n1 / 2.0\nt1 = n0 * 1000.0\nt2 = math.pi * t0**2\nt3 = t1 / t2\nanswer = t3 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "112.04507993669432" + ], + "split": "train" + }, + { + "Input": "if the length , breadth and the height of a cuboid are in the ratio 6 : 5 : 4 and if the total surface area is 33300 cm 2 cm 2 , then the length , breadth and height in cms , are respectively .", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 5.0\nn2 = 4.0\nn3 = 33300.0\nn4 = 2.0\nn5 = 2.0\nt0 = n0 * n1\nt1 = n1 * n2\nt2 = n0 * n2\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = t4 * 2.0\nt6 = n3 / t5\nt7 = math.sqrt(max(0, t6))\nanswer = n0 * t7\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 3 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?", + "Output Program": [ + "n0 = 25.0\nn1 = 15.0\nn2 = 12.0\nn3 = 3.0\nn4 = 6.0\nn5 = 3.0\nn6 = 4.0\nn7 = 3.0\nt0 = n0 + n1\nt1 = n2 * 2.0\nt2 = n4 * n5\nt3 = n5 * n6\nt4 = t0 * t1\nt5 = n5 * t3\nt6 = t4 - t2\nt7 = t6 - t5\nanswer = n3 * t7\nprint(answer)" + ], + "Output Answer": [ + "2718" + ], + "split": "train" + }, + { + "Input": "a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . how many feet does the squirrel travels if the post is 12 feet tall and 3 feet in circumference ?", + "Output Program": [ + "n0 = 4.0\nn1 = 12.0\nn2 = 3.0\nt0 = n1 / n0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "what is the area of a square field whose diagonal of length 12 m ?", + "Output Program": [ + "n0 = 12.0\nt0 = n0**2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "the area of sector of a circle whose radius is 12 metro and whose angle at the center is 54 \u00e2 \u00b0 is ?", + "Output Program": [ + "n0 = 12.0\nn1 = 54.0\nt0 = 3.0 + 4.0\nt1 = 3600.0 / 10.0\nt2 = 10.0 * 2.0\nt3 = n0**min(2.0, 5)\nt4 = t2 + 2.0\nt5 = n1 / t1\nt6 = t4 / t0\nt7 = t6 * t3\nanswer = t5 * t7\nprint(answer)" + ], + "Output Answer": [ + "67.88571428571429" + ], + "split": "train" + }, + { + "Input": "a rectangular rug with side lengths of 2 feet and 7 feet is placed on a square floor that has an area of 64 square feet . if the surface of the rug does not extend beyond the area of the floor , what fraction of the area of the floor is not covered by the rug ?", + "Output Program": [ + "n0 = 2.0\nn1 = 7.0\nn2 = 64.0\nt0 = n0 * n1\nt1 = n2 - t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "0.78125" + ], + "split": "train" + }, + { + "Input": "if y is the smallest positive integer such that 4410 multiplied by y is the square of an integer , then y must be", + "Output Program": [ + "n0 = 4410.0\nt0 = 2.0 + 3.0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the base of pyramid p is an isosceles right triangle whose leg is 3 . if the height of p is 4 , what is the volume of p ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nt0 = n0**min(2.0, 5)\nt1 = t0 / 2.0\nt2 = n1 * t1\nanswer = t2 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the perimeter of an isosceles right triangle is 8 + 8 sq rt 2 . what is the length of the hypotenuse of the triangle ?", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 8.0\nn2 = 2.0\nt0 = math.sqrt(max(0, n2))\nt1 = n0 * t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "5.656854249492381" + ], + "split": "train" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 120 sq . feet , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 20.0\nn1 = 120.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "guadalupe owns 2 rectangular tracts of land . one is 300 m by 500 m and the other is 250 m by 630 m . the combined area of these 2 tracts is how many square meters ?", + "Output Program": [ + "n0 = 2.0\nn1 = 300.0\nn2 = 500.0\nn3 = 250.0\nn4 = 630.0\nn5 = 2.0\nt0 = n1 * n2 # area of rectangle\nt1 = n3 * n4 # area of rectangle\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "307500" + ], + "split": "train" + }, + { + "Input": "the parameter of a square is equal to the perimeter of a rectangle of length 22 cm and breadth 20 cm . find the circumference of a semicircle whose diameter is equal to the side of the square .", + "Output Program": [ + "import math\nn0 = 22.0\nn1 = 20.0\nt0 = 2 * (n0 + n1) # perimetere of rectangle\nt1 = t0 / 4. # square edge given perimeter\nt2 = t1 / 2.0\nt3 = 2 * math.pi * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "32.98672286269283" + ], + "split": "train" + }, + { + "Input": "the area of a rectangular field is equal to 300 square meters . its perimeter is equal to 70 meters . find the length and width of this rectangle .", + "Output Program": [ + "import math\nn0 = 300.0\nn1 = 70.0\nt0 = n1 / 2.0\nt1 = n0 * 4.0\nt2 = t0**min(2.0, 5)\nt3 = t2 - t1\nt4 = math.sqrt(max(0, t3))\nt5 = t0 - t4\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "in measuring the sides of a rectangle , one side is taken 8 % in excess , and the other 7 % in deficit . find the error percent in the area calculated from these measurements .", + "Output Program": [ + "n0 = 8.0\nn1 = 7.0\nt0 = n0 * n1\nt1 = n0 - n1\nt2 = t0 / 100.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.43999999999999995" + ], + "split": "train" + }, + { + "Input": "a metallic sheet is of rectangular shape with dimensions 40 m x 30 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m cube ) is :", + "Output Program": [ + "n0 = 40.0\nn1 = 30.0\nn2 = 8.0\nt0 = n2 * 2.0\nt1 = n0 - t0\nt2 = n1 - t0\nanswer = n2 * t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "2688" + ], + "split": "train" + }, + { + "Input": "find the area of a parallelogram with base 26 cm and height 14 cm ?", + "Output Program": [ + "n0 = 26.0\nn1 = 14.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "364" + ], + "split": "train" + }, + { + "Input": "a cylinder and a cone have the same height and same radius of base . the ratio between the volumes of the cylinder and the cone is :", + "Output Program": [ + "import math\nt0 = math.pi * 1.0**2 * 1.0 / 3\nt1 = math.pi * 1.0**2 * 1.0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "what is the ratio between perimeters of two squares one having 5 times the diagonal then the other ?", + "Output Program": [ + "n0 = 5.0\nt0 = n0 / n0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "find the area of a parallelogram with base 48 cm and height 36 cm ?", + "Output Program": [ + "n0 = 48.0\nn1 = 36.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "1728" + ], + "split": "train" + }, + { + "Input": "what is the area of square field whose side of length 5 m ?", + "Output Program": [ + "n0 = 5.0\n\nanswer = n0**2\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "the perimeter of a triangle is 32 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle", + "Output Program": [ + "n0 = 32.0\nn1 = 2.5\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "the width of a rectangular hall is \u00bd of its length . if the area of the hall is 800 sq . m , what is the difference between its length and breadth ?", + "Output Program": [ + "import math\nn0 = 800.0\nt0 = 1.0 / 2.0\nt1 = n0 / t0\nt2 = math.sqrt(max(0, t1))\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the area of an isosceles trapezoid with sides of length 5 and bases of length 11 and 17 is ?", + "Output Program": [ + "n0 = 5.0\nn1 = 11.0\nn2 = 17.0\n\nanswer = 4.0 * (n2 + n1) / 2 # quadrilateral area\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "find the area of a parallelogram with base 36 cm and height 18 cm ?", + "Output Program": [ + "n0 = 36.0\nn1 = 18.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "648" + ], + "split": "train" + }, + { + "Input": "a circular wire of radius 42 cm is cut and bent into the form of a rectangle whose sides are in the ratio of 6 : 5 . the smaller side of the rectangle is :", + "Output Program": [ + "import math\nn0 = 42.0\nn1 = 6.0\nn2 = 5.0\nt0 = n1 + n2\nt1 = 2 * math.pi * n0\nt2 = t0 * 2.0\nt3 = t1 / t2\nanswer = n2 * t3\nprint(answer)" + ], + "Output Answer": [ + "59.975859750350594" + ], + "split": "train" + }, + { + "Input": "the side of a rhombus is 22 m and length of one of its diagonals is 16 m . the area of the rhombus is ?", + "Output Program": [ + "import math\nn0 = 22.0\nn1 = 16.0\nt0 = n0 * 2.0\nt1 = n1**min(2.0, 5)\nt2 = t0**min(2.0, 5)\nt3 = t2 - t1\nt4 = math.sqrt(max(0, t3))\nt5 = n1 * t4\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "327.90242451070714" + ], + "split": "train" + }, + { + "Input": "the side of a square is increased by 15 % then how much % does its area increases ?", + "Output Program": [ + "n0 = 15.0\nt0 = n0 + 100.0\nt1 = 100.0**2\nt2 = t0**2\nt3 = t2 - t1\nt4 = t3 * 100.0\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "32.25" + ], + "split": "train" + }, + { + "Input": "if the volume of two cubes are in the ratio 27 : 8 , the ratio of their edges is :", + "Output Program": [ + "n0 = 27.0\nn1 = 8.0\n\nanswer = n0**(1 / 3)\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a box measuring 30 inches long by 48 inches wide by 12 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?", + "Output Program": [ + "n0 = 30.0\nn1 = 48.0\nn2 = 12.0\nt0 = n2 / 2.0\nt1 = n0 * n1\nt2 = n2 * t1\nt3 = t0**3\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "rain is falling at a rate of 10 centimeters per hour all over north carolina . somewhere downtown in north carolina a group of people are waiting for the rain to stop . if the rain filled a round puddle the with a base area of 300 square centimeters and a depth of 30 centimeters , how long did the people wait for the rain to stop ?", + "Output Program": [ + "n0 = 10.0\nn1 = 300.0\nn2 = 30.0\n\nanswer = n2 / n0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the diagonals of a rhombus are 20 cm and 25 cm . find its area ?", + "Output Program": [ + "n0 = 20.0\nn1 = 25.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "250" + ], + "split": "train" + }, + { + "Input": "a rectangular tank needs to be coated with insulation . the tank has dimensions of 4 feet , 5 feet , and 2 feet . each square foot of insulation costs $ 20 . how much will it cost to cover the surface of the tank with insulation ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 2.0\nn3 = 20.0\nt0 = 2 * (n0 * n1 + n0 * n2 + n1 * n2) # surface of a rectangular prism\nanswer = n3 * t0\nprint(answer)" + ], + "Output Answer": [ + "1520" + ], + "split": "train" + }, + { + "Input": "the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 2 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?", + "Output Program": [ + "n0 = 25.0\nn1 = 15.0\nn2 = 12.0\nn3 = 2.0\nn4 = 6.0\nn5 = 3.0\nn6 = 4.0\nn7 = 3.0\nt0 = n0 + n1\nt1 = n2 * 2.0\nt2 = n4 * n5\nt3 = n5 * n6\nt4 = t0 * t1\nt5 = n5 * t3\nt6 = t4 - t2\nt7 = t6 - t5\nanswer = n3 * t7\nprint(answer)" + ], + "Output Answer": [ + "1812" + ], + "split": "train" + }, + { + "Input": "huey ' s hip pizza sells two sizes of square pizzas : a small pizza that measures 8 inches on a side and costs $ 10 , and a large pizza that measures 12 inches on a side and costs $ 20 . if two friends go to huey ' s with $ 30 apiece , how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone ?", + "Output Program": [ + "n0 = 8.0\nn1 = 10.0\nn2 = 12.0\nn3 = 20.0\nn4 = 30.0\nt0 = n2**min(2.0, 5)\nt1 = n0**min(2.0, 5)\nt2 = t1 + t0\nt3 = t0 * 3.0\nt4 = t2 + t2\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "20 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?", + "Output Program": [ + "n0 = 20.0\nn1 = 7.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nt2 = n0 * t1\nt3 = t2 / 2.0\nanswer = t3 + t0\nprint(answer)" + ], + "Output Answer": [ + "330" + ], + "split": "train" + }, + { + "Input": "what is the area of square field whose side of length 25 m ?", + "Output Program": [ + "n0 = 25.0\n\nanswer = n0**2\nprint(answer)" + ], + "Output Answer": [ + "625" + ], + "split": "train" + }, + { + "Input": "abcd is a square where ab = \u00e2 \u02c6 \u0161 4008 . let x be a point on ab and y be a point on cd such that ax = cy . compute the area of trapezoid axyd .", + "Output Program": [ + "n0 = 4008.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "2004" + ], + "split": "train" + }, + { + "Input": "what would be the perimeter of the square whose side is equal to the diameter of the circle whose perimeter is 52.5 cm ?", + "Output Program": [ + "n0 = 52.5\nt0 = n0 / 3.141592653589793\nanswer = 4 * t0\nprint(answer)" + ], + "Output Answer": [ + "66.84507609859604" + ], + "split": "train" + }, + { + "Input": "carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 5 inches by 24 inches and jordan ' s rectangle is 8 inches long , how wide is jordan ' s rectangle , in inches ?", + "Output Program": [ + "n0 = 5.0\nn1 = 24.0\nn2 = 8.0\nt0 = n0 * n1 # area of rectangle\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "if the sides of a triangle are 26 cm , 24 cm and 10 cm , what is its area ?", + "Output Program": [ + "n0 = 26.0\nn1 = 24.0\nn2 = 10.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "the breath of a rectangular landscape is 6 times its length . there is a playground in it whose area is 4200 square mtr & which is 1 / 7 th of the total landscape . what is the breath of the landscape ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 4200.0\nn2 = 1.0\nn3 = 7.0\nt0 = n1 * n3\nt1 = t0 / n0\nt2 = math.sqrt(max(0, t1))\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "420" + ], + "split": "train" + }, + { + "Input": "in a certain circle there are 10 points . what is the number of the triangles connecting 5 points of the 10 points ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 5.0\nn2 = 10.0\nt0 = 10.0 / 2.0\nt1 = math.factorial(min(15, int(n0)))\nt2 = math.factorial(min(15, int(n1)))\nt3 = math.factorial(min(15, int(t0)))\nt4 = t3 * t2\nanswer = t1 / t4\nprint(answer)" + ], + "Output Answer": [ + "252" + ], + "split": "train" + }, + { + "Input": "what is the area of a rectangle whose length is twice its width and whose perimeter is equal to that of a square whose area is 1 ?", + "Output Program": [ + "n0 = 1.0\nt0 = n0 * 4.0\nt1 = t0 / 2.0\nt2 = t1 / 3.0\nt3 = t2 * 2.0\nanswer = t2 * t3 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "0.8888888888888888" + ], + "split": "train" + }, + { + "Input": "the edge of a cube is 7 a cm . find its surface ?", + "Output Program": [ + "n0 = 7.0\n\nanswer = 6 * n0**2 # surface of a cube\nprint(answer)" + ], + "Output Answer": [ + "294" + ], + "split": "train" + }, + { + "Input": "the area of a square field is 400 km 2 . how long will it take for a horse to run around at the speed of 20 km / h ?", + "Output Program": [ + "import math\nn0 = 400.0\nn1 = 2.0\nn2 = 20.0\nt0 = math.sqrt(max(0, n0))\nt1 = t0 * 4.0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "huey ' s hip pizza sells two sizes of square pizzas : a small pizza that measures 9 inches on a side and costs $ 10 , and a large pizza that measures 14 inches on a side and costs $ 20 . if two friends go to huey ' s with $ 30 apiece , how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone ?", + "Output Program": [ + "n0 = 9.0\nn1 = 10.0\nn2 = 14.0\nn3 = 20.0\nn4 = 30.0\nt0 = n2**min(2.0, 5)\nt1 = n0**min(2.0, 5)\nt2 = t1 + t0\nt3 = t0 * 3.0\nt4 = t2 + t2\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "if f is the smallest positive integer such that 3,150 multiplied by f is the square of an integer , then f must be", + "Output Program": [ + "n0 = 3150.0\n\nanswer = 10.0 + 4.0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "the area of a circle of radius 5 is numerically what percent of its circumference ?", + "Output Program": [ + "import math\nn0 = 5.0\nt0 = math.pi * n0**2\nt1 = 2 * math.pi * n0\nt2 = t0 / t1\nanswer = t2 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "250" + ], + "split": "train" + }, + { + "Input": "the length and breadth of a rectangle is increased by 10 % and 25 % respectively . what is the increase in the area ?", + "Output Program": [ + "n0 = 10.0\nn1 = 25.0\nt0 = n0 + 100.0\nt1 = n1 + 100.0\nt2 = 100.0 * 100.0 # area of rectangle\nt3 = t0 * t1 # area of rectangle\nt4 = t3 - t2\nt5 = t4 * 100.0\nanswer = t5 / t2\nprint(answer)" + ], + "Output Answer": [ + "37.5" + ], + "split": "train" + }, + { + "Input": "if the sides of a square are multiplied by sqrt ( 5 ) , the area of the original square is how many times as large as the area of the resultant square ?", + "Output Program": [ + "n0 = 5.0\n\nanswer = 4 * n0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "if the length of the sides of two cubes are in the ratio 2 : 1 , what is the ratio of their total surface area ?", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\n\nanswer = n0 * n0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "juan and his five friends will sit on six fixed seats around a circular table . if juan must sit on the seat closest to the window and jamal must sit next to juan , in how many can juan and his five friends sit ?", + "Output Program": [ + "import math\nt0 = math.factorial(min(15, int(4.0)))\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 \u03c0 \u00b7 r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many q grams ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 0.15\nn3 = 8.0\nn4 = 0.3\n\nanswer = n0 * n3\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "14 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?", + "Output Program": [ + "n0 = 14.0\nn1 = 7.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nt2 = n0 * t1\nt3 = t2 / 2.0\nanswer = t3 + t0\nprint(answer)" + ], + "Output Answer": [ + "189" + ], + "split": "train" + }, + { + "Input": "when magnified 1,000 times by an electron microscope , the image of a certain circular piece of tissue has a diameter of 5 centimeter . the actual diameter of the tissue , in centimeters , is", + "Output Program": [ + "n0 = 1000.0\nn1 = 5.0\n\nanswer = n1 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.005" + ], + "split": "train" + }, + { + "Input": "if the sides of a triangle are 21 cm , 19 cm and 5 cm , what is its area ?", + "Output Program": [ + "n0 = 21.0\nn1 = 19.0\nn2 = 5.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "47.5" + ], + "split": "train" + }, + { + "Input": "find the area of a rhombus having each side equal to 13 cm and one of whose diagonal is 24 cm .", + "Output Program": [ + "import math\nn0 = 13.0\nn1 = 24.0\nt0 = n1 / 2.0\nt1 = n0**min(2.0, 5)\nt2 = t0**min(2.0, 5)\nt3 = t1 - t2\nt4 = math.sqrt(max(0, t3))\nt5 = t4 * 2.0\nanswer = n1 * t5 / 2\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "a rectangular grass field is 75 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 10 per sq m ?", + "Output Program": [ + "n0 = 75.0\nn1 = 55.0\nn2 = 2.5\nn3 = 10.0\nt0 = n2 * 2.0\nt1 = n0 * n1 # area of rectangle\nt2 = n0 + t0\nt3 = n1 + t0\nt4 = t2 * t3 # area of rectangle\nt5 = t4 - t1\nanswer = n3 * t5\nprint(answer)" + ], + "Output Answer": [ + "6750" + ], + "split": "train" + }, + { + "Input": "the water level in a rectangular swimming pool measuring 60 feet by 20 feet is to be lowered by 6 inches . how many gallons of water must be removed ? ( 1 cu ft = 7.5 gallons )", + "Output Program": [ + "n0 = 60.0\nn1 = 20.0\nn2 = 6.0\nn3 = 1.0\nn4 = 7.5\nt0 = 10.0 + 2.0\nt1 = n2 / t0\nt2 = n0 * n1 * t1\nanswer = n4 * t2\nprint(answer)" + ], + "Output Answer": [ + "4500" + ], + "split": "train" + }, + { + "Input": "what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 57 ?", + "Output Program": [ + "import math\nn0 = 289.0\nn1 = 57.0\nt0 = math.sqrt(max(0, n0))\nt1 = 4 * t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "3876" + ], + "split": "train" + }, + { + "Input": "if the height of a cone is increased by 160 % then its volume is increased by ?", + "Output Program": [ + "n0 = 160.0\n\nanswer = n0 * 1.0 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "160" + ], + "split": "train" + }, + { + "Input": "a rectangular lawn of dimensions 80 m * 50 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?", + "Output Program": [ + "n0 = 80.0\nn1 = 50.0\nn2 = 10.0\nn3 = 3.0\nt0 = n0 + n1\nt1 = t0 - n2\nt2 = n2 * t1\nanswer = n3 * t2\nprint(answer)" + ], + "Output Answer": [ + "3600" + ], + "split": "train" + }, + { + "Input": "carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 15 inches by 20 inches and jordan ' s rectangle is 6 inches long , how wide is jordan ' s rectangle , in inches ?", + "Output Program": [ + "n0 = 15.0\nn1 = 20.0\nn2 = 6.0\nt0 = n0 * n1 # area of rectangle\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "in measuring the sides of a rectangle , one side is taken 14 % in excess and other 5 % in deficit . find the error percentage in the area calculated from these measurements .", + "Output Program": [ + "n0 = 14.0\nn1 = 5.0\nt0 = n0 * n1\nt1 = n0 - n1\nt2 = t0 / 100.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "8.3" + ], + "split": "train" + }, + { + "Input": "a lady builds 12 cm length , 16 cm width , and 6 cm height box using 3 cubic cm cubes . what is the minimum number of cubes required to build the box ?", + "Output Program": [ + "n0 = 12.0\nn1 = 16.0\nn2 = 6.0\nn3 = 3.0\nt0 = n0 * n1\nt1 = n2 * t0\nanswer = t1 / n3\nprint(answer)" + ], + "Output Answer": [ + "384" + ], + "split": "train" + }, + { + "Input": "the area of a parallelogram is 162 sq m and its altitude is twice the corresponding base . then the length of the base is ?", + "Output Program": [ + "import math\nn0 = 162.0\nt0 = n0 / 2.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "if n is the smallest integer such that 432 times n is the square of an integer , what is the value of n ?", + "Output Program": [ + "n0 = 432.0\nt0 = n0 / 2.0\nt1 = t0 / 2.0\nt2 = t1 / 2.0\nt3 = t2 / 2.0\nt4 = t3 / 3.0\nanswer = t4 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the cube root of what integer power of 2 is closest to 50 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 50.0\nt0 = 4.0 + 4.0\nt1 = n1 / n0\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "in triangle pqr , the angle q = 90 degree , pq = 2 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz", + "Output Program": [ + "n0 = 90.0\nn1 = 2.0\nn2 = 8.0\nt0 = n1 * n2\nanswer = t0 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "1.6" + ], + "split": "train" + }, + { + "Input": "if the sides of a triangle are 28 cm , 24 cm and 15 cm , what is its area ?", + "Output Program": [ + "n0 = 28.0\nn1 = 24.0\nn2 = 15.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "train" + }, + { + "Input": "carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 8 inches by 15 inches and jordan ' s rectangle is 4 inches long , how wide is jordan ' s rectangle , in inches ?", + "Output Program": [ + "n0 = 8.0\nn1 = 15.0\nn2 = 4.0\nt0 = n0 * n1 # area of rectangle\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "the perimeter of a triangle is 32 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ?", + "Output Program": [ + "n0 = 32.0\nn1 = 2.5\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "the perimeter of a triangle is 35 cm and the inradius of the triangle is 4.5 cm . what is the area of the triangle ?", + "Output Program": [ + "n0 = 35.0\nn1 = 4.5\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "78.75" + ], + "split": "train" + }, + { + "Input": "a larger cube has 216 cubic inch as a volume and in the cube there are 216 smaller cubes such that their volume is 1 cubic inch . what is the difference between the surface areas \u2019 sum of the 216 smaller cubes and the surface area of the larger cube , in square inch ?", + "Output Program": [ + "n0 = 216.0\nn1 = 216.0\nn2 = 1.0\nn3 = 216.0\nt0 = n2**(1 / 3)\nt1 = n0**(1 / 3)\nt2 = 6 * t0**2 # surface of a cube\nt3 = 6 * t1**2 # surface of a cube\nt4 = n0 * t2\nanswer = t4 - t3\nprint(answer)" + ], + "Output Answer": [ + "1080" + ], + "split": "train" + }, + { + "Input": "approximately how many cubic feet of water are needed to fill a circular swimming pool that is 80 feet across and 10 feet deep ?", + "Output Program": [ + "import math\nn0 = 80.0\nn1 = 10.0\nt0 = n0 / 2.0\nanswer = math.pi * t0**2 * n1\nprint(answer)" + ], + "Output Answer": [ + "50265.482457436694" + ], + "split": "train" + }, + { + "Input": "if the area of a circle decreases by 36 % , then the radius of a circle decreases by", + "Output Program": [ + "import math\nn0 = 36.0\nt0 = 100.0 - n0\nt1 = t0 / 100.0\nt2 = math.sqrt(max(0, t1))\nt3 = 1.0 - t2\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "19.999999999999996" + ], + "split": "train" + }, + { + "Input": "find the area of a triangle whose sides are 41 cm , 28 cm , 15 cm . also , find the length of the altitude corresponding to the largest side of the triangle .", + "Output Program": [ + "import math\nn0 = 41.0\nn1 = 28.0\nn2 = 15.0\nt0 = (lambda s, a, b, c: math.sqrt(max(0, s * (s - a) * (s - b) * (s - c))))((n0 + n1 + n2) / 2, n0, n1, n2) # Heron's formula\nt1 = t0 * 2.0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "6.146341463414634" + ], + "split": "train" + }, + { + "Input": "36 people { a 1 , a 2 \u2026 a 36 } meet and shake hands in a circular fashion . in other words , there are totally 36 handshakes involving the pairs , { a 1 , a 2 } , { a 2 , a 3 } , \u2026 , { a 35 , a 36 } , { a 36 , a 1 } . then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is", + "Output Program": [ + "n0 = 36.0\nn1 = 1.0\nn2 = 2.0\nn3 = 36.0\nn4 = 36.0\nn5 = 1.0\nn6 = 2.0\nn7 = 2.0\nn8 = 3.0\nn9 = 35.0\nn10 = 36.0\nn11 = 36.0\nn12 = 1.0\n\nanswer = n0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the diagonals of a rhombus are 25 cm and 30 cm . find its area ?", + "Output Program": [ + "n0 = 25.0\nn1 = 30.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "375" + ], + "split": "train" + }, + { + "Input": "how many internal diagonals does a hexagon ( 6 sided polygon ) have ?", + "Output Program": [ + "n0 = 6.0\nt0 = n0 - 3.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular landscape is 4 times its breadth . there is a playground in it whose area is 1200 square mtr & which is 1 / 3 rd of the total landscape . what is the length of the landscape ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1200.0\nn2 = 1.0\nn3 = 3.0\nt0 = n0 * n3\nanswer = t0 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "two isosceles triangles have equal vertical angles and their areas are in the ratio 16 : 36 . find the ratio of their corresponding heights .", + "Output Program": [ + "import math\nn0 = 16.0\nn1 = 36.0\nt0 = math.sqrt(max(0, n0))\nt1 = math.sqrt(max(0, n1))\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666666" + ], + "split": "train" + }, + { + "Input": "the size of a television screen is given as the length of the screen ' s diagonal . if the screens were flat , then the area of a square 18 - inch screen would be how many square inches greater than the area of a square 16 - inch screen ?", + "Output Program": [ + "n0 = 18.0\nn1 = 16.0\nt0 = n0**min(2.0, 5)\nt1 = n1**min(2.0, 5)\nt2 = t0 - t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "34" + ], + "split": "train" + }, + { + "Input": "when magnified 1000 times by an electron microscope , the image of a certain circular piece of tissue has a diameter of 0.3 centimeter . the actual diameter of the tissue , in centimeters , is", + "Output Program": [ + "n0 = 1000.0\nn1 = 0.3\n\nanswer = n1 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.0003" + ], + "split": "train" + }, + { + "Input": "a circular garden is surrounded by a fence of negligible width along the boundary . if the length of the fence is 1 / 5 of th area of the garden . what is the radius of the circular garden ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 5.0\nt0 = n1**min(2.0, 5)\nt1 = math.sqrt(max(0, t0))\nanswer = t1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "if the length of the longest chord of a certain circle is 22 , what is the radius of that certain circle ?", + "Output Program": [ + "n0 = 22.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "an isosceles triangle those sides are 13 cm , 13 cm , 10 cm long inscribed in a circle . find the radius of the circle", + "Output Program": [ + "import math\nn0 = 13.0\nn1 = 13.0\nn2 = 10.0\nt0 = n2 / 2.0\nt1 = n0**min(2.0, 5)\nt2 = t0**min(2.0, 5)\nt3 = t1 - t2\nt4 = t2 + t3\nt5 = math.sqrt(max(0, t3))\nt6 = t5 * 2.0\nt7 = t4 / t6\nanswer = t7 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "8.041666666666668" + ], + "split": "train" + }, + { + "Input": "a horse is tethered to one corner of a rectangular grassy field 45 m by 25 m with a rope 22 m long . over how much area of the field can it graze ?", + "Output Program": [ + "n0 = 45.0\nn1 = 25.0\nn2 = 22.0\nt0 = n2**min(2.0, 5)\nt1 = t0 * 3.141592653589793\nanswer = t1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "380.132711084365" + ], + "split": "train" + }, + { + "Input": "an oil cylinder was 3 / 4 th full . when 4 bottles of oil is poured into it , it is 4 / 5 th full . how many bottles of oil can the full cylinder hold ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 4.0\nn3 = 4.0\nn4 = 5.0\nt0 = n1 / n4\nt1 = n0 / n1\nt2 = t0 - t1\nt3 = t2 / n1\nanswer = 1.0 / t3\nprint(answer)" + ], + "Output Answer": [ + "79.99999999999993" + ], + "split": "train" + }, + { + "Input": "find the sum of divisors of 544 which are perfect squares", + "Output Program": [ + "import math\nn0 = 544.0\nt0 = n0 / 2.0\nt1 = t0 / 2.0\nt2 = t1 / 2.0\nt3 = t2 / 2.0\nt4 = t3 / 2.0\nt5 = n0 / t4\nt6 = t5 / 2.0\nt7 = math.sqrt(max(0, t6))\nt8 = t7 + 1.0\nanswer = t8 + t6\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "find the surface area of a 10 cm x 4 cm x 3 cm brick", + "Output Program": [ + "n0 = 10.0\nn1 = 4.0\nn2 = 3.0\n\nanswer = 2 * (n0 * n1 + n0 * n2 + n1 * n2) # surface of a rectangular prism\nprint(answer)" + ], + "Output Answer": [ + "164" + ], + "split": "train" + }, + { + "Input": "a box measuring 35 inches long by 20 inches wide by 10 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?", + "Output Program": [ + "n0 = 35.0\nn1 = 20.0\nn2 = 10.0\nt0 = n2 / 2.0\nt1 = n0 * n1\nt2 = n2 * t1\nt3 = t0**3\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "find the area of a parallelogram with base 24 cm and height 16 cm ?", + "Output Program": [ + "n0 = 24.0\nn1 = 16.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "384" + ], + "split": "train" + }, + { + "Input": "a cylindrical container of radius 6 cm and height 15 cm is filled with ice - cream . the whole icecream has to be distributed to 10 children in equal cones with hemispherical tops . if the height of the conical portion is four times the radius of its base , find the radius of the ice - cream cone .", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 15.0\nn2 = 10.0\nt0 = 1.0 / 3.0\nt1 = 2.0 / 3.0\nt2 = math.pi * n0**2 * n1\nt3 = t2 / 10.0\nt4 = t0 * 3.141592653589793\nt5 = t1 * 3.141592653589793\nt6 = t4 * 4.0\nt7 = t6 + t5\nt8 = t3 / t7\nt9 = t8 / 3.0\nanswer = math.sqrt(max(0, t9))\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "people were sitting in a circle . 7 th one is direct opposite to 18 th one . . then how many were there in that group ?", + "Output Program": [ + "n0 = 7.0\nn1 = 18.0\nt0 = n1 - n0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "a certain cube floating in a bucket of water has between 80 and 90 percent of its volume below the surface of the water . if between 6 and 13 cubic centimeters of the cube ' s volume is above the surface of the water , then the length of a side of the cube is approximately", + "Output Program": [ + "n0 = 80.0\nn1 = 90.0\nn2 = 6.0\nn3 = 13.0\nt0 = n3 * 100.0\nt1 = 100.0 - n0\nt2 = t0 / t1\nanswer = t2**(1 / 3)\nprint(answer)" + ], + "Output Answer": [ + "4.020725758589058" + ], + "split": "train" + }, + { + "Input": "what is the total surface area in square meters of a rectangular solid whose length is 10 meters , width is 9 meters , and depth is 6 meters ?", + "Output Program": [ + "n0 = 10.0\nn1 = 9.0\nn2 = 6.0\n\nanswer = 2 * (n0 * n1 + n0 * n2 + n1 * n2) # surface of a rectangular prism\nprint(answer)" + ], + "Output Answer": [ + "408" + ], + "split": "train" + }, + { + "Input": "f and e are midpoints of ab and ad respectively . if the side of square abcd is 8 , what is the area of triangle cef ?", + "Output Program": [ + "n0 = 8.0\nt0 = n0 / 2.0\nt1 = n0**2\nt2 = n0 * t0 / 2\nt3 = t0 * t0 / 2\nt4 = t1 - t2\nt5 = t4 - t2\nanswer = t5 - t3\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "find the area of a parallelogram with base 60 cm and height 16 cm ?", + "Output Program": [ + "n0 = 60.0\nn1 = 16.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "960" + ], + "split": "train" + }, + { + "Input": "in front of you lies a figure made up with 20 x 10 square blocks . will you be able to find out the number of unique squares and rectangles that are being formed inside this figure by combining two or more distinct squares ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nt0 = n0 + 1.0\nt1 = n1 + 1.0\nt2 = n0 * t0\nt3 = n1 * t1\nt4 = t2 / 2.0\nt5 = t3 / 2.0\nanswer = t4 * t5\nprint(answer)" + ], + "Output Answer": [ + "11550" + ], + "split": "train" + }, + { + "Input": "the sides of the triangle are in the ratio 1 / 2 : 1 / 3 : 1 / 4 and its perimeter is 104 cm . the length of the longest side is ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 3.0\nn4 = 1.0\nn5 = 4.0\nn6 = 104.0\nt0 = n0 / n5\nt1 = n0 / n3\nt2 = n0 / n1\nt3 = t0 + t1\nt4 = t3 + t2\nt5 = n6 / t4\nanswer = t5 * t2\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "find the area of a parallelogram with base 32 cm and height 18 cm ?", + "Output Program": [ + "n0 = 32.0\nn1 = 18.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "576" + ], + "split": "train" + }, + { + "Input": "if the sum of a number and its square is 132 , what is the number ?", + "Output Program": [ + "import math\nn0 = 132.0\nt0 = math.sqrt(max(0, n0))\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "what should be added to 4440 so that it may become a perfect square ?", + "Output Program": [ + "n0 = 4440.0\nt0 = 10.0 + 10.0\nt1 = 3.0 + 4.0\nt2 = t0 + t0\nt3 = t2 + t0\nt4 = t3 + t1\nt5 = t4 * t4\nanswer = t5 - n0\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "train" + }, + { + "Input": "a cubical block of metal weighs 5 pounds . how much will another cube of the same metal weigh if its sides are twice as long ?", + "Output Program": [ + "n0 = 5.0\nt0 = 2.0 * 4.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "the area of a square garden is q square feet and the perimeter is p feet . if q = 2 p + 20 , what is the perimeter of the garden in feet ?", + "Output Program": [ + "n0 = 2.0\nn1 = 20.0\n\nanswer = n1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "a volume of 11780 l water is in a container of sphere . how many hemisphere of volume 4 l each will be required to transfer all the water into the small hemispheres ?", + "Output Program": [ + "n0 = 11780.0\nn1 = 4.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "2945" + ], + "split": "train" + }, + { + "Input": "when magnified 1,000 times by an electron microscope , the image of a certain circular piece of tissue has a diameter of 0.2 centimeter . the actual diameter of the tissue , in centimeters , is", + "Output Program": [ + "n0 = 1000.0\nn1 = 0.2\n\nanswer = n1 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.0002" + ], + "split": "train" + }, + { + "Input": "in measuring the sides of a rectangle , one side is taken 16 % in excess and other 5 % in deficit . find the error percentage in the area calculated from these measurements .", + "Output Program": [ + "n0 = 16.0\nn1 = 5.0\nt0 = n0 * n1\nt1 = n0 - n1\nt2 = t0 / 100.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "10.2" + ], + "split": "train" + }, + { + "Input": "a making a cube with dimension 5 * 5 * 5 using 1 * 1 * 1 cubes . what is the number of cubes needed to make hollow cube looking of the same shape .", + "Output Program": [ + "n0 = 5.0\nn1 = 5.0\nn2 = 5.0\nn3 = 1.0\nn4 = 1.0\nn5 = 1.0\nt0 = n0 * n0\nt1 = n0 - 2.0\nt2 = n0 * t0\nt3 = t1 * t1\nt4 = t3 * 3.0\nanswer = t2 - t4\nprint(answer)" + ], + "Output Answer": [ + "98" + ], + "split": "train" + }, + { + "Input": "find the area of a parallelogram with base 18 cm and height 16 cm ?", + "Output Program": [ + "n0 = 18.0\nn1 = 16.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "288" + ], + "split": "train" + }, + { + "Input": "a football field is 9600 square yards . if 800 pounds of fertilizer are spread evenly across the entire field , how many pounds of fertilizer were spread over an area of the field totaling 3600 square yards ?", + "Output Program": [ + "n0 = 9600.0\nn1 = 800.0\nn2 = 3600.0\nt0 = n1 / n0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "the breath of a rectangular landscape is 8 times its length . there is a playground in it whose area is 3200 square mtr & which is 1 / 9 rd of the total landscape . what is the breath of the landscape ?", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 3200.0\nn2 = 1.0\nn3 = 9.0\nt0 = n1 * n3\nt1 = t0 / n0\nt2 = math.sqrt(max(0, t1))\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "480" + ], + "split": "train" + }, + { + "Input": "the area of a square field is 1225 km 2 . how long will it take for a horse to run around at the speed of 20 km / h ?", + "Output Program": [ + "import math\nn0 = 1225.0\nn1 = 2.0\nn2 = 20.0\nt0 = math.sqrt(max(0, n0))\nt1 = t0 * 4.0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "it has been raining at the rate of 5 centimeters per hour . if the rain filled a cylindrical drum with a depth of 15 centimeters , and area 300 square centimeters , how long did it take to fill the drum completely ?", + "Output Program": [ + "n0 = 5.0\nn1 = 15.0\nn2 = 300.0\n\nanswer = n1 / n0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the diameter of a cylindrical tin is 10 cm and height is 5 cm . find the volume of the cylinder ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 5.0\nt0 = n0 / 2.0\nt1 = math.pi * t0**2 * n1\nanswer = t1 / 3.141592653589793\nprint(answer)" + ], + "Output Answer": [ + "125.00000000000001" + ], + "split": "train" + }, + { + "Input": "the diameter of a cylindrical tin is 14 cm and height is 2 cm . find the volume of the cylinder ?", + "Output Program": [ + "import math\nn0 = 14.0\nn1 = 2.0\nt0 = n0 / 2.0\nt1 = math.pi * t0**2 * n1\nanswer = t1 / 3.141592653589793\nprint(answer)" + ], + "Output Answer": [ + "98" + ], + "split": "train" + }, + { + "Input": "what is the area of a square field whose diagonal of length 16 m ?", + "Output Program": [ + "n0 = 16.0\nt0 = n0**2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "128" + ], + "split": "train" + }, + { + "Input": "find the circumference and area of radius 13 cm .", + "Output Program": [ + "import math\nn0 = 13.0\n\nanswer = math.pi * n0**2\nprint(answer)" + ], + "Output Answer": [ + "530.929158456675" + ], + "split": "train" + }, + { + "Input": "a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 7 m , the volume of the box ( in m 3 ) is :", + "Output Program": [ + "n0 = 48.0\nn1 = 36.0\nn2 = 7.0\nn3 = 3.0\nt0 = n2 * 2.0\nt1 = n0 - t0\nt2 = n1 - t0\nanswer = n2 * t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "5236" + ], + "split": "train" + }, + { + "Input": "the diagonal of a rhombus are 40 m and 30 m . its area is :", + "Output Program": [ + "n0 = 40.0\nn1 = 30.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "train" + }, + { + "Input": "a snooker tournament charges $ 40.00 for vip seats and $ 15.00 for general admission ( \u201c regular \u201d seats ) . on a certain night , a total of 320 tickets were sold , for a total cost of $ 7,500 . how many fewer tickets were sold that night for vip seats than for general admission seats ?", + "Output Program": [ + "n0 = 40.0\nn1 = 15.0\nn2 = 320.0\nn3 = 7500.0\nt0 = 3.0 + 4.0\nt1 = 2.0 + 3.0\nt2 = n1 * n2\nt3 = t0 * 1000.0\nt4 = t1 * 100.0\nt5 = t1 * t1\nt6 = t3 + t4\nt7 = t6 - t2\nt8 = t7 / t5\nanswer = n2 - t8\nprint(answer)" + ], + "Output Answer": [ + "212" + ], + "split": "train" + }, + { + "Input": "the area of a rectangle is 360 sq . m . if its length is increased by 10 m and its width is decreased by 6 m , then its area does not change . find the perimeter of the original rectangle .", + "Output Program": [ + "n0 = 360.0\nn1 = 10.0\nn2 = 6.0\nt0 = n2 * 3.0\nt1 = n0 / t0\nanswer = 2 * (t1 + t0) # perimetere of rectangle\nprint(answer)" + ], + "Output Answer": [ + "76" + ], + "split": "train" + }, + { + "Input": "in measuring the sides of a rectangle , one side is taken 7 % in excess , and the other 6 % in deficit . find the error percent in the area calculated from these measurements .", + "Output Program": [ + "n0 = 7.0\nn1 = 6.0\nt0 = n0 * n1\nt1 = n0 - n1\nt2 = t0 / 100.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.5800000000000001" + ], + "split": "train" + }, + { + "Input": "how many squares are there between 2011 to 2300 ? ? ? ?", + "Output Program": [ + "import math\nn0 = 2011.0\nn1 = 2300.0\nt0 = math.sqrt(max(0, n1))\nt1 = math.sqrt(max(0, n0))\nt2 = math.floor(t0)\nt3 = math.floor(t1)\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the perimeter of a triangle is 20 cm and the inradius of the triangle is 3 cm . what is the area of the triangle ?", + "Output Program": [ + "n0 = 20.0\nn1 = 3.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "if a cube has a volume of 125 , what is the surface area of one side ?", + "Output Program": [ + "n0 = 125.0\nt0 = n0**(1 / 3)\nanswer = t0**2\nprint(answer)" + ], + "Output Answer": [ + "24.99999999999999" + ], + "split": "train" + }, + { + "Input": "right triangle pqr is the base of the prism in the figure above . if pq = pr = \u00e2 \u02c6 \u0161 5 and the height of the prism is 10 , what is the volume of the prism ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 10.0\nt0 = math.sqrt(max(0, n0))\nt1 = t0 * t0 / 2\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "25.000000000000004" + ], + "split": "train" + }, + { + "Input": "what is the ratio between perimeters of two squares one having 2.5 times the diagonal then the other ?", + "Output Program": [ + "n0 = 2.5\nt0 = n0 / n0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "2.5" + ], + "split": "train" + }, + { + "Input": "all the faces of a cube are painted with blue colour . then it is cut into 125 small equal cubes . how many small cubes will be formed having only one face coloured ?", + "Output Program": [ + "n0 = 125.0\nt0 = 1.0 / 3.0\nt1 = n0**min(t0, 5)\nt2 = t1 - 2.0\nt3 = t2**min(2.0, 5)\nt4 = t3 * 60.0\nanswer = t4 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "53.999999999999964" + ], + "split": "train" + }, + { + "Input": "a rectangular courty 3.78 metres long and 5.25 metres wide is to be paved exactly with square tiles , all of the same size . what is the largest size of the tile which could be used for the purpose ?", + "Output Program": [ + "n0 = 3.78\nn1 = 5.25\nt0 = n0 * 100.0\nt1 = t0 / 3.0\nt2 = t1 / 3.0\nt3 = t2 / 3.0\nt4 = t3 / 2.0\nanswer = t4 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "the diagonal of a rhombus are 80 m and 120 m . its area is :", + "Output Program": [ + "n0 = 80.0\nn1 = 120.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "4800" + ], + "split": "train" + }, + { + "Input": "an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 45 cm , find the sum of the perimeters of all the triangles .", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 3.0\nn3 = 2.0\nn4 = 1.0\nn5 = 45.0\nt0 = n5 + n5 + n5 # perimeter of a triangle\nanswer = t0 + t0\nprint(answer)" + ], + "Output Answer": [ + "270" + ], + "split": "train" + }, + { + "Input": "find the perimeter and area of a square of side 19 cm .", + "Output Program": [ + "n0 = 19.0\n\nanswer = n0**2\nprint(answer)" + ], + "Output Answer": [ + "361" + ], + "split": "train" + }, + { + "Input": "there are 7 non - collinear points . how many triangles can be drawn by joining these points ?", + "Output Program": [ + "n0 = 7.0\nt0 = 1.0 + 4.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "the area of an equilateral triangle is subtracted from its base , and the perimeter is then added to this total , the result is 4 . what is the height of the equilateral triangle if its base is 2 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nt0 = n1 * 3.0\nt1 = n1 - n0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "find the area of a parallelogram with base 34 cm and height 18 cm ?", + "Output Program": [ + "n0 = 34.0\nn1 = 18.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "612" + ], + "split": "train" + }, + { + "Input": "in the rectangular coordinate system , points ( 8 , 0 ) and ( \u2013 8 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c ?", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 0.0\nn2 = 8.0\nn3 = 0.0\nt0 = n0**min(2.0, 5)\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a lady builds 10 cm length , 18 cm width , and 4 cm height box using 12 cubic cm cubes . what is the minimum number of cubes required to build the box ?", + "Output Program": [ + "n0 = 10.0\nn1 = 18.0\nn2 = 4.0\nn3 = 12.0\nt0 = n0 * n1\nt1 = n2 * t0\nanswer = t1 / n3\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "the diagonal of the floor of a rectangular closet is 7 feet . the shorter side of the closet is 4 feet . what is the area of the closet in square feet ?", + "Output Program": [ + "import math\nn0 = 7.0\nn1 = 4.0\nt0 = 2.0 * 4.0\nt1 = n0 * 2.0\nt2 = t0 + 1.0\nt3 = t1 + 1.0\nt4 = t2 / 2.0\nt5 = t3 / 2.0\nt6 = t5**min(2.0, 5)\nt7 = t4**min(2.0, 5)\nt8 = t6 - t7\nt9 = math.sqrt(max(0, t8))\nanswer = t4 * t9 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "the diagonal of a rectangle is cm and its area is 20 sq . cm . the perimeter of the rectangle must be :", + "Output Program": [ + "import math\nn0 = 20.0\nt0 = n0 + n0\nt1 = t0 + 1.0\nt2 = t0 + t1\nt3 = math.sqrt(max(0, t2))\nanswer = t3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "what is the ratio between perimeters of two squares one having 4 times the diagonal then the other ?", + "Output Program": [ + "n0 = 4.0\nt0 = n0 / n0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "calculate the area of a triangle , if the sides are 13 cm , 12 cm and 5 cm , what is its area ?", + "Output Program": [ + "n0 = 13.0\nn1 = 12.0\nn2 = 5.0\nt0 = n1 / 2.0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "in a certain circle there are 9 points . what is the number of the triangles connecting 4 points of the 9 points ?", + "Output Program": [ + "import math\nn0 = 9.0\nn1 = 4.0\nn2 = 9.0\nt0 = 10.0 / 2.0\nt1 = math.factorial(min(15, int(n0)))\nt2 = math.factorial(min(15, int(n1)))\nt3 = math.factorial(min(15, int(t0)))\nt4 = t3 * t2\nanswer = t1 / t4\nprint(answer)" + ], + "Output Answer": [ + "126" + ], + "split": "train" + }, + { + "Input": "if the height of a cone is increased by 100 % then its volume is increased by ?", + "Output Program": [ + "n0 = 100.0\n\nanswer = n0 * 1.0 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "34 . the side surface of a cylinder is rolled with a rectangle . if the height of a cylinder is 16 feet and the perimeter of the circular base . is 12 feet , what is the diagonal of the rectangle ?", + "Output Program": [ + "import math\nn0 = 34.0\nn1 = 16.0\nn2 = 12.0\nt0 = n1 * n1\nt1 = n2 * n2\nt2 = t0 + t1\nanswer = math.sqrt(max(0, t2))\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a rectangular pig farm has a fence along three sides and a wall along the fourth side . the fenced side opposite the wall is twice the length of each of the other two fenced sides . if the area of the rectangular region is 1250 square feet , what is the total length of the fence , in feet ?", + "Output Program": [ + "import math\nn0 = 1250.0\nt0 = n0 / 2.0\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * 2.0\nanswer = 2 * (t2 + t1) # perimetere of rectangle\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "by combining number of small cubes , a larger cube is produced . the ratio between volume of larger cube and small cube is 1000 : 8 then how many small cubes are required to produce a larger cube ?", + "Output Program": [ + "n0 = 1000.0\nn1 = 8.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "abcd is a square where ab = \u00e2 \u02c6 \u0161 6000 . let x be a point on ab and y be a point on cd such that ax = cy . compute the area of trapezoid axyd .", + "Output Program": [ + "n0 = 6000.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "3000" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is one - sixth of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1296 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?", + "Output Program": [ + "import math\nn0 = 1296.0\nn1 = 10.0\nt0 = math.sqrt(max(0, n0))\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "if the area of a square with sides of length 4 centimeters is equal to the area of a rectangle with a width of 4 centimeters , what is the length of the rectangle , in centimeters ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nt0 = n0**min(2.0, 5)\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "three walls have wallpaper covering a combined area of 300 square meters . by overlapping the wallpaper to cover a wall with an area of 180 square meters , the area that is covered by exactly two layers of wallpaper is 30 square meters . what is the area that is covered with three layers of wallpaper ?", + "Output Program": [ + "n0 = 300.0\nn1 = 180.0\nn2 = 30.0\nt0 = n0 - n1\nt1 = t0 - n2\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "the two sides of a triangle are 32 and 68 . the area is 960 sq . cm . find the third side of triangle ?", + "Output Program": [ + "import math\nn0 = 32.0\nn1 = 68.0\nn2 = 960.0\nt0 = n0 + n1\nt1 = n0 * n1\nt2 = n2**min(2.0, 5)\nt3 = t2 * 4.0\nt4 = t0**min(2.0, 5)\nt5 = t1**min(2.0, 5)\nt6 = t5 - t3\nt7 = math.sqrt(max(0, t6))\nt8 = t1 + t7\nt9 = t8 / 2.0\nt10 = t9 * 4.0\nt11 = t4 - t10\nt12 = math.sqrt(max(0, t11))\nt13 = t0 + t12\nt14 = t13 / 2.0\nt15 = t14 * 2.0\nanswer = t15 - t0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "can n and can \u0432 are both right circular cylinders . the radius of can n is twice the radius of can b , while the height of can n is half the height of can b . if it costs $ 4.00 to fill half of can b with a certain brand of gasoline , how much would it cost to completely fill can n with the same brand of gasoline ?", + "Output Program": [ + "n0 = 4.0\nt0 = n0 * 2.0\nt1 = 2.0**min(2.0, 5)\nt2 = t1 / 2.0\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "if the sides of a triangle are 39 cm , 36 cm and 15 cm , what is its area ?", + "Output Program": [ + "n0 = 39.0\nn1 = 36.0\nn2 = 15.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "270" + ], + "split": "train" + }, + { + "Input": "if paint costs $ 3.20 per quart , and a quart covers 1200 square feet , how much will it cost to paint the outside of a cube 10 feet on each edge ?", + "Output Program": [ + "n0 = 3.2\nn1 = 1200.0\nn2 = 10.0\nt0 = n0 / n1\nt1 = 6 * n2**2 # surface of a cube\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "1.6000000000000003" + ], + "split": "train" + }, + { + "Input": "the surface of a cube is 96 sq cm . find its volume ?", + "Output Program": [ + "import math\nn0 = 96.0\nt0 = 2.0 + 4.0\nt1 = n0 / t0\nt2 = math.sqrt(max(0, t1))\nanswer = t2**3\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "the roof of an apartment building is rectangular and its length is 4 times longer than its width . if the area of the roof is 784 feet squared , what is the difference between the length and the width of the roof ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 784.0\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * n0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "the perimeter of a square is 48 m . find the area of the square .", + "Output Program": [ + "n0 = 48.0\nt0 = n0 / 4.0\nanswer = t0**2\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "train" + }, + { + "Input": "rectangular tile each of size 25 cm by 16 cm must be laid horizontally on a rectangular floor of size 180 cm by 120 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :", + "Output Program": [ + "n0 = 25.0\nn1 = 16.0\nn2 = 180.0\nn3 = 120.0\nt0 = n2 * n3\nt1 = n0 * n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 2028 sq m , then what is the breadth of the rectangular plot ?", + "Output Program": [ + "import math\nn0 = 2028.0\nt0 = n0 / 3.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "the area of an isosceles trapezoid with sides of length 5 and bases of length 7 and 13 is ?", + "Output Program": [ + "n0 = 5.0\nn1 = 7.0\nn2 = 13.0\n\nanswer = 4.0 * (n2 + n1) / 2 # quadrilateral area\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "in a rectangular axis system , what is the area of a parallelogram with the coordinates : ( 4,4 ) , ( 7,4 ) , ( 5,9 ) , ( 8,9 ) ?", + "Output Program": [ + "n0 = 4.0\nn1 = 4.0\nn2 = 7.0\nn3 = 4.0\nn4 = 5.0\nn5 = 9.0\nn6 = 8.0\nn7 = 9.0\n\nanswer = 2.0 + 3.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "find the surface area of a 8 cm x 6 cm x 2 cm brick .", + "Output Program": [ + "n0 = 8.0\nn1 = 6.0\nn2 = 2.0\n\nanswer = 2 * (n0 * n1 + n0 * n2 + n1 * n2) # surface of a rectangular prism\nprint(answer)" + ], + "Output Answer": [ + "152" + ], + "split": "train" + }, + { + "Input": "in measuring the sides of a rectangle , one side is taken 12 % in excess and other 5 % in deficit . find the error percentage in the area calculated from these measurements .", + "Output Program": [ + "n0 = 12.0\nn1 = 5.0\nt0 = n0 * n1\nt1 = n0 - n1\nt2 = t0 / 100.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "6.4" + ], + "split": "train" + }, + { + "Input": "the percentage increase in the area of a rectangle , if each of its sides is increased by 20 %", + "Output Program": [ + "n0 = 20.0\nt0 = n0 + 100.0\nt1 = t0 / 100.0\nt2 = t1 * t1\nt3 = t2 - 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "43.99999999999999" + ], + "split": "train" + }, + { + "Input": "a rectangular lawn of dimensions 100 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?", + "Output Program": [ + "n0 = 100.0\nn1 = 60.0\nn2 = 10.0\nn3 = 3.0\nt0 = n0 + n1\nt1 = t0 - n2\nt2 = n2 * t1\nanswer = n3 * t2\nprint(answer)" + ], + "Output Answer": [ + "4500" + ], + "split": "train" + }, + { + "Input": "thin rectangular slab of potato was cut into two pieces for an osmosis lab . one piece is 50 mm greater than the other . if the original uncut slab is 600 mm , what is the length of the other piece of the potato after it is cut .", + "Output Program": [ + "n0 = 50.0\nn1 = 600.0\nt0 = n1 - n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "275" + ], + "split": "train" + }, + { + "Input": "in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 12 , 0 ) , ( 0 , - 3.5 ) , ( - 12 , 0 ) ?", + "Output Program": [ + "n0 = 0.0\nn1 = 3.5\nn2 = 12.0\nn3 = 0.0\nn4 = 0.0\nn5 = 3.5\nn6 = 12.0\nn7 = 0.0\nt0 = n2 * 2.0\nt1 = n1 * 2.0\nanswer = t0 * t1 / 2\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "the slant height of a cone is 14 cm and radius of the base is 12 cm , find the curved surface of the cone .", + "Output Program": [ + "n0 = 14.0\nn1 = 12.0\nt0 = n1 * 3.141592653589793\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "527.7875658030853" + ], + "split": "train" + }, + { + "Input": "triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 49 , what is the measure of side xy ?", + "Output Program": [ + "import math\nn0 = 49.0\nt0 = math.sqrt(max(0, n0))\nt1 = math.sqrt(max(0, 2.0))\nt2 = t0 * t1\nt3 = t2**min(2.0, 5)\nt4 = t3 + t3\nanswer = math.sqrt(max(0, t4))\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "the area of a circular field is 13.86 hectares . find the cost of fencing it at the rate of rs . 4.50 per metre .", + "Output Program": [ + "import math\nn0 = 13.86\nn1 = 4.5\nt0 = n0 / 3.141592653589793\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * 100.0\nt3 = 2 * math.pi * t2\nanswer = t3 * n1\nprint(answer)" + ], + "Output Answer": [ + "5938.804937425641" + ], + "split": "train" + }, + { + "Input": "if the sides of a triangle are 26 cm , 25 cm and 10 cm , what is its area ?", + "Output Program": [ + "n0 = 26.0\nn1 = 25.0\nn2 = 10.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "find the area of the quadrilateral of one of its diagonals is 22 cm and its off sets 9 cm and 6 cm ?", + "Output Program": [ + "n0 = 22.0\nn1 = 9.0\nn2 = 6.0\nt0 = n1 + n2\nt1 = 1.0 / 2.0\nt2 = t0 * t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "165" + ], + "split": "train" + }, + { + "Input": "find the area of a parallelogram with base 18 cm and height 10 cm ?", + "Output Program": [ + "n0 = 18.0\nn1 = 10.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "train" + }, + { + "Input": "the parameter of a square is equal to the perimeter of a rectangle of length 24 cm and breadth 16 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )", + "Output Program": [ + "import math\nn0 = 24.0\nn1 = 16.0\nt0 = 2 * (n0 + n1) # perimetere of rectangle\nt1 = t0 / 4. # square edge given perimeter\nt2 = t1 / 2.0\nt3 = 2 * math.pi * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "31.41592653589793" + ], + "split": "train" + }, + { + "Input": "12 points lie on a circle . how many cyclic quadrilaterals can be drawn by using these points ?", + "Output Program": [ + "import math\nn0 = 12.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(4.0)))\nt2 = n0 - 4.0\nt3 = math.factorial(min(15, int(t2)))\nt4 = t1 * t3\nanswer = t0 / t4\nprint(answer)" + ], + "Output Answer": [ + "495" + ], + "split": "train" + }, + { + "Input": "the radius of the circle is reduced from 5 cm to 4 cm then the % change of area .", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 4.0\nt0 = math.pi * n1**2\nt1 = math.pi * n0**2\nt2 = t0 / t1\nt3 = t2 * 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "what will be the cost of building a fence around a square plot with area equal to 25 sq ft , if the price per foot of building the fence is rs . 58 ?", + "Output Program": [ + "import math\nn0 = 25.0\nn1 = 58.0\nt0 = math.sqrt(max(0, n0))\nt1 = 4 * t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "1160" + ], + "split": "train" + }, + { + "Input": "if the length of the longest chord of a certain circle is 24 , what is the radius of that certain circle ?", + "Output Program": [ + "n0 = 24.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "rectangle a has sides a and b , and rectangle b has sides c and d . if a / c = b / d = 3 / 4 , what is the ratio of rectangle a \u2019 s area to rectangle b \u2019 s area ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nt0 = n0**min(2.0, 5)\nt1 = n1**min(2.0, 5)\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.5625" + ], + "split": "train" + }, + { + "Input": "the area of a square garden is a square feet and the perimeter is p feet . if a = 2 p + 14.25 , what is the perimeter of the garden , in feet ?", + "Output Program": [ + "n0 = 2.0\nn1 = 14.25\nt0 = n0 * n1\nt1 = t0 + 10.0\nt2 = t1 - 0.25\nanswer = t2 - 0.25\nprint(answer)" + ], + "Output Answer": [ + "38" + ], + "split": "train" + }, + { + "Input": "a rectangular tank needs to be coated with insulation . the tank has dimensions of 3 feet , 7 feet , and 2 feet . each square foot of insulation costs $ 20 . how much will it cost to cover the surface of the tank with insulation ?", + "Output Program": [ + "n0 = 3.0\nn1 = 7.0\nn2 = 2.0\nn3 = 20.0\nt0 = 2 * (n0 * n1 + n0 * n2 + n1 * n2) # surface of a rectangular prism\nanswer = n3 * t0\nprint(answer)" + ], + "Output Answer": [ + "1640" + ], + "split": "train" + }, + { + "Input": "a cube of sides 9 is first painted red and then cut into smaller cubes of side 3 . how many of the smaller cube have painted on exactly 2 sides ?", + "Output Program": [ + "n0 = 9.0\nn1 = 3.0\nn2 = 2.0\nt0 = n1 + 4.0\nt1 = n0 * n1\nt2 = n2 * 4.0\nt3 = t1 - t0\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the volume of the largest right circular cone that can be cut out of a cube of edge 7 cm is :", + "Output Program": [ + "n0 = 7.0\nt0 = n0 / 2.0\nt1 = n0 * 3.0\nt2 = t1 + 1.0\nt3 = t2 * 1.0\nt4 = t0 * t3\nt5 = t0 * t4\nt6 = n0 * t5\nanswer = t6 / t1\nprint(answer)" + ], + "Output Answer": [ + "89.83333333333333" + ], + "split": "train" + }, + { + "Input": "in an electric circuit , two resistors with resistances 8 ohms and 9 ohms are connected in parallel . in this case , if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of two resistors . what is r value ?", + "Output Program": [ + "n0 = 8.0\nn1 = 9.0\nt0 = n0 + n1\nt1 = n0 * n1\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "4.235294117647059" + ], + "split": "train" + }, + { + "Input": "the side of a square is increased by 10 % then how much % does its area increases ?", + "Output Program": [ + "n0 = 10.0\nt0 = n0 + 100.0\nt1 = 100.0**2\nt2 = t0**2\nt3 = t2 - t1\nt4 = t3 * 100.0\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "train" + }, + { + "Input": "a square of side 8 cm has been made to a rectangle by combining it with a rectangle of dimensions of length 8 cm and breadth 4 cm . what is the perimeter of the newly formed rectangle ?", + "Output Program": [ + "n0 = 8.0\nn1 = 8.0\nn2 = 4.0\nt0 = n0 + n2\nanswer = 2 * (n0 + t0) # perimetere of rectangle\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 6 m , the volume of the box ( in m 3 ) is :", + "Output Program": [ + "n0 = 48.0\nn1 = 36.0\nn2 = 6.0\nn3 = 3.0\nt0 = n2 * 2.0\nt1 = n0 - t0\nt2 = n1 - t0\nanswer = n2 * t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "5184" + ], + "split": "train" + }, + { + "Input": "the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 10 cm each . the radius of the sphere is", + "Output Program": [ + "import math\nn0 = 10.0\nt0 = n0 / 2.0\nt1 = 4.0 * 3.141592653589793\nt2 = n0 * t0\nt3 = t2 * 3.141592653589793\nt4 = t3 * 2.0\nt5 = t4 / t1\nanswer = math.sqrt(max(0, t5))\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 60 cm , find the sum of the perimeters of all the triangles .", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 3.0\nn3 = 2.0\nn4 = 1.0\nn5 = 60.0\nt0 = n5 + n5 + n5 # perimeter of a triangle\nanswer = t0 + t0\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "if the sides of a triangle are 36 cm , 34 cm and 20 cm , what is its area ?", + "Output Program": [ + "n0 = 36.0\nn1 = 34.0\nn2 = 20.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "340" + ], + "split": "train" + }, + { + "Input": "rectangle a has sides a and b , and rectangle b has sides c and d . if a / c = b / d = 4 / 5 , what is the ratio of rectangle a \u2019 s area to rectangle b \u2019 s area ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nt0 = n0**min(2.0, 5)\nt1 = n1**min(2.0, 5)\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.64" + ], + "split": "train" + }, + { + "Input": "the perimeter of one square is 24 m & that of another is 32 m . perimeter of a square whose area is equal to the sum of the areas of the 2 squares will be", + "Output Program": [ + "import math\nn0 = 24.0\nn1 = 32.0\nn2 = 2.0\nt0 = n0 / 4.0\nt1 = n1 / 4.0\nt2 = t0**2\nt3 = t1**2\nt4 = t2 + t3\nt5 = math.sqrt(max(0, t4))\nanswer = t5 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "volume of a right circular cylinder is 6 o l . if radius of cylinder is doubled , then what will be the increase in volume ?", + "Output Program": [ + "n0 = 6.0\nt0 = n0 * 10.0\nt1 = t0 * 4.0\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "train" + }, + { + "Input": "a 10 meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point ?", + "Output Program": [ + "n0 = 10.0\nn1 = 4.0\nt0 = 2.0 / n0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.4" + ], + "split": "train" + }, + { + "Input": "points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction s of the area of triangle abc is the area of triangle xyz ?", + "Output Program": [ + "n0 = 2.0\nn1 = 0.0\nn2 = 8.0\nn3 = 12.0\nn4 = 14.0\nn5 = 0.0\nn6 = 6.0\nn7 = 0.0\nn8 = 8.0\nn9 = 4.0\nn10 = 10.0\nn11 = 0.0\nt0 = 10.0 + 2.0\nt1 = 4.0**min(2.0, 5)\nt2 = t1 / 2.0\nt3 = t0**min(2.0, 5)\nt4 = t3 / 2.0\nanswer = t2 / t4\nprint(answer)" + ], + "Output Answer": [ + "0.1111111111111111" + ], + "split": "train" + }, + { + "Input": "a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . how many feet does the squirrel travels if the post is 16 feet tall and 2 feet in circumference ?", + "Output Program": [ + "n0 = 4.0\nn1 = 16.0\nn2 = 2.0\nt0 = n1 / n0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "in the rectangular coordinate system , points ( 4 , 0 ) and ( \u2013 4 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 0.0\nn2 = 4.0\nn3 = 0.0\nt0 = n0**min(2.0, 5)\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the side of a rhombus is 24 m and length of one of its diagonals is 18 m . the area of the rhombus is ?", + "Output Program": [ + "import math\nn0 = 24.0\nn1 = 18.0\nt0 = n0 * 2.0\nt1 = n1**min(2.0, 5)\nt2 = t0**min(2.0, 5)\nt3 = t2 - t1\nt4 = math.sqrt(max(0, t3))\nt5 = n1 * t4\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "400.4747183031658" + ], + "split": "train" + }, + { + "Input": "if g is the smallest positive integer such that 3150 multiplied by g is the square of an integer , then g must be", + "Output Program": [ + "n0 = 3150.0\nt0 = 2.0 + 3.0\nt1 = n0 / 2.0\nt2 = t1 / t0\nt3 = t2 / t0\nt4 = t3 / 3.0\nt5 = t4 / 3.0\nanswer = t5 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "in a triangle abc , point d is on side ab and point e is on side ac , such that bced is a trapezium . de : bc = 3 : 5 . calculate the ratio of the area of triangle ade and the trapezium bced .", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nt0 = n0**min(2.0, 5)\nt1 = n1**min(2.0, 5)\nt2 = t1 - t0\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.5625" + ], + "split": "train" + }, + { + "Input": "if radius of a circle is diminished by 10 % then its area is diminished by", + "Output Program": [ + "import math\nn0 = 10.0\nt0 = math.pi * 1.0**2\nt1 = n0 / 100.0\nt2 = 1.0 - t1\nt3 = math.pi * t2**2\nt4 = t0 - t3\nt5 = t4 / t0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "18.999999999999993" + ], + "split": "train" + }, + { + "Input": "the ratio of the areas of two squares , one having double its diagonal then the other is :", + "Output Program": [ + "t0 = 1 / 2.0\nt1 = t0 * 4.0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "find the area of the quadrilateral of one of its diagonals is 40 cm and its off sets 9 cm and 6 cm ?", + "Output Program": [ + "n0 = 40.0\nn1 = 9.0\nn2 = 6.0\nt0 = n1 + n2\nt1 = 1.0 / 2.0\nt2 = t0 * t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "50 square stone slabs of equal size were needed to cover a floor area of 72 sq . m . find the length of each stone slab ?", + "Output Program": [ + "import math\nn0 = 50.0\nn1 = 72.0\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "a certain rectangular crate measures 8 feet by 12 feet by 14 feet . a cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces . what should the radius of the tank be if it is to be of the largest possible volume ?", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 12.0\nn2 = 14.0\nt0 = n1 / 2.0\nt1 = n0 * 3.141592653589793\nt2 = math.pi * t0**2 * n0\nt3 = t2 / t1\nanswer = math.sqrt(max(0, t3))\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "an entry in an unshaded square is obtained by adding the entries connected to it from the row above ( 11 is one such number ) . write the value of n ?", + "Output Program": [ + "n0 = 11.0\nt0 = n0 * 3.0\nt1 = t0 - 3.0\nanswer = t1 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "a cube has a volume of 343 cubic feet . if a similar cube is twice as long , twice as wide , and twice as high , then the volume , in cubic feet of such cube is ?", + "Output Program": [ + "n0 = 343.0\nt0 = n0**(1 / 3)\nt1 = t0 * 2.0\nanswer = t1**3\nprint(answer)" + ], + "Output Answer": [ + "2743.999999999999" + ], + "split": "train" + }, + { + "Input": "cubes with each side one inch long are glued together to form a larger cube . the larger cube ' s face is painted with red color and the entire assembly is taken apart . 26 small cubes are found with no paints on them . how many of unit cubes have at least one face that is painted red ?", + "Output Program": [ + "n0 = 26.0\nt0 = 1.0 + 3.0\nt1 = t0 + 1.0\nt2 = t1**min(3.0, 5)\nanswer = t2 - n0\nprint(answer)" + ], + "Output Answer": [ + "99" + ], + "split": "train" + }, + { + "Input": "triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 36 , what is the measure of side xy ?", + "Output Program": [ + "import math\nn0 = 36.0\nt0 = math.sqrt(max(0, n0))\nt1 = math.sqrt(max(0, 2.0))\nt2 = t0 * t1\nt3 = t2**min(2.0, 5)\nt4 = t3 + t3\nanswer = math.sqrt(max(0, t4))\nprint(answer)" + ], + "Output Answer": [ + "12.000000000000002" + ], + "split": "train" + }, + { + "Input": "ratio between length and breath of a rectangle is 25 : 16 . the area of the rectangle is same with a square whose side is 200 . find the breadth and length of the rectangle ?", + "Output Program": [ + "import math\nn0 = 25.0\nn1 = 16.0\nn2 = 200.0\nt0 = n0 * n1\nt1 = n2**2\nt2 = t1 / t0\nt3 = math.sqrt(max(0, t2))\nt4 = n1 * t3\nt5 = n0 * t3\nt6 = t4 * 1000.0\nanswer = t6 + t5\nprint(answer)" + ], + "Output Answer": [ + "160250" + ], + "split": "train" + }, + { + "Input": "if there is one larger cube with surface area 600 and no . of smaller cubes with surface area 24 . then how many small cubes are required to make a larger cube with surface area of 600 ?", + "Output Program": [ + "import math\nn0 = 600.0\nn1 = 24.0\nn2 = 600.0\nt0 = n0 / 100.0\nt1 = n0 / t0\nt2 = n1 / t0\nt3 = math.sqrt(max(0, t1))\nt4 = math.sqrt(max(0, t2))\nt5 = t3 / t4\nanswer = t5**3\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "a circular ground whose radius is 15 metres , has a 1.2 metre - broad garden around it . what is the area of the garden in square metres ?", + "Output Program": [ + "import math\nn0 = 15.0\nn1 = 1.2\nt0 = n0 + n1\nt1 = math.pi * n0**2\nt2 = math.pi * t0**2\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "117.62122895040181" + ], + "split": "train" + }, + { + "Input": "the side of a rhombus is 26 m and length of one of its diagonals is 20 m . the area of the rhombus is ?", + "Output Program": [ + "import math\nn0 = 26.0\nn1 = 20.0\nt0 = n0 * 2.0\nt1 = n1**min(2.0, 5)\nt2 = t0**min(2.0, 5)\nt3 = t2 - t1\nt4 = math.sqrt(max(0, t3))\nt5 = n1 * t4\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "480" + ], + "split": "train" + }, + { + "Input": "the length of each side of square a is increased by 100 percent to make square b . if the length of the side of square b is increased by 75 percent to make square c , by what percent is the area of square c greater than the sum of the areas of squares a and b ?", + "Output Program": [ + "n0 = 100.0\nn1 = 75.0\nt0 = n0 / n0\nt1 = t0 + 1.0\nt2 = n1 * t1\nt3 = t1**2\nt4 = t3 + 1.0\nt5 = t2 / n0\nt6 = t1 + t5\nt7 = t6**2\nt8 = t7 - 1.0\nt9 = t8 - 4.0\nt10 = t9 / t4\nanswer = n0 * t10\nprint(answer)" + ], + "Output Answer": [ + "145" + ], + "split": "train" + }, + { + "Input": "the area of the largest circle that can be drawn inside a rectangle with sides 18 cm by 14 cm is", + "Output Program": [ + "import math\nn0 = 18.0\nn1 = 14.0\nt0 = n1 / 2.0\nanswer = math.pi * t0**2\nprint(answer)" + ], + "Output Answer": [ + "153.93804002589985" + ], + "split": "train" + }, + { + "Input": "the cost of the paint is rs . 36.50 per kg . if 1 kg of paint covers 16 squares feet , how much will it cost to paint outside of a cube having 8 feet each side ?", + "Output Program": [ + "n0 = 36.5\nn1 = 1.0\nn2 = 16.0\nn3 = 8.0\nt0 = 6 * n3**2 # surface of a cube\nt1 = t0 / n2\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "876" + ], + "split": "train" + }, + { + "Input": "find the circumference and area of radius 4 cm .", + "Output Program": [ + "import math\nn0 = 4.0\n\nanswer = math.pi * n0**2\nprint(answer)" + ], + "Output Answer": [ + "50.26548245743669" + ], + "split": "train" + }, + { + "Input": "a circular well with a diameter of 2 metres , is dug to a depth of 8 metres . what is the volume of the earth dug out ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 8.0\nt0 = n0 / n0\nanswer = math.pi * t0**2 * n1\nprint(answer)" + ], + "Output Answer": [ + "25.132741228718345" + ], + "split": "train" + }, + { + "Input": "what is the ratio between perimeters of two squares one having 7 times the diagonal then the other ?", + "Output Program": [ + "n0 = 7.0\nt0 = n0 / n0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "square a has an area of 65 square centimeters . square b has a perimeter of 16 centimeters . if square b is placed within square a and a random point is chosen within square a , what is the probability the point is not within square b ?", + "Output Program": [ + "n0 = 65.0\nn1 = 16.0\nt0 = n1 / 4.0\nt1 = t0**min(2.0, 5)\nt2 = n0 - t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.7538461538461538" + ], + "split": "train" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 560 sq . feet , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 20.0\nn1 = 560.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "76" + ], + "split": "train" + }, + { + "Input": "how many internal diagonals does a octagon ( eight sided polygon ) have ?", + "Output Program": [ + "t0 = 2.0 * 4.0\nt1 = t0 / 2.0\nt2 = t0 - 3.0\nanswer = t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the length of rectangle is thrice its breadth and its perimeter is 48 m , find the area of the rectangle ?", + "Output Program": [ + "n0 = 48.0\nt0 = 2.0 * 3.0\nt1 = 1.0 * 2.0\nt2 = t0 + t1\nt3 = n0 / t2\nt4 = t3 * 3.0\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "108" + ], + "split": "train" + }, + { + "Input": "the perimeter of a triangle is 48 cm and the in radius of the triangle is 2.5 cm . what is the area of the triangle ?", + "Output Program": [ + "n0 = 48.0\nn1 = 2.5\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "what will be the cost of house to paint which area equal to 484 sq ft , if the price per foot of building is rs . 20", + "Output Program": [ + "import math\nn0 = 484.0\nn1 = 20.0\nt0 = math.sqrt(max(0, n0))\nt1 = t0 * 4.0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "1760" + ], + "split": "train" + }, + { + "Input": "the area of sector of a circle whose radius is 12 metro and whose angle at the center is 38 \u00b0 is ?", + "Output Program": [ + "n0 = 12.0\nn1 = 38.0\nt0 = 3.0 + 4.0\nt1 = 3600.0 / 10.0\nt2 = 10.0 * 2.0\nt3 = n0**min(2.0, 5)\nt4 = t2 + 2.0\nt5 = n1 / t1\nt6 = t4 / t0\nt7 = t6 * t3\nanswer = t5 * t7\nprint(answer)" + ], + "Output Answer": [ + "47.77142857142857" + ], + "split": "train" + }, + { + "Input": "if the sides of a triangle are 65 cm , 60 cm and 25 cm , what is its area ?", + "Output Program": [ + "n0 = 65.0\nn1 = 60.0\nn2 = 25.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "750" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is three times of its width . if the length of the diagonal is 8 \u221a 10 then find the perimeter of the rectangle .", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 10.0\nt0 = n0**min(2.0, 5)\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * 3.0\nt3 = t2 + t1\nanswer = t3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "each side of a rectangular field diminished by 40 % . by how much per cent is the area of the field diminished ?", + "Output Program": [ + "n0 = 40.0\nt0 = 100.0 * 100.0\nt1 = 100.0 - n0\nt2 = t1 * t1\nt3 = t0 - t2\nt4 = t3 / t0\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "if a number is subtracted from its square we get 272 . find the number ?", + "Output Program": [ + "import math\nn0 = 272.0\nt0 = n0 * 4.0\nt1 = t0 + 1.0\nt2 = math.sqrt(max(0, t1))\nt3 = t2 + 1.0\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "the area of a circular field is 13.86 hectares . find the cost of fencing it at the rate of rs . 4.40 per metre .", + "Output Program": [ + "import math\nn0 = 13.86\nn1 = 4.4\nt0 = n0 / 3.141592653589793\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * 100.0\nt3 = 2 * math.pi * t2\nanswer = t3 * n1\nprint(answer)" + ], + "Output Answer": [ + "5806.831494371739" + ], + "split": "train" + }, + { + "Input": "the diagonals of a rhombus are 11 cm and 16 cm . find its area ?", + "Output Program": [ + "n0 = 11.0\nn1 = 16.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "88" + ], + "split": "train" + }, + { + "Input": "find the perimeter of a triangle with sides measuring 7 centimeters , 10 centimeters and 15 centimeters .", + "Output Program": [ + "n0 = 7.0\nn1 = 10.0\nn2 = 15.0\n\nanswer = n0 + n1 + n2 # perimeter of a triangle\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "two isosceles triangles have equal vertical angles and their areas are in the ratio 25 : 49 . find the ratio of their corresponding heights .", + "Output Program": [ + "import math\nn0 = 25.0\nn1 = 49.0\nt0 = math.sqrt(max(0, n0))\nt1 = math.sqrt(max(0, n1))\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.7142857142857143" + ], + "split": "train" + }, + { + "Input": "mr . loyd wants to fence his square shaped land of 150 sqft each side . if a pole is laid every 30 ft how many poles do he need ?", + "Output Program": [ + "n0 = 150.0\nn1 = 30.0\nt0 = n0 * 4.0\nt1 = t0 / 10.0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "the parameter of a square is equal to the perimeter of a rectangle of length 8 cm and breadth 6 cm . find the circumference of a semicircle whose diameter is equal to the side of the square .", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 6.0\nt0 = 2 * (n0 + n1) # perimetere of rectangle\nt1 = t0 / 4. # square edge given perimeter\nt2 = t1 / 2.0\nt3 = 2 * math.pi * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "10.995574287564276" + ], + "split": "train" + }, + { + "Input": "in a new housing development , trees are to be planted along the sidewalk of a certain street . each tree takes up one square foot of sidewalk space , and there are to be 14 feet between each tree . how many trees can be planted if the road is 151 feet long ?", + "Output Program": [ + "n0 = 14.0\nn1 = 151.0\nt0 = n0 + 1.0\nt1 = n1 - 1.0\nt2 = t1 / t0\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "what is the perimeter , in meters , of a rectangular garden 12 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide ?", + "Output Program": [ + "n0 = 12.0\nn1 = 16.0\nn2 = 12.0\nt0 = n1 * n2 # area of rectangle\nt1 = t0 / n0\nanswer = 2 * (n0 + t1) # perimetere of rectangle\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "a diagonal of a polygon is an segment between two non - adjacent vertices of the polygon . how many diagonals does a regular 45 - sided polygon have ?", + "Output Program": [ + "n0 = 45.0\nt0 = n0 - 3.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "945" + ], + "split": "train" + }, + { + "Input": "what is the maximum number t of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?", + "Output Program": [ + "n0 = 27.0\nn1 = 8.0\nn2 = 9.0\nn3 = 12.0\nt0 = n0**(1 / 3)\nt1 = 2.0 * 3.0\nt2 = n3 / t0\nt3 = t1 / t0\nt4 = n2 / t0\nt5 = t3 * t4\nanswer = t2 * t5\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "the edge of a cube is 4 a cm . find its surface ?", + "Output Program": [ + "n0 = 4.0\n\nanswer = 6 * n0**2 # surface of a cube\nprint(answer)" + ], + "Output Answer": [ + "96" + ], + "split": "train" + }, + { + "Input": "the length and breadth of a rectangle is increased by 11 % and 22 % respectively . what is the increase in the area ?", + "Output Program": [ + "n0 = 11.0\nn1 = 22.0\nt0 = n0 + 100.0\nt1 = n1 + 100.0\nt2 = 100.0 * 100.0 # area of rectangle\nt3 = t0 * t1 # area of rectangle\nt4 = t3 - t2\nt5 = t4 * 100.0\nanswer = t5 / t2\nprint(answer)" + ], + "Output Answer": [ + "35.42" + ], + "split": "train" + }, + { + "Input": "a rectangular wall is covered entirely with two kinds of decorative tiles : regular and jumbo . 1 / 3 of the tiles are jumbo tiles , which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles . if regular tiles cover 70 square feet of the wall , and no tiles overlap , what is the area of the entire wall ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 70.0\nt0 = n2 * n1\nt1 = t0 / 2.0\nt2 = n1 * t1\nanswer = n2 + t2\nprint(answer)" + ], + "Output Answer": [ + "385" + ], + "split": "train" + }, + { + "Input": "the circumferences of two circles are 132 meters and 352 meters . find the difference between the areas of the larger and the smaller circles ?", + "Output Program": [ + "import math\nn0 = 132.0\nn1 = 352.0\nt0 = 2.0 * 3.141592653589793\nt1 = n1 / t0\nt2 = n0 / t0\nt3 = math.pi * t1**2\nt4 = math.pi * t2**2\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "8473.409170212508" + ], + "split": "train" + }, + { + "Input": "if the perimeter and diagonal of a rectangle are 14 and 5 cms respectively , find its area .", + "Output Program": [ + "n0 = 14.0\nn1 = 5.0\nt0 = n0 / 2.0\nt1 = n1**min(2.0, 5)\nt2 = t0**min(2.0, 5)\nt3 = t2 - t1\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a rectangular wall is covered entirely with two kinds of decorative tiles : regular and jumbo . 1 / 3 of the tiles are jumbo tiles , which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles . if regular tiles cover 90 square feet of the wall , and no tiles overlap , what is the area of the entire wall ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 90.0\nt0 = n2 * n1\nt1 = t0 / 2.0\nt2 = n1 * t1\nanswer = n2 + t2\nprint(answer)" + ], + "Output Answer": [ + "495" + ], + "split": "train" + }, + { + "Input": "the side of a cube is 12 m , find the lateral surface area ?", + "Output Program": [ + "n0 = 12.0\nt0 = 10.0 * 4.0\nt1 = t0 + 3.0\nanswer = n0 * t1 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "516" + ], + "split": "train" + }, + { + "Input": "we have a rectangular metallic piece of paper that covers exactly the area of a cube . the length of the piece of paper is 120 inches and the width is 108 inches . what is the volume of the cube in cubic feet is 1 feet is 12 inches ?", + "Output Program": [ + "n0 = 120.0\nn1 = 108.0\nn2 = 1.0\nn3 = 12.0\nt0 = n0**(1 / 3)\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "124.93242414866094" + ], + "split": "train" + }, + { + "Input": "the volume of a cube is 1000 cc . find its surface .", + "Output Program": [ + "n0 = 1000.0\nt0 = n0**(1 / 3)\nanswer = 6 * t0**2 # surface of a cube\nprint(answer)" + ], + "Output Answer": [ + "599.9999999999998" + ], + "split": "train" + }, + { + "Input": "a circular well with a diameter of 2 meters , is dug to a depth of 14 meters . what is the volume of the earth dug out .", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 14.0\nt0 = n0 / 2.0\nanswer = math.pi * t0**2 * n1\nprint(answer)" + ], + "Output Answer": [ + "43.982297150257104" + ], + "split": "train" + }, + { + "Input": "the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 18 of the area of the field . what is the length of the field ?", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 1.0\nn2 = 18.0\nt0 = 1 / 2.0\nt1 = n0**2\nt2 = n2 * t1\nt3 = t2 / t0\nanswer = math.sqrt(max(0, t3))\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "unit size cubes are stacked inside a big rectangular box having dimensions corresponding to three consecutive multiples of 5 . choose exact number of cubes that can completely fill the box .", + "Output Program": [ + "n0 = 5.0\nt0 = n0 * 2.0\nt1 = n0 * 3.0\nt2 = 1.0**3\nt3 = n0 * t0 * t1\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "750" + ], + "split": "train" + }, + { + "Input": "what is the maximum number q of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?", + "Output Program": [ + "n0 = 27.0\nn1 = 8.0\nn2 = 9.0\nn3 = 12.0\nt0 = 2.0 * 3.0\nt1 = n2 * n3 * t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "what is the % change in the area of a rectangle when its length increases by 30 % and its width decreases by 30 % ?", + "Output Program": [ + "n0 = 30.0\nn1 = 30.0\nt0 = n0 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 58 ?", + "Output Program": [ + "import math\nn0 = 289.0\nn1 = 58.0\nt0 = math.sqrt(max(0, n0))\nt1 = 4 * t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "3944" + ], + "split": "train" + }, + { + "Input": "the ratio of male to female in a class is 2 : 3 . the career preference of the students in the class are to be represented in a circle graph . if the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one of the males and one of the females in the class ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nt0 = n0 + n1\nt1 = 1.0 / n1\nt2 = n1 / t0\nt3 = t2 * 360.0\nanswer = t1 * t3\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "the size of a flat - screen television is given as the length of the screen \u2019 s diagonal . how many square inches greater is the screen of a square 24 - inch flat - screen television than a square 17 - inch flat - screen television ?", + "Output Program": [ + "n0 = 24.0\nn1 = 17.0\nt0 = n0**min(2.0, 5)\nt1 = n1**min(2.0, 5)\nt2 = t0 / 2.0\nt3 = t1 / 2.0\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "143.5" + ], + "split": "train" + }, + { + "Input": "a rectangular tank needs to be coated with insulation . the tank has dimensions of 3 feet , 5 feet , and 2 feet . each square foot of insulation costs $ 20 . how much will it cost to cover the surface of the tank with insulation ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 2.0\nn3 = 20.0\nt0 = 2 * (n0 * n1 + n0 * n2 + n1 * n2) # surface of a rectangular prism\nanswer = n3 * t0\nprint(answer)" + ], + "Output Answer": [ + "1240" + ], + "split": "train" + }, + { + "Input": "a semicircular cubicle has a radius of 14 . what is the approximate perimeter of the cubicle ?", + "Output Program": [ + "n0 = 14.0\nt0 = n0 * 3.141592653589793\nt1 = n0 * 2.0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "71.9822971502571" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular field is 7 / 5 its width . if the perimeter of the field is 240 meters , what is the width of the field ?", + "Output Program": [ + "n0 = 7.0\nn1 = 5.0\nn2 = 240.0\nt0 = n0 / n1\nt1 = t0 + t0\nt2 = t1 + 2.0\nanswer = n2 / t2\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "rectangular tile each of size 45 cm by 50 cm must be laid horizontally on a rectangular floor of size 250 cm by 180 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :", + "Output Program": [ + "n0 = 45.0\nn1 = 50.0\nn2 = 250.0\nn3 = 180.0\nt0 = n2 * n3\nt1 = n0 * n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a water tank , having the shape of a rectangular prism of base 100 square centimeters , is being filled at the rate of 1 liter per minute . find the rate at which the height of the water in the water tank increases . express your answer in centimeters per minute .", + "Output Program": [ + "n0 = 100.0\nn1 = 1.0\n\nanswer = 1000.0 / n0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the roof of an apartment building is rectangular and its length is 3 times longer than its width . if the area of the roof is 675 feet squared , what is the difference between the length and the width of the roof ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 675.0\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * n0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "in measuring the sides of a rectangle , one side is taken 5 % in excess , and the other 4 % in deficit . find the error percent in the area calculated from these measurements .", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nt0 = n0 * n1\nt1 = n0 - n1\nt2 = t0 / 100.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.8" + ], + "split": "train" + }, + { + "Input": "what is the total surface area in square meters of a rectangular solid whose length is 5 meters , width is 4 meters , and depth is 1 meters ?", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 1.0\n\nanswer = 2 * (n0 * n1 + n0 * n2 + n1 * n2) # surface of a rectangular prism\nprint(answer)" + ], + "Output Answer": [ + "58" + ], + "split": "train" + }, + { + "Input": "a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many v cubes are painted on only 2 faces ?", + "Output Program": [ + "n0 = 27.0\nn1 = 2.0\nt0 = 1.0 / 3.0\nt1 = n0**min(t0, 5)\nanswer = t1 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the perimeter of a triangle is 28 cm and the inradius of the triangle is 2.0 cm . what is the area of the triangle ?", + "Output Program": [ + "n0 = 28.0\nn1 = 2.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "the area of a triangle will be when a = 1 m , b = 2 m , c = 7 m , a , b , c being lengths of respective sides ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 7.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 11 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?", + "Output Program": [ + "import math\nn0 = 11.0\nn1 = 1200.0\nn2 = 2.0\nn3 = 30.0\nt0 = n1 / n3\nt1 = n3**min(n2, 5)\nt2 = n3 + t0\nt3 = t0**min(n2, 5)\nt4 = t1 + t3\nt5 = math.sqrt(max(0, t4))\nt6 = t2 + t5\nanswer = n0 * t6\nprint(answer)" + ], + "Output Answer": [ + "1320" + ], + "split": "train" + }, + { + "Input": "a rectangular cube has sides measuring 3 inches long by 2 inches wide by 0.5 inches high . if the surface area of the rectangle is the same as a cube , what do the sides / walls of the cube measure ? round to the nearest whole number .", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 2.0\nn2 = 0.5\nt0 = 2.0 * 3.0\nt1 = 2 * (n0 * n1 + n0 * n2 + n1 * n2) # surface of a rectangular prism\nt2 = t1 / t0\nanswer = math.floor(t2)\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "if the sides of a triangle are 30 cm , 26 cm and 10 cm , what is its area ?", + "Output Program": [ + "n0 = 30.0\nn1 = 26.0\nn2 = 10.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "130" + ], + "split": "train" + }, + { + "Input": "the base of a triangular field is three times its altitude . if the cost of cultivating the field at rs . 24.68 per hectare be rs . 333.18 , find its base and height .", + "Output Program": [ + "n0 = 24.68\nn1 = 333.18\nt0 = n1 / n0\nt1 = 3.0 / 2.0\nt2 = t0 * 1000.0\nt3 = t2 / 3.0\nt4 = t3 / 10.0\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "the perimeter of a triangle is 39 cm and the inradius of the triangle is 1.5 cm . what is the area of the triangle ?", + "Output Program": [ + "n0 = 39.0\nn1 = 1.5\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "29.25" + ], + "split": "train" + }, + { + "Input": "a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 15 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?", + "Output Program": [ + "import math\nn0 = 15.0\nn1 = 1200.0\nn2 = 2.0\nn3 = 30.0\nt0 = n1 / n3\nt1 = n3**min(2.0, 5)\nt2 = n3 + t0\nt3 = t0**min(2.0, 5)\nt4 = t1 + t3\nt5 = math.sqrt(max(0, t4))\nt6 = t2 + t5\nanswer = n0 * t6\nprint(answer)" + ], + "Output Answer": [ + "1800" + ], + "split": "train" + }, + { + "Input": "the diagonals of a rhombus are 12 cm and 15 cm . find its area ?", + "Output Program": [ + "n0 = 12.0\nn1 = 15.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "in a circle with a radius of 6 , what is the area of the biggest rectangle that can be cut out of this circle ?", + "Output Program": [ + "import math\nn0 = 6.0\nt0 = n0 * 2.0\nt1 = t0**min(2.0, 5)\nt2 = t1 / 2.0\nt3 = math.sqrt(max(0, t2))\nanswer = t3**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "71.99999999999999" + ], + "split": "train" + }, + { + "Input": "what is the % change in the area of a rectangle when its length increases by 10 % and its width decreases by 10 % ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nt0 = n0 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 3 per metre approximately", + "Output Program": [ + "import math\nn0 = 17.56\nn1 = 3.0\nt0 = n0 / 3.141592653589793\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * 100.0\nt3 = 2 * math.pi * t2\nanswer = t3 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "4456.443887106987" + ], + "split": "train" + }, + { + "Input": "the area of an isosceles trapezoid with sides of length 5 and bases of length 8 and 14 is ?", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 14.0\n\nanswer = 4.0 * (n2 + n1) / 2 # quadrilateral area\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "the radius of a circle is increased by 1 % . find how much % does its area increases ?", + "Output Program": [ + "n0 = 1.0\nt0 = 100.0 * 2.0\nt1 = n0 + t0\nanswer = t1 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "2.01" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular plot is 10 mtr more than its width . the cost of fencing the plot along its perimeter at the rate of rs . 6.5 mtr is rs . 1950 . the perimeter of the plot is ?", + "Output Program": [ + "n0 = 10.0\nn1 = 6.5\nn2 = 1950.0\nt0 = n2 / n1\nt1 = t0 / 2.0\nt2 = t1 - 10.0\nt3 = t2 / 2.0\nt4 = t3 + 10.0\nt5 = t4 + t3\nanswer = t5 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "a circular ground whose diameter is 34 metres , has a 2 metre - broad garden around it . what is the area of the garden in square metres ?", + "Output Program": [ + "import math\nn0 = 34.0\nn1 = 2.0\nt0 = n0 / 2.0\nt1 = n1 + t0\nt2 = math.pi * t0**2\nt3 = math.pi * t1**2\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "226.19467105846502" + ], + "split": "train" + }, + { + "Input": "the sides of a square region , measured to the nearest centimeter , are 7 centimeters long . the least possible value of the actual area of the square region is", + "Output Program": [ + "n0 = 7.0\nt0 = n0 - 0.25\nt1 = t0 - 0.25\nanswer = t1**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "42.25" + ], + "split": "train" + }, + { + "Input": "frank the fencemaker needs to fence in a rectangular yard . he fences in the entire yard , except for one full side of the yard , which equals 40 feet . the yard has an area of 480 square feet . how many feet offence does frank use ?", + "Output Program": [ + "n0 = 40.0\nn1 = 480.0\nt0 = n1 / n0\nt1 = t0 + t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "if the height of a right cone c is 3 and the diameter of the base of c is 8 , what is the distance from the apex of c to any point on the circumference of the base of c ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 8.0\nt0 = n1 / 2.0\nt1 = n0**min(2.0, 5)\nt2 = t0**min(2.0, 5)\nt3 = t2 + t1\nanswer = math.sqrt(max(0, t3))\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if the difference between the length and breadth of a rectangle is 23 m and its perimeter is 246 m , what is its area ?", + "Output Program": [ + "n0 = 23.0\nn1 = 246.0\nt0 = n0 * 2.0\nt1 = n1 - t0\nt2 = t1 / 4.0\nt3 = n0 + t2\nanswer = t3 * t2 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "3650" + ], + "split": "train" + }, + { + "Input": "perimeter of an equilateral and isosceles is 45 and 40 respectively . at least one of the sides of isosceles is equal to the equilateral . what ' s the base of isosceles triangle ?", + "Output Program": [ + "n0 = 45.0\nn1 = 40.0\nt0 = n0 / 3.0\nt1 = t0 * 2.0\nanswer = n1 - t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the volume of a cube is 1728 cc . find its surface ?", + "Output Program": [ + "n0 = 1728.0\nt0 = n0**(1 / 3)\nanswer = 6 * t0**2 # surface of a cube\nprint(answer)" + ], + "Output Answer": [ + "863.9999999999997" + ], + "split": "train" + }, + { + "Input": "two isosceles triangles have equal vertical angles and their areas are in the ratio 4 : 9 . find the ratio of their corresponding heights .", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 9.0\nt0 = math.sqrt(max(0, 4.0))\nt1 = math.sqrt(max(0, n1))\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666666" + ], + "split": "train" + }, + { + "Input": "a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is :", + "Output Program": [ + "n0 = 48.0\nn1 = 36.0\nn2 = 8.0\nn3 = 3.0\nt0 = n2 * 2.0\nt1 = n0 - t0\nt2 = n1 - t0\nanswer = n2 * t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "5120" + ], + "split": "train" + }, + { + "Input": "the diagonals of a rhombus are 12 cm and 20 cm . find its area ?", + "Output Program": [ + "n0 = 12.0\nn1 = 20.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 80 cm , find the sum of the perimeters of all the triangles .", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 3.0\nn3 = 2.0\nn4 = 1.0\nn5 = 80.0\nt0 = n5 + n5 + n5 # perimeter of a triangle\nanswer = t0 + t0\nprint(answer)" + ], + "Output Answer": [ + "480" + ], + "split": "train" + }, + { + "Input": "a small , rectangular park has a perimeter of 560 feet and a diagonal measurement of 300 feet . what is its area , in square feet ?", + "Output Program": [ + "n0 = 560.0\nn1 = 300.0\nt0 = 2.0 + 3.0\nt1 = n1 / t0\nt2 = t1 * 3.0\nt3 = t1 * 4.0\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "43200" + ], + "split": "train" + }, + { + "Input": "the area of the largest circle that can be drawn inside a square of side 70 cm in length is :", + "Output Program": [ + "import math\nn0 = 70.0\nt0 = n0 / 2.0\nanswer = math.pi * t0**2\nprint(answer)" + ], + "Output Answer": [ + "3848.4510006474966" + ], + "split": "train" + }, + { + "Input": "what is the ratio e of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled ?", + "Output Program": [ + "t0 = 1.0 * 1.0\nt1 = 2.0 * 3.0\nt2 = 1.0 * 2.0\nt3 = t0 * t1\nt4 = t0 * 2.0\nt5 = t2 * 4.0\nt6 = t4 + t5\nanswer = t3 / t6\nprint(answer)" + ], + "Output Answer": [ + "0.6" + ], + "split": "train" + }, + { + "Input": "the roof of an apartment building is rectangular and its length is 7 times longer than its width . if the area of the roof is 847 feet squared , what is the difference between the length and the width of the roof ?", + "Output Program": [ + "import math\nn0 = 7.0\nn1 = 847.0\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * n0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "66" + ], + "split": "train" + }, + { + "Input": "the circumferences of two circles are 660 meters and 704 meters . find the difference between the areas of the larger and the smaller circles ?", + "Output Program": [ + "import math\nn0 = 660.0\nn1 = 704.0\nt0 = 2.0 * 3.141592653589793\nt1 = n1 / t0\nt2 = n0 / t0\nt3 = math.pi * t1**2\nt4 = math.pi * t2**2\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "4775.921532301596" + ], + "split": "train" + }, + { + "Input": "if a rectangular billboard has an area of 91 square feet and a perimeter of 40 feet , what is the length of each of the shorter sides ?", + "Output Program": [ + "import math\nn0 = 91.0\nn1 = 40.0\nt0 = n1 / 2.0\nt1 = n0 * 4.0\nt2 = t0**min(2.0, 5)\nt3 = t2 - t1\nt4 = math.sqrt(max(0, t3))\nt5 = t0 - t4\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 5 cm and 4 cm ?", + "Output Program": [ + "n0 = 20.0\nn1 = 5.0\nn2 = 4.0\nt0 = n1 + n2\nt1 = 1.0 / 2.0\nt2 = t0 * t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "a certain rectangular crate measures 20 feet by 20 feet by 20 feet . a cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces . what should the radius of the tank be if it is to be of the largest possible volume ?", + "Output Program": [ + "import math\nn0 = 20.0\nn1 = 20.0\nn2 = 20.0\nt0 = n1 / 2.0\nt1 = n0 * 3.141592653589793\nt2 = math.pi * t0**2 * n0\nt3 = t2 / t1\nanswer = math.sqrt(max(0, t3))\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "if the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm , a square with the same area as the original rectangle would result . find the perimeter of the original rectangle .", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nt0 = n0 + n1\nt1 = n0 * n1\nt2 = n1 * t0\nt3 = t2 - t1\nt4 = t0 + t3\nt5 = t4 + t3\nanswer = t5 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "the area of sector of a circle whose radius is 12 metro and whose angle at the center is 40 \u00b0 is ?", + "Output Program": [ + "n0 = 12.0\nn1 = 40.0\nt0 = 3.0 + 4.0\nt1 = 3600.0 / 10.0\nt2 = 10.0 * 2.0\nt3 = n0**min(2.0, 5)\nt4 = t2 + 2.0\nt5 = n1 / t1\nt6 = t4 / t0\nt7 = t6 * t3\nanswer = t5 * t7\nprint(answer)" + ], + "Output Answer": [ + "50.28571428571428" + ], + "split": "train" + }, + { + "Input": "the diagonals of a rhombus are 16 cm and 20 cm . find its area ?", + "Output Program": [ + "n0 = 16.0\nn1 = 20.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "160" + ], + "split": "train" + }, + { + "Input": "in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 5.5 ) , ( 8 , 0 ) , ( 0 , - 5.5 ) , ( - 8 , 0 ) ?", + "Output Program": [ + "n0 = 0.0\nn1 = 5.5\nn2 = 8.0\nn3 = 0.0\nn4 = 0.0\nn5 = 5.5\nn6 = 8.0\nn7 = 0.0\nt0 = n2 * 2.0\nt1 = n1 * 2.0\nanswer = t0 * t1 / 2\nprint(answer)" + ], + "Output Answer": [ + "88" + ], + "split": "train" + }, + { + "Input": "the base of a right triangle is 8 and hypotenuse is 10 . its area is ?", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 10.0\nt0 = n1 * n1\nt1 = n0 * n0\nt2 = t0 - t1\nt3 = math.sqrt(max(0, t2))\nt4 = n0 * t3\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "square a has an area of 81 square centimeters . square b has a perimeter of 32 centimeters . if square b is placed within square a and a random point is chosen within square a , what is the probability the point is not within square b ?", + "Output Program": [ + "n0 = 81.0\nn1 = 32.0\nt0 = n1 / 4.0\nt1 = t0**min(2.0, 5)\nt2 = n0 - t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.20987654320987653" + ], + "split": "train" + }, + { + "Input": "the area of a rectangular plot is 24 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?", + "Output Program": [ + "n0 = 24.0\nn1 = 10.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "a rectangular grass field is 75 m * 40 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?", + "Output Program": [ + "n0 = 75.0\nn1 = 40.0\nn2 = 2.5\nn3 = 2.0\nt0 = n2 * 2.0\nt1 = n0 * n1 # area of rectangle\nt2 = n0 + t0\nt3 = n1 + t0\nt4 = t2 * t3 # area of rectangle\nt5 = t4 - t1\nanswer = n3 * t5\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "train" + }, + { + "Input": "the mass of 1 cubic meter of a substance is 100 kg under certain conditions . what is the volume in cubic centimeters of 1 gram of this substance under these conditions ? ( 1 kg = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )", + "Output Program": [ + "n0 = 1.0\nn1 = 100.0\nn2 = 1.0\nn3 = 1.0\nn4 = 1000.0\nn5 = 1.0\nn6 = 1.0\nn7 = 0.0\nt0 = n4 * n4\nt1 = n1 * n4\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "a cubical block of metal weighs 3 pounds . how much will another cube of the same metal weigh if its sides are twice as long ?", + "Output Program": [ + "n0 = 3.0\nt0 = 2.0 * 4.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "there is a rectangular prism made of 1 in cubes that has been covered in tin foil . there are exactly 128 cubes that are not touching any tin foil on any of their sides . if the width of the figure created by these 128 cubes is twice the length and twice the height , what is the p measure in inches of the width of the foil covered prism ?", + "Output Program": [ + "n0 = 1.0\nn1 = 128.0\nn2 = 128.0\nt0 = 1 / 3.0\nt1 = n0 * 2.0\nt2 = n0 * t1\nt3 = n1 / t2\nt4 = t3**min(t0, 5)\nt5 = t1 * t4\nanswer = t5 + t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "a regular 10 sided area is inscribed in a circle . if a and b are adjacent vertices of the pentagon and o is the center of the circle , what is the value of \u2220 oab ?", + "Output Program": [ + "n0 = 10.0\nt0 = 360.0 / n0\nt1 = 180.0 - t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "the monthly rent of a shop of dimension 20 feet \u00d7 15 feet is rs . 3600 . what is the annual rent per square foot of the shop ?", + "Output Program": [ + "n0 = 20.0\nn1 = 15.0\nn2 = 3600.0\nt0 = 10.0 + 2.0\nt1 = n0 * n1 # area of rectangle\nt2 = n2 / t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "train" + }, + { + "Input": "a circular well with a diameter of 2 metres , is dug to a depth of 14 metres . what is the volume of the earth dug out ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 14.0\nt0 = n0 / n0\nanswer = math.pi * t0**2 * n1\nprint(answer)" + ], + "Output Answer": [ + "43.982297150257104" + ], + "split": "train" + }, + { + "Input": "a rectangle having length 140 cm and width 40 cm . if the length of the rectangle is increased by thirty percent then how much percent the breadth should be decreased so as to maintain the same area .", + "Output Program": [ + "n0 = 140.0\nn1 = 40.0\nt0 = n0 * n1\nt1 = 10.0 * 3.0\nt2 = n0 * t1\nt3 = t2 / 100.0\nt4 = n0 + t3\nt5 = t0 / t4\nt6 = t5 / n1\nt7 = t6 + 1.0\nanswer = t7 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "17.692307692307693" + ], + "split": "train" + }, + { + "Input": "the cost of painting the whole surface area of a cube at the rate of 13 paise per sq . cm is rs . 343.98 . then the volume of the cube is", + "Output Program": [ + "import math\nn0 = 13.0\nn1 = 343.98\nt0 = n0 / 100.0\nt1 = 2.0 * 3.0\nt2 = n1 / t0\nt3 = t2 / t1\nt4 = math.sqrt(max(0, t3))\nanswer = t4**3\nprint(answer)" + ], + "Output Answer": [ + "9261" + ], + "split": "train" + }, + { + "Input": "a circular grass lawn of 35 metres in radius has a path 7 metres wide running around it on the outside . find the area of path .", + "Output Program": [ + "import math\nn0 = 35.0\nn1 = 7.0\nt0 = n0 + n1\nt1 = math.pi * n0**2\nt2 = math.pi * t0**2\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "1693.3184402848983" + ], + "split": "train" + }, + { + "Input": "a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 3 m , the volume of the box ( in m 3 ) is :", + "Output Program": [ + "n0 = 48.0\nn1 = 36.0\nn2 = 3.0\nn3 = 3.0\nt0 = n2 * 2.0\nt1 = n0 - t0\nt2 = n1 - t0\nanswer = n2 * t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "3780" + ], + "split": "train" + }, + { + "Input": "susan made a block with small cubes of 8 cubic cm volume to make a block , 3 small cubes long , 9 small cubes wide and 5 small cubes deep . she realizes that she has used more small cubes than she really needed . she realized that she could have glued a fewer number of cubes together to lock like a block with same dimensions , if it were made hollow . what is the minimum number of cubes that she needs to make the block ?", + "Output Program": [ + "n0 = 8.0\nn1 = 3.0\nn2 = 9.0\nn3 = 5.0\nt0 = 3.0 + 4.0\nt1 = n2 * 1.0\nt2 = n3 * t1\nt3 = t0 * 3.0\nt4 = t2 - t3\nt5 = t2 + t4\nanswer = t5 + t2\nprint(answer)" + ], + "Output Answer": [ + "114" + ], + "split": "train" + }, + { + "Input": "which is the smallest no which divides 2880 and gives a perfect square ?", + "Output Program": [ + "n0 = 2880.0\nt0 = n0 / 4.0\nt1 = t0 / 3.0\nt2 = t1 / 4.0\nt3 = t2 / 3.0\nt4 = t3 / 2.0\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "cubes with each side one inch long are glued together to form a larger cube . the larger cube ' s face is painted with red color and the entire assembly is taken apart . 25 small cubes are found with no paints on them . how many of unit cubes have at least one face that is painted red ?", + "Output Program": [ + "n0 = 25.0\nt0 = 1.0 + 3.0\nt1 = t0 + 1.0\nt2 = t1**min(3.0, 5)\nanswer = t2 - n0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "a rectangle a has an area of 30 square centimeters . square b has a perimeter of 16 centimeters . if square b is placed within square a and a random point is chosen within square a , what is the probability the point is not within square b ?", + "Output Program": [ + "n0 = 30.0\nn1 = 16.0\nt0 = n1 / 4. # square edge given perimeter\nt1 = t0**2\nt2 = n0 - t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.4666666666666667" + ], + "split": "train" + }, + { + "Input": "how many diagonals does a polygon with 19 sides have , if one of its vertices does not connect to any diagonal ?", + "Output Program": [ + "n0 = 19.0\nt0 = n0 - 1.0\nt1 = t0 - 3.0\nt2 = t0 * t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "135" + ], + "split": "train" + }, + { + "Input": "the diagonal of a square is 40 m . the area of the square is :", + "Output Program": [ + "n0 = 40.0\nt0 = n0**min(2.0, 5)\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is five times of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 16 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 11 units ?", + "Output Program": [ + "import math\nn0 = 16.0\nn1 = 11.0\nt0 = 2.0 + 3.0\nt1 = math.sqrt(max(0, n0))\nt2 = t0 * t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "220" + ], + "split": "train" + }, + { + "Input": "a wire can be bent in the form of a circle of radius 56 cm . if it is bent in the form of a square , then its area will be ?", + "Output Program": [ + "import math\nn0 = 56.0\nt0 = 2 * math.pi * n0\nt1 = t0 / 4.0\nanswer = t1**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "7737.769850454057" + ], + "split": "train" + }, + { + "Input": "a rectangular courtyard , the sides of which are in the ratio of 4 : 3 , cost rs . 600 for paving at 50 p per m 2 ; find the length of the diagonal of the courtyard ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 3.0\nn2 = 600.0\nn3 = 50.0\nn4 = 2.0\nt0 = 2.0 + 3.0\nt1 = n3 / 100.0\nt2 = n0 * n1\nt3 = n2 / t1\nt4 = t3 / t2\nt5 = math.sqrt(max(0, t4))\nt6 = n0 * t5\nt7 = n1 * t5\nt8 = t6**min(n4, 5)\nt9 = t7**min(n4, 5)\nt10 = t8 + t9\nt11 = math.sqrt(max(0, t10))\nanswer = t11 - t0\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "if the area of a circle decreases by 42 % , then the radius of a circle decreases by", + "Output Program": [ + "import math\nn0 = 42.0\nt0 = 100.0 - n0\nt1 = t0 / 100.0\nt2 = math.sqrt(max(0, t1))\nt3 = 1.0 - t2\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "23.84226894136092" + ], + "split": "train" + }, + { + "Input": "a rectangular parking space is marked out by painting three of its sides . if the length of the unpainted side is 9 feet , and the sum of the lengths of the painted sides is 37 feet , find out the area of the parking space in square feet ?", + "Output Program": [ + "n0 = 9.0\nn1 = 37.0\nt0 = n1 + n1\nt1 = n1 + t0\nt2 = t1 + 10.0\nanswer = t2 + 4.0\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "in measuring the sides of a rectangle , one side is taken 5 % in excess , and the other 4 % in deficit . find the error percent in the error percent in the area calculated from these measurements .", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nt0 = n0 * n1\nt1 = n0 - n1\nt2 = t0 / 100.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.8" + ], + "split": "train" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 80 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 80.0\nn1 = 680.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "97" + ], + "split": "train" + }, + { + "Input": "a rope can make 70 rounds of the circumference of a cylinder whose radius of the base is 14 cm . how many times can it go round a cylinder having radius 20 cm ?", + "Output Program": [ + "import math\nn0 = 70.0\nn1 = 14.0\nn2 = 20.0\nt0 = 2 * math.pi * n1\nt1 = 2 * math.pi * n2\nt2 = n0 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "train" + }, + { + "Input": "the circumferences of two circles are 264 meters and 352 meters . find the difference between the areas of the larger and the smaller circles ?", + "Output Program": [ + "import math\nn0 = 264.0\nn1 = 352.0\nt0 = 2.0 * 3.141592653589793\nt1 = n1 / t0\nt2 = n0 / t0\nt3 = math.pi * t1**2\nt4 = math.pi * t2**2\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "4313.735577562732" + ], + "split": "train" + }, + { + "Input": "the rhombus ( afce ) is inscribed in rectangle ( abcd ) . the length of bf = de . if the rectangle has a width of 20 yards and a length of 25 yards , what would be the total length ( the perimeter ) of a fence along the sides defined by afce ?", + "Output Program": [ + "n0 = 20.0\nn1 = 25.0\nt0 = n1 * 2.0\nt1 = n1**min(2.0, 5)\nt2 = n0**min(2.0, 5)\nt3 = t1 - t2\nt4 = t3 / t0\nt5 = n1 - t4\nanswer = t5 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "82" + ], + "split": "train" + }, + { + "Input": "a rectangular lawn of dimensions 110 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?", + "Output Program": [ + "n0 = 110.0\nn1 = 60.0\nn2 = 10.0\nn3 = 3.0\nt0 = n0 + n1\nt1 = t0 - n2\nt2 = n2 * t1\nanswer = n3 * t2\nprint(answer)" + ], + "Output Answer": [ + "4800" + ], + "split": "train" + }, + { + "Input": "a cube of edge 5 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 10 cm * 5 cm , find the rise in water level ?", + "Output Program": [ + "n0 = 5.0\nn1 = 10.0\nn2 = 5.0\nt0 = n1 * n2\nt1 = n0**3\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "2.5" + ], + "split": "train" + }, + { + "Input": "question : a sporting good store sells one type of baseball bat and one type of baseball . the cost for 2 bats and 4 balls is $ 180 . the cost for 1 bat and 6 balls is $ 190 , as well . if someone were to buy an equal number of bats and balls , at most how many bats can he purchase if he has a budget of $ 195 for the purchase ? options :", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 180.0\nn3 = 1.0\nn4 = 6.0\nn5 = 190.0\nn6 = 195.0\nt0 = -n0\nt1 = n5 * t0\nt2 = n4 * t0\nt3 = n2 + t1\nt4 = n1 + t2\nt5 = t3 / t4\nt6 = n4 * t5\nt7 = n5 - t6\nt8 = t5 + t7\nanswer = n6 / t8\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the cost of the paint is rs . 36.50 per kg . if 1 kg of paint covers 16 sq . ft , how much will it cost to paint outside of a cube having 8 feet each side", + "Output Program": [ + "n0 = 36.5\nn1 = 1.0\nn2 = 16.0\nn3 = 8.0\nt0 = 6 * n3**2 # surface of a cube\nt1 = t0 / n2\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "876" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1225 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?", + "Output Program": [ + "import math\nn0 = 1225.0\nn1 = 10.0\nt0 = 10.0 / 2.0\nt1 = math.sqrt(max(0, n0))\nt2 = t1 / t0\nt3 = t2 * 2.0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "train" + }, + { + "Input": "a crate measures 2 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still fit in the crate ?", + "Output Program": [ + "n0 = 2.0\nn1 = 8.0\nn2 = 12.0\nt0 = n1 * n2\nt1 = n0 * t0\nt2 = t1 / n2\nanswer = t2 / n1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the 4 walls of the room at rs . 3 per square feet if there is one door of dimensions 6 feet * 3 feet and 3 windows of dimensions 4 feet * 3 feet each ?", + "Output Program": [ + "n0 = 25.0\nn1 = 15.0\nn2 = 12.0\nn3 = 4.0\nn4 = 3.0\nn5 = 6.0\nn6 = 3.0\nn7 = 3.0\nn8 = 4.0\nn9 = 3.0\nt0 = n0 * n2\nt1 = n1 * n2\nt2 = n3 * n4\nt3 = n4 * n5\nt4 = t0 + t1\nt5 = n4 * t2\nt6 = t5 + t3\nt7 = t4 * 2.0\nt8 = t7 - t6\nanswer = n4 * t8\nprint(answer)" + ], + "Output Answer": [ + "2718" + ], + "split": "train" + }, + { + "Input": "area of square with side x is equal to the area of a triangle with base x . the altitude of the triangle is", + "Output Program": [ + "t0 = 1.0**min(2.0, 5)\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "a rectangular garden is 12 m by 5 m , what is its area ?", + "Output Program": [ + "n0 = 12.0\nn1 = 5.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 3 feet . how many feet does the squirrel travels if the post is 27 feet tall and 3 feet in circumference ?", + "Output Program": [ + "n0 = 3.0\nn1 = 27.0\nn2 = 3.0\nt0 = n1 / n0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "the perimeter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )", + "Output Program": [ + "import math\nn0 = 18.0\nn1 = 14.0\nt0 = n0 + n1\nt1 = t0 * 2.0\nt2 = t1 / 4.0\nt3 = t2 / 2.0\nt4 = 2 * math.pi * t3\nt5 = t4 / 2.0\nanswer = math.floor(t5)\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "if radius of a circle is reduced by 10 % , then how much % of its area will be reduced ?", + "Output Program": [ + "n0 = 10.0\nt0 = 100.0 - n0\nt1 = t0 / 100.0\nt2 = t1**min(2.0, 5)\nt3 = 1.0 - t2\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "18.999999999999993" + ], + "split": "train" + }, + { + "Input": "the area of a square field is a square feet and the perimeter is p feet . if 6 a = 6 ( 2 p + 9 ) , what is the perimeter of the field , in feet ? ( here a = a ^ 2 )", + "Output Program": [ + "n0 = 6.0\nn1 = 6.0\nn2 = 2.0\nn3 = 9.0\nn4 = 2.0\n\nanswer = n3 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "in a company of 148 employees , 92 are females . a total of 78 employees have advanced degrees and the rest have a college degree only . if 31 employees are males with college degree only , how many employees are females with advanced degrees ?", + "Output Program": [ + "n0 = 148.0\nn1 = 92.0\nn2 = 78.0\nn3 = 31.0\nt0 = n0 - n1\nt1 = t0 - n3\nanswer = n2 - t1\nprint(answer)" + ], + "Output Answer": [ + "53" + ], + "split": "train" + }, + { + "Input": "find the area of a parallelogram with base 28 cm and height 32 cm .", + "Output Program": [ + "n0 = 28.0\nn1 = 32.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "896" + ], + "split": "train" + }, + { + "Input": "triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 25 , what is the measure of side xy ?", + "Output Program": [ + "import math\nn0 = 25.0\nt0 = math.sqrt(max(0, n0))\nt1 = math.sqrt(max(0, 2.0))\nt2 = t0 * t1\nt3 = t2**min(2.0, 5)\nt4 = t3 + t3\nanswer = math.sqrt(max(0, t4))\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the area of rhombus is 150 cm square . the length of one of the its diagonals is 10 cm . the length of the other diagonal is :", + "Output Program": [ + "n0 = 150.0\nn1 = 10.0\nt0 = n0 * 2.0\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "if the radius of a circle decreased by 50 % its area is decreased by :", + "Output Program": [ + "n0 = 50.0\nt0 = n0 / 100.0\nt1 = t0**min(2.0, 5)\nt2 = t1 * 100.0\nanswer = 100.0 - t2\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "the mass of 1 cubic meter of a substance is 500 kg under certain conditions . what is the volume in cubic centimeters of 1 gram of this substance under these conditions ? ( 1 kg = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )", + "Output Program": [ + "n0 = 1.0\nn1 = 500.0\nn2 = 1.0\nn3 = 1.0\nn4 = 1000.0\nn5 = 1.0\nn6 = 1.0\nn7 = 0.0\nt0 = n4 * n4\nt1 = n1 * n4\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the water level in a rectangular swimming pool measuring 50 feet by 25 feet is to be lowered by 6 inches . how many gallons of water must be removed ? ( 1 cu ft = 7.5 gallons )", + "Output Program": [ + "n0 = 50.0\nn1 = 25.0\nn2 = 6.0\nn3 = 1.0\nn4 = 7.5\nt0 = 10.0 + 2.0\nt1 = n2 / t0\nt2 = n0 * n1 * t1\nanswer = n4 * t2\nprint(answer)" + ], + "Output Answer": [ + "4687.5" + ], + "split": "train" + }, + { + "Input": "an equilateral triangle and three squares are combined as shown above , forming a shape of area 48 + 4 \u221a 3 . what is the perimeter of the shape formed by the triangle and squares ?", + "Output Program": [ + "n0 = 48.0\nn1 = 4.0\nn2 = 3.0\nt0 = n2**min(2.0, 5)\nanswer = n1 * t0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "an error 2 % in excess ismade while measuring the side ofa square . the % of error in the calculated area of the square is ?", + "Output Program": [ + "n0 = 2.0\nt0 = n0 + 100.0\nt1 = 100.0 * 100.0\nt2 = t0 * t0\nt3 = t2 - t1\nanswer = t3 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "4.04" + ], + "split": "train" + }, + { + "Input": "the area of a triangle is with base 3 m and height 4 m ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a cube has a volume of 64 cubic feet . if a similar cube is twice as long , twice as wide , and twice as high , then the volume , in cubic feet of such cube is ?", + "Output Program": [ + "n0 = 64.0\nt0 = n0**(1 / 3)\nt1 = t0 * 2.0\nanswer = t1**3\nprint(answer)" + ], + "Output Answer": [ + "511.99999999999983" + ], + "split": "train" + }, + { + "Input": "a circular well with a diameter of 6 metres , is dug to a depth of 24 metres . what is the volume of the earth dug out ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 24.0\nt0 = n0 / 2.0\nanswer = math.pi * t0**2 * n1\nprint(answer)" + ], + "Output Answer": [ + "678.5840131753953" + ], + "split": "train" + }, + { + "Input": "sand is poured into a box so that the box is being filled at the rate of 3 cubic feet per hour . if the empty rectangular box is 5 feet long , 4 feet wide , and 3 feet deep , approximately how many hours does it take to fill the box ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nn2 = 4.0\nn3 = 3.0\nt0 = n1 * n2\nt1 = n3 * t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a larger cube has 343 cubic inch as a volume and in the cube there are 343 smaller cubes such that their volume is 1 cubic inch . what is the difference between the surface areas \u2019 sum of the 343 smaller cubes and the surface area of the larger cube , in square inch ?", + "Output Program": [ + "n0 = 343.0\nn1 = 343.0\nn2 = 1.0\nn3 = 343.0\nt0 = n2**(1 / 3)\nt1 = n0**(1 / 3)\nt2 = 6 * t0**2 # surface of a cube\nt3 = 6 * t1**2 # surface of a cube\nt4 = n0 * t2\nanswer = t4 - t3\nprint(answer)" + ], + "Output Answer": [ + "1764" + ], + "split": "train" + }, + { + "Input": "a circle graph shows how the budget of a certain company was spent : 60 percent for salaries , 9 percent for research and development , 5 percent for utilities , 4 percent for equipment , 2 percent for supplies , and the remainder for transportation . if the area of each sector of the graph is proportional to the percent of the budget it represents , how many degrees of the circle are used to represent transportation ?", + "Output Program": [ + "n0 = 60.0\nn1 = 9.0\nn2 = 5.0\nn3 = 4.0\nn4 = 2.0\nt0 = n0 + n1\nt1 = n2 + t0\nt2 = n3 + t1\nt3 = n4 + t2\nt4 = 100.0 - t3\nt5 = t4 * 360.0\nanswer = t5 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 432 sq m , then what is the breadth of the rectangular plot ?", + "Output Program": [ + "import math\nn0 = 432.0\nt0 = n0 / 3.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a rectangular tank needs to be coated with insulation . the tank has dimensions of 3 feet , 6 feet , and 2 feet . each square foot of insulation costs $ 20 . how much will it cost to cover the surface of the tank with insulation ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nn2 = 2.0\nn3 = 20.0\nt0 = 2 * (n0 * n1 + n0 * n2 + n1 * n2) # surface of a rectangular prism\nanswer = n3 * t0\nprint(answer)" + ], + "Output Answer": [ + "1440" + ], + "split": "train" + }, + { + "Input": "the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 8 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?", + "Output Program": [ + "n0 = 25.0\nn1 = 15.0\nn2 = 12.0\nn3 = 8.0\nn4 = 6.0\nn5 = 3.0\nn6 = 4.0\nn7 = 3.0\nt0 = n0 + n1\nt1 = n2 * 2.0\nt2 = n4 * 3.0\nt3 = n5 * n6\nt4 = t0 * t1\nt5 = n5 * t3\nt6 = t4 - t2\nt7 = t6 - t5\nanswer = n3 * t7\nprint(answer)" + ], + "Output Answer": [ + "7248" + ], + "split": "train" + }, + { + "Input": "the surface area of a sphere is 4 \u03c0 r 2 , where r is the radius of the sphere . if the area of the base of a hemisphere is 3 , what is the surface area r of that hemisphere ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 3.0\nt0 = n2 / 3.141592653589793\nt1 = n0 * 3.141592653589793\nt2 = t0 * t1\nt3 = t0 * 3.141592653589793\nt4 = t2 / n1\nanswer = t4 + t3\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "8 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?", + "Output Program": [ + "n0 = 8.0\nn1 = 7.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nt2 = n0 * t1\nt3 = t2 / 2.0\nanswer = t3 + t0\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "there is a rectangular prism made of 1 in cubes that has been covered in tin foil . there are exactly 128 cubes that are not touching any tin foil on any of their sides . if the width of the figure created by these 128 cubes is twice the length and twice the height , what is the measure e in inches of the width of the foil covered prism ?", + "Output Program": [ + "n0 = 1.0\nn1 = 128.0\nn2 = 128.0\nt0 = 1 / 3.0\nt1 = n0 * 2.0\nt2 = n0 * t1\nt3 = n1 / t2\nt4 = t3**min(t0, 5)\nt5 = t1 * t4\nanswer = t5 + t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "danny is sitting on a rectangular box . the area of the front face of the box is half the area of the top face , and the area of the top face is 1.5 times the area of the side face . if the volume of the box is 3000 , what is the area of the side face of the box ?", + "Output Program": [ + "n0 = 1.5\nn1 = 3000.0\nt0 = 1.0 / 3.0\nt1 = n1**min(2.0, 5)\nt2 = t1 * 3.0\nt3 = t2**min(t0, 5)\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "199.99999999999991" + ], + "split": "train" + }, + { + "Input": "if the sum of a number and its square is 272 , what is the number ?", + "Output Program": [ + "import math\nn0 = 272.0\nt0 = math.sqrt(max(0, n0))\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "2 corner most boxes of a chess board ( diagonally opposite ) haven been cut out there ' s a rectangular block = 2 sqaures of chess board , how many such blocks can be placed on the chess board ? \u201d", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nt0 = n0 * n0\nt1 = t0 * t0\nt2 = n0 * t1\nanswer = t2 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "the parameter of a square is equal to the perimeter of a rectangle of length 9 cm and breadth 6 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ?", + "Output Program": [ + "import math\nn0 = 9.0\nn1 = 6.0\nt0 = 2 * (n0 + n1) # perimetere of rectangle\nt1 = t0 / 4. # square edge given perimeter\nt2 = t1 / 2.0\nt3 = 2 * math.pi * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "11.780972450961723" + ], + "split": "train" + }, + { + "Input": "the area of a rectangle is 63 sq m . the width is two meters shorter than the length . what is the width ?", + "Output Program": [ + "import math\nn0 = 63.0\nt0 = n0 * 4.0\nt1 = 2.0**min(2.0, 5)\nt2 = t0 + t1\nt3 = math.sqrt(max(0, t2))\nt4 = t3 - 2.0\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a rectangular wall is covered entirely with two kinds of decorative tiles : regular and jumbo . 1 / 3 of the tiles are jumbo tiles , which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles . if regular tiles cover 40 square feet of the wall , and no tiles overlap , what is the area of the entire wall ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 40.0\nt0 = n2 * n1\nt1 = t0 / 2.0\nt2 = n1 * t1\nanswer = n2 + t2\nprint(answer)" + ], + "Output Answer": [ + "220" + ], + "split": "train" + }, + { + "Input": "the diameter of a cylindrical tin is 8 cm and height is 5 cm . find the volume of the cylinder ?", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 5.0\nt0 = n0 / 2.0\nt1 = math.pi * t0**2 * n1\nanswer = t1 / 3.141592653589793\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "a rectangular grass field is 75 m * 55 m , it has a path of 2.8 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?", + "Output Program": [ + "n0 = 75.0\nn1 = 55.0\nn2 = 2.8\nn3 = 2.0\nt0 = n2 * n3\nt1 = n0 * n1 # area of rectangle\nt2 = n0 + t0\nt3 = n1 + t0\nt4 = t2 * t3 # area of rectangle\nt5 = t4 - t1\nanswer = n3 * t5\nprint(answer)" + ], + "Output Answer": [ + "1518.7199999999993" + ], + "split": "train" + }, + { + "Input": "a circular logo is enlarged to fit the lid of a jar . the new diameter is 60 per cent larger than the original . by what percentage has the area of the logo increased ?", + "Output Program": [ + "n0 = 60.0\nt0 = n0 * 2.0\nt1 = t0 / 1000.0\nt2 = t1 + 3.0\nt3 = t2**min(2.0, 5)\nt4 = t3 - 4.0\nt5 = t4 / 4.0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "143.36" + ], + "split": "train" + }, + { + "Input": "two isosceles triangles have equal vertical angles and their areas are in the ratio 9 : 25 . find the ratio of their corresponding heights .", + "Output Program": [ + "import math\nn0 = 9.0\nn1 = 25.0\nt0 = math.sqrt(max(0, n0))\nt1 = math.sqrt(max(0, n1))\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.6" + ], + "split": "train" + }, + { + "Input": "the length of each side of square a is increased by 100 percent to make square b . if the length of the side of square b is increased by 40 percent to make square c , by what percent is the area of square c greater than the sum of the areas of squares a and b ?", + "Output Program": [ + "n0 = 100.0\nn1 = 40.0\nt0 = n0 / n0\nt1 = t0 + 1.0\nt2 = n1 * t1\nt3 = t1**2\nt4 = t3 + 1.0\nt5 = t2 / n0\nt6 = t1 + t5\nt7 = t6**2\nt8 = t7 - 1.0\nt9 = t8 - 4.0\nt10 = t9 / t4\nanswer = n0 * t10\nprint(answer)" + ], + "Output Answer": [ + "56.79999999999998" + ], + "split": "train" + }, + { + "Input": "a circular garden is surrounded by a fence of negligible width along the boundary . if the length of the fence is 1 / 3 of th area of the garden . what is the radius of the circular garden ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 3.0\nt0 = n1**min(2.0, 5)\nt1 = math.sqrt(max(0, t0))\nanswer = t1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "when magnified 1,000 times by an electron microscope , the image of a certain circular piece of tissue has a diameter of 2 centimeter . the actual diameter of the tissue , in centimeters , is", + "Output Program": [ + "n0 = 1000.0\nn1 = 2.0\n\nanswer = n1 / 1000.0\nprint(answer)" + ], + "Output Answer": [ + "0.002" + ], + "split": "train" + }, + { + "Input": "can v and can \u0432 are both right circular cylinders . the radius of can v is twice the radius of can b , while the height of can v is half the height of can b . if it costs $ 4.00 to fill half of can b with a certain brand of gasoline , how much would it cost to completely fill can v with the same brand of gasoline ?", + "Output Program": [ + "n0 = 4.0\nt0 = 2.0**min(4.0, 5)\nt1 = 2.0**min(2.0, 5)\nt2 = t0 * 2.0\nt3 = t1 * 2.0\nt4 = t2 * 2.0\nt5 = t3 * 4.0\nt6 = t5 / 2.0\nt7 = t4 / t6\nanswer = n0 * t7\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 390 sq . feet , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 20.0\nn1 = 390.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "59" + ], + "split": "train" + }, + { + "Input": "what is the smallest positive integer that can be multiplied by 1,008 to make it a perfect square ?", + "Output Program": [ + "n0 = 1008.0\n\nanswer = 3.0 + 4.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a crate measures 6 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still fit in the crate ?", + "Output Program": [ + "n0 = 6.0\nn1 = 8.0\nn2 = 12.0\nt0 = n1 * n2\nt1 = n0 * t0\nt2 = t1 / n2\nanswer = t2 / n1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "in a certain parallelogram the degree measure of one angle exceeds that of the other by 40 what is the degree measure of the smaller angle ?", + "Output Program": [ + "n0 = 40.0\nt0 = 3600.0 / 10.0\nt1 = n0 * 2.0\nt2 = t0 - t1\nanswer = t2 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "a farmer built a fence around his square plot . he used 27 fence poles on each side of the square . how many poles did he need altogether ?", + "Output Program": [ + "n0 = 27.0\nt0 = n0 - 2.0\nt1 = t0 * 4.0\nanswer = t1 + 4.0\nprint(answer)" + ], + "Output Answer": [ + "104" + ], + "split": "train" + }, + { + "Input": "a rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 4 per sq m ?", + "Output Program": [ + "n0 = 80.0\nn1 = 60.0\nn2 = 10.0\nn3 = 4.0\nt0 = n0 + n1\nt1 = t0 - n2\nt2 = n2 * t1\nanswer = n3 * t2\nprint(answer)" + ], + "Output Answer": [ + "5200" + ], + "split": "train" + }, + { + "Input": "the perimeter of a triangle is 24 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ?", + "Output Program": [ + "n0 = 24.0\nn1 = 2.5\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "for any even integer p , 300 multiplied by p is square of an integer . what is the least value of p ?", + "Output Program": [ + "n0 = 300.0\n\nanswer = n0 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a football field is 10800 square yards . if 1200 pounds of fertilizer are spread evenly across the entire field , how many pounds of fertilizer were spread over an area of the field totaling 3600 square yards ?", + "Output Program": [ + "n0 = 10800.0\nn1 = 1200.0\nn2 = 3600.0\nt0 = n1 / n0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "what is the perimeter , in meters , of a rectangular garden 24 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide ?", + "Output Program": [ + "n0 = 24.0\nn1 = 16.0\nn2 = 12.0\nt0 = n1 * n2 # area of rectangle\nt1 = t0 / n0\nanswer = 2 * (n0 + t1) # perimetere of rectangle\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corner , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is", + "Output Program": [ + "n0 = 48.0\nn1 = 36.0\nn2 = 8.0\nn3 = 3.0\nt0 = n2 * 2.0\nt1 = n0 - t0\nt2 = n1 - t0\nanswer = n2 * t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "5120" + ], + "split": "train" + }, + { + "Input": "the perimeter of a triangle is 36 cm and the in radius of the triangle is 2.5 cm . what is the area of the triangle ?", + "Output Program": [ + "n0 = 36.0\nn1 = 2.5\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "the length of rectangle is thrice its breadth and its perimeter is 88 m , find the area of the rectangle ?", + "Output Program": [ + "n0 = 88.0\nt0 = 2.0 * 3.0\nt1 = 1.0 * 2.0\nt2 = t0 + t1\nt3 = n0 / t2\nt4 = t3 * 3.0\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "363" + ], + "split": "train" + }, + { + "Input": "two circular signs are to be painted . if the diameter of the larger sign is 7 times that of the smaller sign , how many times more paint is needed to paint the larger sign ? ( we can assume that a given amount of paint covers the same area on both signs . )", + "Output Program": [ + "n0 = 7.0\n\nanswer = n0**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "train" + }, + { + "Input": "the diagonals of a rhombus are 30 cm and 20 cm . find its area ?", + "Output Program": [ + "n0 = 30.0\nn1 = 20.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 7.5 ) , ( 8 , 0 ) , ( 0 , - 7.5 ) , ( - 8 , 0 ) ?", + "Output Program": [ + "n0 = 0.0\nn1 = 7.5\nn2 = 8.0\nn3 = 0.0\nn4 = 0.0\nn5 = 7.5\nn6 = 8.0\nn7 = 0.0\nt0 = n2 * 2.0\nt1 = n1 * 2.0\nanswer = t0 * t1 / 2\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "find the area of a parallelogram with base 36 cm and height 24 cm ?", + "Output Program": [ + "n0 = 36.0\nn1 = 24.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "864" + ], + "split": "train" + }, + { + "Input": "the size of a flat - screen television is given as the length of the screen \u2019 s diagonal . how many square inches greater is the screen of a square 28 - inch flat - screen television than a square 25 - inch flat - screen television ?", + "Output Program": [ + "n0 = 28.0\nn1 = 25.0\nt0 = n0**min(2.0, 5)\nt1 = n1**min(2.0, 5)\nt2 = t0 / 2.0\nt3 = t1 / 2.0\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "79.5" + ], + "split": "train" + }, + { + "Input": "a rectangular grass field is 75 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?", + "Output Program": [ + "n0 = 75.0\nn1 = 55.0\nn2 = 2.5\nn3 = 2.0\nt0 = n2 * n3\nt1 = n0 * n1 # area of rectangle\nt2 = n0 + t0\nt3 = n1 + t0\nt4 = t2 * t3 # area of rectangle\nt5 = t4 - t1\nanswer = n3 * t5\nprint(answer)" + ], + "Output Answer": [ + "1350" + ], + "split": "train" + }, + { + "Input": "the hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle . the shorter side of the triangle is 7 centimeters less than the longer side . find the length of the hypotenuse .", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 7.0\nt0 = n0 + n1\nt1 = n1**min(2.0, 5)\nt2 = n0**min(2.0, 5)\nt3 = n0 * t0\nt4 = t1 - t2\nt5 = t4 * 4.0\nt6 = t3**min(2.0, 5)\nt7 = t6 - t5\nt8 = math.sqrt(max(0, t7))\nt9 = t3 + t8\nt10 = t9 / 2.0\nanswer = n0 + t10\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered . if the area of the field is 600 sq . ft , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 30.0\nn1 = 600.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "if the volume of a cube is x ^ 3 cubic units , what is the number of square units in the surface area of the cube ?", + "Output Program": [ + "n0 = 3.0\nt0 = 2.0 * 3.0\nt1 = 1.0 * 1.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the monthly rent of a shop of dimension 10 feet \u00d7 10 feet is rs . 1300 . what is the annual rent per square foot of the shop ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 1300.0\nt0 = 10.0 + 2.0\nt1 = n0 * n1 # area of rectangle\nt2 = n2 / t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "156" + ], + "split": "train" + }, + { + "Input": "a box is in the shape of a semicircle with a radius of 12 . what is the approximate perimeter of the semicircle ?", + "Output Program": [ + "n0 = 12.0\nt0 = n0 * 3.141592653589793\nt1 = n0 * 2.0\nanswer = t0 + t1\nprint(answer)" + ], + "Output Answer": [ + "61.69911184307752" + ], + "split": "train" + }, + { + "Input": "find the area of a parallelogram with base 12 cm and height 8 cm ?", + "Output Program": [ + "n0 = 12.0\nn1 = 8.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "96" + ], + "split": "train" + }, + { + "Input": "the diagonals of a rhombus are 13 cm and 20 cm . find its area ?", + "Output Program": [ + "n0 = 13.0\nn1 = 20.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "130" + ], + "split": "train" + }, + { + "Input": "a rectangular lawn 70 m \u00d7 30 m has two roads each 5 metres wide , running in the middle of it , one parallel to the length and the other parallel to the breadth . find the cost of gravelling the road at the rate of 4 per square metre .", + "Output Program": [ + "n0 = 70.0\nn1 = 30.0\nn2 = 5.0\nn3 = 4.0\nt0 = n0 * n2\nt1 = n1 * n2\nt2 = n2 * n2\nt3 = t0 + t1\nt4 = t3 - t2\nanswer = n3 * t4\nprint(answer)" + ], + "Output Answer": [ + "1900" + ], + "split": "train" + }, + { + "Input": "in how many r ways can 5 people from a group of 6 people be seated around a circular table", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 6.0\nt0 = n0 - 1.0\nt1 = math.factorial(min(15, int(t0)))\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "train" + }, + { + "Input": "a horse is tethered to one corner of a rectangular grassy field 40 m by 24 m with a rope 14 m long . over how much area of the field can it graze ?", + "Output Program": [ + "n0 = 40.0\nn1 = 24.0\nn2 = 14.0\nt0 = n2**min(2.0, 5)\nt1 = t0 * 3.141592653589793\nanswer = t1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "153.93804002589985" + ], + "split": "train" + }, + { + "Input": "a circular garden is surrounded by a fence of negligible width along the boundary . if the length of the fence is 1 / 8 of th area of the garden . what is the radius of the circular garden ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 8.0\nt0 = n1**min(2.0, 5)\nt1 = math.sqrt(max(0, t0))\nanswer = t1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the parameter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )", + "Output Program": [ + "import math\nn0 = 18.0\nn1 = 14.0\nt0 = 2 * (n0 + n1) # perimetere of rectangle\nt1 = t0 / 4. # square edge given perimeter\nt2 = t1 / 2.0\nt3 = 2 * math.pi * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "25.132741228718345" + ], + "split": "train" + }, + { + "Input": "the area of the floor of a room is 20 m 2 that of a longer wall 15 m 2 and of the shorter wall 12 m 2 , find the edge of the new cube ?", + "Output Program": [ + "import math\nn0 = 20.0\nn1 = 2.0\nn2 = 15.0\nn3 = 2.0\nn4 = 12.0\nn5 = 2.0\nt0 = math.sqrt(max(0, n2))\nt1 = math.sqrt(max(0, n4))\nt2 = math.sqrt(max(0, n0))\nanswer = t0 * t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "find the area of a parallelogram with base 22 cm and height 21 cm ?", + "Output Program": [ + "n0 = 22.0\nn1 = 21.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "462" + ], + "split": "train" + }, + { + "Input": "the width of a rectangular hall is \u00bd of its length . if the area of the hall is 288 sq . m , what is the difference between its length and breadth ?", + "Output Program": [ + "import math\nn0 = 288.0\nt0 = 1.0 / 2.0\nt1 = n0 / t0\nt2 = math.sqrt(max(0, t1))\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a steel vessel has a base of length 60 cm and breadth 30 cm . water is poured in the vessel . a cubical steel box having edge of 30 cm is immersed completely in the vessel . how much will the water rise ?", + "Output Program": [ + "n0 = 60.0\nn1 = 30.0\nn2 = 30.0\nt0 = n0 * n1\nt1 = n1**min(3.0, 5)\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "if the sides of a triangle are 30 cm , 28 cm and 14 cm , what is its area ?", + "Output Program": [ + "n0 = 30.0\nn1 = 28.0\nn2 = 14.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "196" + ], + "split": "train" + }, + { + "Input": "the parameter of a square is equal to the perimeter of a rectangle of length 4 cm and breadth 2 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 2.0\nt0 = 2 * (n0 + n1) # perimetere of rectangle\nt1 = t0 / 4. # square edge given perimeter\nt2 = t1 / 2.0\nt3 = 2 * math.pi * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "4.71238898038469" + ], + "split": "train" + }, + { + "Input": "if the sides of a triangle are 28 cm , 26 cm and 10 cm , what is its area ?", + "Output Program": [ + "n0 = 28.0\nn1 = 26.0\nn2 = 10.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "130" + ], + "split": "train" + }, + { + "Input": "the area of a parallelogram is 242 sq m and its altitude is twice the corresponding base . then the length of the base is ?", + "Output Program": [ + "import math\nn0 = 242.0\nt0 = n0 / 2.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "rectangular tile each of size 25 cm by 65 cm must be laid horizontally on a rectangular floor of size 150 cm by 390 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :", + "Output Program": [ + "n0 = 25.0\nn1 = 65.0\nn2 = 150.0\nn3 = 390.0\nt0 = n2 * n3\nt1 = n0 * n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "the area of a triangle is with base 3 m and height 6 m ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "on dividing a number by 5 , we get 3 as remainder . what will the remainder when the square of the this number is divided by 5 ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 3.0\nn2 = 5.0\nt0 = n1**min(2.0, 5)\nt1 = t0 / n0\nt2 = math.floor(t1)\nt3 = t1 - t2\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the side of a square is increased by 30 % then how much % does its area increases ?", + "Output Program": [ + "n0 = 30.0\nt0 = n0 + 100.0\nt1 = 100.0**2\nt2 = t0**2\nt3 = t2 - t1\nt4 = t3 * 100.0\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "69" + ], + "split": "train" + }, + { + "Input": "if the length of the sides of two cubes are in the ratio 7 : 1 , what is the ratio of their total surface area ?", + "Output Program": [ + "n0 = 7.0\nn1 = 1.0\n\nanswer = n0 * n0\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "train" + }, + { + "Input": "the area of a parallelogram is 128 sq m . then the area of a triangle formed by its diagonal is - - - - - - - - - - ?", + "Output Program": [ + "n0 = 128.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "the radius of a semicircle is 7 . what is the approximate perimeter of the semicircle ?", + "Output Program": [ + "import math\nn0 = 7.0\nt0 = n0 + n0\nt1 = 2 * math.pi * n0\nt2 = t1 / 2.0\nanswer = t0 + t2\nprint(answer)" + ], + "Output Answer": [ + "35.99114857512855" + ], + "split": "train" + }, + { + "Input": "one side of a rectangular field is 13 m and one of its diagonal is 17 m . find the area of the field .", + "Output Program": [ + "import math\nn0 = 13.0\nn1 = 17.0\nt0 = n1**min(2.0, 5)\nt1 = n0**min(2.0, 5)\nt2 = t0 - t1\nt3 = math.sqrt(max(0, t2))\nanswer = n0 * t3 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "142.40786495134319" + ], + "split": "train" + }, + { + "Input": "the perimeter of a triangle is 40 cm and the in radius of the triangle is 2.5 cm . what is the area of the triangle ?", + "Output Program": [ + "n0 = 40.0\nn1 = 2.5\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a rectangular parking space is marked out by painting three of its sides . if the length of the unpainted side is 9 feet , and the sum of the lengths of the painted sides is 37 feet , then what is the area of the parking space in square feet ?", + "Output Program": [ + "n0 = 9.0\nn1 = 37.0\nt0 = n1 + n1\nt1 = n1 + t0\nt2 = t1 + 10.0\nanswer = t2 + 4.0\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 6 , 0 ) , ( 0 , - 3.5 ) , ( - 6 , 0 ) ?", + "Output Program": [ + "n0 = 0.0\nn1 = 3.5\nn2 = 6.0\nn3 = 0.0\nn4 = 0.0\nn5 = 3.5\nn6 = 6.0\nn7 = 0.0\nt0 = n2 * 2.0\nt1 = n1 * 2.0\nanswer = t0 * t1 / 2\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "the perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ?", + "Output Program": [ + "n0 = 28.0\nn1 = 2.5\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "train" + }, + { + "Input": "the average length of the sides of triangle abc is 12 . what is the perimeter of triangle abc ?", + "Output Program": [ + "n0 = 12.0\n\nanswer = n0 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "cubes with each side one inch long are glued together to form a larger cube . the larger cube ' s face is painted with red color and the entire assembly is taken apart . 23 small cubes are found with no paints on them . how many of unit cubes have at least one face that is painted red ?", + "Output Program": [ + "n0 = 23.0\nt0 = 1.0 + 3.0\nt1 = t0 + 1.0\nt2 = t1**min(3.0, 5)\nanswer = t2 - n0\nprint(answer)" + ], + "Output Answer": [ + "102" + ], + "split": "train" + }, + { + "Input": "the number 90 can be written as the sum of the squares of 4 different positive integers . what is the sum of these 4 integers ?", + "Output Program": [ + "n0 = 90.0\nn1 = 4.0\nn2 = 4.0\nt0 = 3.0 + 4.0\nt1 = 2.0 + 3.0\nt2 = t0 + t1\nanswer = n1 + t2\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a rectangular of certain dimensions is chopped off from one corner of a larger rectangle as shown . ab = 8 cm and bc = 4 cm . the perimeter of the figure abcpqra ( in cm ) is :", + "Output Program": [ + "n0 = 8.0\nn1 = 4.0\nt0 = n0 + n1\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "the length of rectangle is thrice its breadth and its perimeter is 56 m , find the area of the rectangle ?", + "Output Program": [ + "n0 = 56.0\nt0 = 2.0 * 3.0\nt1 = 1.0 * 2.0\nt2 = t0 + t1\nt3 = n0 / t2\nt4 = t3 * 3.0\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "147" + ], + "split": "train" + }, + { + "Input": "the length of rectangle is thrice its breadth and its perimeter is 112 m , find the area of the rectangle ?", + "Output Program": [ + "n0 = 112.0\nt0 = 2.0 * 3.0\nt1 = 1.0 * 2.0\nt2 = t0 + t1\nt3 = n0 / t2\nt4 = t3 * 3.0\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "588" + ], + "split": "train" + }, + { + "Input": "in measuring the sides of a rectangle , one side is taken 5 % in excess and the other 4 % in deficit . find the error percent in the area , calculate from the those measurements .", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nt0 = n0 * n1\nt1 = n0 - n1\nt2 = t0 / 100.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.8" + ], + "split": "train" + }, + { + "Input": "if the sum of a number and its square is 210 , what is the number ?", + "Output Program": [ + "import math\nn0 = 210.0\nt0 = math.sqrt(max(0, n0))\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "16 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?", + "Output Program": [ + "n0 = 16.0\nn1 = 7.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nt2 = n0 * t1\nt3 = t2 / 2.0\nanswer = t3 + t0\nprint(answer)" + ], + "Output Answer": [ + "232" + ], + "split": "train" + }, + { + "Input": "the area of a rectangular field is equal to 200 square meters . its perimeter is equal to 60 meters . find the width of this rectangle .", + "Output Program": [ + "import math\nn0 = 200.0\nn1 = 60.0\nt0 = n1 / 2.0\nt1 = n0 * 4.0\nt2 = t0 * t0\nt3 = t2 - t1\nt4 = math.sqrt(max(0, t3))\nt5 = t0 - t4\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 10 inches tall . carmen places her sculpture on a base that is 2 inches tall . how tall are the sculpture andbase together ?", + "Output Program": [ + "n0 = 2.0\nn1 = 10.0\nn2 = 2.0\nt0 = n0 + n1\nt1 = n0 * t0\nt2 = t1 + n1\nt3 = n2 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the perimeter of a rectangle is equal to 280 meters . the ratio of its length to its width is 5 : 2 . find the area of the rectangle .", + "Output Program": [ + "n0 = 280.0\nn1 = 5.0\nn2 = 2.0\nt0 = n1 + n2\nt1 = t0 * 2.0\nt2 = n0 / t1\nt3 = t2**min(2.0, 5)\nt4 = n1 * t3\nanswer = n2 * t4\nprint(answer)" + ], + "Output Answer": [ + "4000" + ], + "split": "train" + }, + { + "Input": "the area of sector of a circle whose radius is 18 metro and whose angle at the center is 42 \u00e2 \u00b0 is ?", + "Output Program": [ + "n0 = 18.0\nn1 = 42.0\nt0 = 3.0 + 4.0\nt1 = 3600.0 / 10.0\nt2 = 10.0 * 2.0\nt3 = n0**min(2.0, 5)\nt4 = t2 + 2.0\nt5 = n1 / t1\nt6 = t4 / t0\nt7 = t6 * t3\nanswer = t5 * t7\nprint(answer)" + ], + "Output Answer": [ + "118.8" + ], + "split": "train" + }, + { + "Input": "danny is sitting on a rectangular box . the area of the front face of the box is half the area of the top face , and the area of the top face is 1.5 times the area of the side face . if the volume of the box is 192 , what is the area of the side face of the box ?", + "Output Program": [ + "n0 = 1.5\nn1 = 192.0\nt0 = 1.0 / 3.0\nt1 = n1**min(2.0, 5)\nt2 = t1 * 3.0\nt3 = t2**min(t0, 5)\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "31.999999999999996" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 2500 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?", + "Output Program": [ + "import math\nn0 = 2500.0\nn1 = 10.0\nt0 = n1 / 2.0\nt1 = math.sqrt(max(0, n0))\nt2 = t1 / t0\nt3 = t2 * 2.0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "the parameter of a square is equal to the perimeter of a rectangle of length 40 cm and breadth 20 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ?", + "Output Program": [ + "import math\nn0 = 40.0\nn1 = 20.0\nt0 = 2 * (n0 + n1) # perimetere of rectangle\nt1 = t0 / 4. # square edge given perimeter\nt2 = t1 / 2.0\nt3 = 2 * math.pi * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "47.12388980384689" + ], + "split": "train" + }, + { + "Input": "the area of a circular field is 13.86 hectares . find the cost of fencing it at the rate of rs . 4.60 per metre .", + "Output Program": [ + "import math\nn0 = 13.86\nn1 = 4.6\nt0 = n0 / 3.141592653589793\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * 100.0\nt3 = 2 * math.pi * t2\nanswer = t3 * n1\nprint(answer)" + ], + "Output Answer": [ + "6070.778380479544" + ], + "split": "train" + }, + { + "Input": "a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 3 inches wide on each side , the total area would have been ( m + 52 ) square inches . what is the perimeter of the photograph , in inches ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 52.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nt2 = t0**min(2.0, 5)\nt3 = t1**min(2.0, 5)\nt4 = t2 - t3\nt5 = n2 - t4\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the larger interior angle of a parallelogram is 90 \u00b0 more than its smaller interior angle . what is the measure of the smaller interior angle of the parallelogram ?", + "Output Program": [ + "n0 = 90.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 5 per metre approximately", + "Output Program": [ + "import math\nn0 = 17.56\nn1 = 5.0\nt0 = n0 / 3.141592653589793\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * 100.0\nt3 = 2 * math.pi * t2\nanswer = t3 * n1\nprint(answer)" + ], + "Output Answer": [ + "7427.406478511646" + ], + "split": "train" + }, + { + "Input": "the water level in a rectangular swimming pool measuring 20 feet by 25 feet is to be lowered by 6 inches . how many gallons of water must be removed ? ( 1 cu ft = 7.5 gallons )", + "Output Program": [ + "n0 = 20.0\nn1 = 25.0\nn2 = 6.0\nn3 = 1.0\nn4 = 7.5\nt0 = 10.0 + 2.0\nt1 = n2 / t0\nt2 = n0 * n1 * t1\nanswer = n4 * t2\nprint(answer)" + ], + "Output Answer": [ + "1875" + ], + "split": "train" + }, + { + "Input": "the length and breadth of the floor of the room are 20 feet and 10 feet respectively . square tiles of 2 feet length of different colours are to be laid on the floor . black tiles are laid in the first row on all sides . if white tiles are laid in the one - third of the remaining and blue tiles in the rest , how many blue tiles will be there ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nn2 = 2.0\nt0 = n0 + n0\nt1 = 3.0 + 3.0\nt2 = n0 * n1\nt3 = t0 + t1\nt4 = t3 + t1\nt5 = t4 * 2.0\nt6 = t2 - t5\nt7 = t6 / 3.0\nt8 = t6 - t7\nanswer = t8 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular plot is 10 mtr more than its width . the cost of fencing the plot along its perimeter at the rate of rs . 6.5 mtr is rs . 1430 . the perimeter of the plot is ?", + "Output Program": [ + "n0 = 10.0\nn1 = 6.5\nn2 = 1430.0\nt0 = n2 / n1\nt1 = t0 / 2.0\nt2 = t1 - n0\nt3 = t2 / 2.0\nt4 = t3 + n0\nt5 = t4 + t3\nanswer = t5 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "220" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is two third of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 4761 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 13 units ?", + "Output Program": [ + "import math\nn0 = 4761.0\nn1 = 13.0\nt0 = math.sqrt(max(0, n0))\nt1 = t0 * 2.0\nt2 = t1 / 3.0\nanswer = n1 * t2 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "598" + ], + "split": "train" + }, + { + "Input": "the volume of the sphere qq is ( dfrac { 37 } { 64 } % ) less than thevolume of sphere pp and the volume of sphere rr is ( dfrac { 19 } { 27 } % ) less than that of sphere qq . by what is the surface areaof sphere rr less than the surfacearea of sphere pp ?", + "Output Program": [ + "n0 = 37.0\nn1 = 64.0\nn2 = 19.0\nn3 = 27.0\nt0 = 1.0 / 3.0\nt1 = n1**min(t0, 5)\nt2 = n3**min(t0, 5)\nt3 = t1 * t2\nt4 = t3 + t1\nt5 = t4 - t1\nt6 = t1 + t5\nt7 = t6 - t1\nt8 = t7 / t6\nanswer = t8 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "9 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?", + "Output Program": [ + "n0 = 9.0\nn1 = 7.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nt2 = n0 * t1\nt3 = t2 / 2.0\nanswer = t3 + t0\nprint(answer)" + ], + "Output Answer": [ + "99" + ], + "split": "train" + }, + { + "Input": "if the length of rectangle is three times of its breadth . if the area of rectangle is 6075 sq . m , then calculate the length ?", + "Output Program": [ + "import math\nn0 = 6075.0\nt0 = n0 / 3.0\nt1 = math.sqrt(max(0, t0))\nanswer = t1 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "135" + ], + "split": "train" + }, + { + "Input": "while visiting a small town in the united states , i lost my overcoat in a bus . when i reported the matter to the bus company i was asked the number of the bus . though i did not remember the exact number i did remember that the bus number bad a certain peculiarity about it . the number plate showed the bus number as a perfect square and also if the plate was turned upside down . ? the number would still be a perfect square \u2014 of course it was not ? i came to know from the bus company they had only 5 100 buses numbered from 1 to 500 . from this i was able to deduce the bus number . can you tell what was the other number .", + "Output Program": [ + "n0 = 5.0\nn1 = 100.0\nn2 = 1.0\nn3 = 500.0\nt0 = n1 - 4.0\nanswer = t0 + 100.0\nprint(answer)" + ], + "Output Answer": [ + "196" + ], + "split": "train" + }, + { + "Input": "area of a square is 1 / 2 hectare . the diagonal of the square is ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 2.0\nt0 = n0 / n1\nt1 = 100.0 * 100.0\nt2 = t0 * t1\nt3 = t2 * 2.0\nanswer = math.sqrt(max(0, t3))\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "a sporting good store sells one type of baseball bat and one type of baseball . the cost for 2 bats and 4 balls is $ 220 . the cost for 1 bat and 6 balls is $ 190 , as well . if someone were to buy an equal number of bats and balls , at most how many bats can he purchase if he has a budget of $ 270 for the purchase ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 220.0\nn3 = 1.0\nn4 = 6.0\nn5 = 190.0\nn6 = 270.0\nt0 = n2 / n0\nt1 = n5 - t0\nt2 = t1 / n1\nt3 = n4 * t2\nt4 = n5 - t3\nt5 = t2 + t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "two equal triangles constitute rhombus a . if the diagonals of rhombus are 15 cm and 20 cm long . what is the area of each triangle ?", + "Output Program": [ + "n0 = 15.0\nn1 = 20.0\nt0 = n0 * n1\nanswer = t0 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "if the side length of square b is four times that of square a , the area of square b is how many times the area of square a ?", + "Output Program": [ + "\nanswer = 4.0 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a lady grows cabbage in her garden that is in the shape of a square . each cabbage takes 1 square foot of area in her garden . this year , she has increased her output by 211 cabbages when compared to last year . the shape of the area used for growing the cabbage has remained a square in both these years . how many cabbages did she produce this year ?", + "Output Program": [ + "n0 = 1.0\nn1 = 211.0\nt0 = n1 - n0\nt1 = t0 / 2.0\nt2 = n0 + t1\nanswer = t2**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "11236" + ], + "split": "train" + }, + { + "Input": "the area of a square is added to one of its sides , and the perimeter is then subtracted from this total , the result is 4 . what is the length of one side ?", + "Output Program": [ + "n0 = 4.0\nt0 = n0 / 2.0\nanswer = t0**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the circumferences of two circles are 264 meters and 704 meters . find the difference between the areas of the larger and the smaller circles ?", + "Output Program": [ + "import math\nn0 = 264.0\nn1 = 704.0\nt0 = 2.0 * 3.141592653589793\nt1 = n1 / t0\nt2 = n0 / t0\nt3 = math.pi * t1**2\nt4 = math.pi * t2**2\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "33893.63668085003" + ], + "split": "train" + }, + { + "Input": "the width of a rectangle is 10 mtr and its area is 150 square meter . if length of the rectangle is increased , then its new area is 1 ( 1 / 3 ) times of the original area . what is the new perimeter of the rectangle ?", + "Output Program": [ + "n0 = 10.0\nn1 = 150.0\nn2 = 1.0\nn3 = 1.0\nn4 = 3.0\nt0 = n1 * 4.0\nt1 = n0 * 2.0\nt2 = t0 / n4\nt3 = t2 / n0\nt4 = t3 * 2.0\nanswer = t4 + t1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "the side of a square is increased by 40 % then how much % does its area increases ?", + "Output Program": [ + "n0 = 40.0\nt0 = n0 + 100.0\nt1 = 100.0**2\nt2 = t0**2\nt3 = t2 - t1\nt4 = t3 * 100.0\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "96" + ], + "split": "train" + }, + { + "Input": "the perimeter of an equilateral triangle is 45 . if one of the side is the side of an isoceles triangle of perimeter 40 then what is the lenght of base of isoceles triangle .", + "Output Program": [ + "n0 = 45.0\nn1 = 40.0\nt0 = n0 / 3.0\nt1 = n1 - t0\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the circus sells two kinds of tickets : lower seats for $ 30 and upper seats for $ 20 . on a certain night , the circus sells 80 tickets and gets $ 2100 in revenue from the sales . how many tickets for lower seats did they sell ?", + "Output Program": [ + "n0 = 30.0\nn1 = 20.0\nn2 = 80.0\nn3 = 2100.0\nt0 = n0 * n2\nt1 = n0 - n1\nt2 = t0 - n3\nt3 = t2 / t1\nanswer = n2 - t3\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a box has 12 shapes ; 3 circles , 5 squares , and 4 triangles . how many groups of 3 shapes can be made with at least 1 triangle ?", + "Output Program": [ + "n0 = 12.0\nn1 = 3.0\nn2 = 5.0\nn3 = 4.0\nn4 = 3.0\nn5 = 1.0\nt0 = n0 + n0\nt1 = 2.0 + 4.0\nt2 = n1 + n2\nt3 = t0 + 4.0\nt4 = t1 * t2\nt5 = n3 * t3\nt6 = t5 + t4\nanswer = n3 + t6\nprint(answer)" + ], + "Output Answer": [ + "164" + ], + "split": "train" + }, + { + "Input": "the side of a rhombus is 25 m and length of one of its diagonals is 10 m . the area of the rhombus is ?", + "Output Program": [ + "import math\nn0 = 25.0\nn1 = 10.0\nt0 = n0 * 2.0\nt1 = n1**min(2.0, 5)\nt2 = t0**min(2.0, 5)\nt3 = t2 - t1\nt4 = math.sqrt(max(0, t3))\nt5 = n1 * t4\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "244.9489742783178" + ], + "split": "train" + }, + { + "Input": "a metallic sheet is of rectangular shape with dimensions 52 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is :", + "Output Program": [ + "n0 = 52.0\nn1 = 36.0\nn2 = 8.0\nn3 = 3.0\nt0 = n2 * 2.0\nt1 = n0 - t0\nt2 = n1 - t0\nanswer = n2 * t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "5760" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 588 sq m , then what is the breadth of the rectangular plot ?", + "Output Program": [ + "import math\nn0 = 588.0\nt0 = n0 / 3.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "a sixth grade teacher asked her students to draw rectangles with positive integer length and a perimeter of 42 . the difference between the largest and smallest possible ares of the rectangles that the students could have come up with is ?", + "Output Program": [ + "n0 = 42.0\nt0 = n0 / 2.0\nt1 = t0 - 10.0\nt2 = t0 - 1.0\nt3 = t1 * 10.0\nt4 = t2 * 1.0\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "the diagonals of a rhombus are 15 cm and 21 cm . find its area ?", + "Output Program": [ + "n0 = 15.0\nn1 = 21.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "157.5" + ], + "split": "train" + }, + { + "Input": "carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 5 inches by 24 inches and jordan ' s rectangle is 4 inches long , how wide is jordan ' s rectangle , in inches ?", + "Output Program": [ + "n0 = 5.0\nn1 = 24.0\nn2 = 4.0\nt0 = n0 * n1 # area of rectangle\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "a rectangular room has the rectangular shaped rug shown as above figure such that the rug \u2019 s area is 180 square feet and its length is 8 feet longer than its width . if the uniform width between the rug and room is 8 feet , what is the area of the region uncovered by the rug ( shaded region ) , in square feet ?", + "Output Program": [ + "n0 = 180.0\nn1 = 8.0\nn2 = 8.0\nt0 = 180.0 / 10.0\nt1 = t0 - 2.0\nt2 = t1 + 10.0\nt3 = t0 + t1\nt4 = t2 * t3\nanswer = t4 - n0\nprint(answer)" + ], + "Output Answer": [ + "704" + ], + "split": "train" + }, + { + "Input": "what is the % change in the area of a rectangle when its length increases by 20 % and its width decreases by 20 % ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nt0 = n0 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the surface area of a sphere is 4 \u03c0 r 2 , where r is the radius of the sphere . if the area of the base of a hemisphere is 3 , what is the surface area w of that hemisphere ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 3.0\nt0 = n2 / 3.141592653589793\nt1 = n0 * 3.141592653589793\nt2 = t0 * t1\nt3 = t0 * 3.141592653589793\nt4 = t2 / n1\nanswer = t4 + t3\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "if the sum of a number and its square is 132 , then what is the number ?", + "Output Program": [ + "import math\nn0 = 132.0\nt0 = math.sqrt(max(0, n0))\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "what is the smallest number by which 3600 be divided to make it a perfect cube ?", + "Output Program": [ + "n0 = 3600.0\nt0 = 2.0**min(3.0, 5)\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "450" + ], + "split": "train" + }, + { + "Input": "radius of a circle is 5 cm , if we draw a rectangle of maximum size , what is the area of rectangle ?", + "Output Program": [ + "n0 = 5.0\nt0 = n0 * 2.0\nt1 = t0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "what is the area of a square field whose diagonal of length 40 m ?", + "Output Program": [ + "n0 = 40.0\nt0 = n0**2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "train" + }, + { + "Input": "50 square stone slabs of equal size were needed to cover a floor area of 98 sq . m . find the length of each stone slab ?", + "Output Program": [ + "import math\nn0 = 50.0\nn1 = 98.0\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "train" + }, + { + "Input": "10 meters of wire is available to fence off a flower bed in the form of a circular sector . what must the radius of the circle in meters be , if we wish to have a flower bed with the greatest possible surface area ?", + "Output Program": [ + "n0 = 10.0\n\nanswer = n0 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "2.5" + ], + "split": "train" + }, + { + "Input": "if paint costs $ 3.20 per quart , and a quart covers 60 square feet , how much will it cost to paint the outside of a cube 10 feet on each edge ?", + "Output Program": [ + "n0 = 3.2\nn1 = 60.0\nn2 = 10.0\nt0 = n0 / n1\nt1 = 6 * n2**2 # surface of a cube\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "the perimeter of a square is 28 cm . what is the perimeter of a circle whose radius is equal to the side of the square ? ( in cm )", + "Output Program": [ + "import math\nn0 = 28.0\nt0 = n0 / 4.0\nanswer = 2 * math.pi * t0\nprint(answer)" + ], + "Output Answer": [ + "43.982297150257104" + ], + "split": "train" + }, + { + "Input": "the length of the side of a square is represented by x + 2 . the length of the side of an equilateral triangle is 2 x . if the square and the equilateral triangle have equal perimeter , then the value of x is ?", + "Output Program": [ + "n0 = 2.0\nn1 = 2.0\nt0 = n0 * 4.0\nt1 = n0 * 3.0\nt2 = t1 - 4.0\nanswer = t0 / t2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "danny is sitting on a rectangular box . the area of the front face of the box is half the area of the top face , and the area of the top face is 1.5 times the area of the side face . if the volume of the box is 648 , what is the area of the side face of the box ?", + "Output Program": [ + "n0 = 1.5\nn1 = 648.0\nt0 = 1.0 / 3.0\nt1 = n1**min(2.0, 5)\nt2 = t1 * 3.0\nt3 = t2**min(t0, 5)\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "71.99999999999999" + ], + "split": "train" + }, + { + "Input": "find the circumference and area of radius 11 cm .", + "Output Program": [ + "import math\nn0 = 11.0\n\nanswer = math.pi * n0**2\nprint(answer)" + ], + "Output Answer": [ + "380.132711084365" + ], + "split": "train" + }, + { + "Input": "the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 150 square centimeters , what is the length of the rectangle in centimeters ?", + "Output Program": [ + "n0 = 5.0\nn1 = 1.0\nn2 = 150.0\n\nanswer = n2 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "the diagonals of a rhombus are 17 cm and 20 cm . find its area ?", + "Output Program": [ + "n0 = 17.0\nn1 = 20.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "170" + ], + "split": "train" + }, + { + "Input": "a rectangular courtyard 3.78 m lang and 5.25 m broad is to be paved exactly with square tiles , all of the same size . the minimum number of such tiles is :", + "Output Program": [ + "n0 = 3.78\nn1 = 5.25\nt0 = 3.0 + 4.0\nt1 = n0 * 100.0\nt2 = n1 * 100.0\nt3 = t1 * t2\nt4 = t0 * 3.0\nt5 = t4**min(2.0, 5)\nanswer = t3 / t5\nprint(answer)" + ], + "Output Answer": [ + "450" + ], + "split": "train" + }, + { + "Input": "the ratio of boys to girls in a class is 2 : 3 . the career preference of the students in the class are to be represented in a circle graph . if the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one third of the boys and two - third of the girls in the class ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nt0 = n0 + n1\nt1 = n0 / t0\nt2 = 3.0 / t0\nt3 = t1 / 3.0\nt4 = t2 * 2.0\nt5 = t4 / 3.0\nt6 = t3 + t5\nanswer = t6 * 360.0\nprint(answer)" + ], + "Output Answer": [ + "192" + ], + "split": "train" + }, + { + "Input": "consider a square of diagonal length d . let another square be formed with d as its side . find the ratio of the area of the bigger square to that of the smaller square .", + "Output Program": [ + "import math\nt0 = 1.0 + 1.0\nt1 = 1.0**min(2.0, 5)\nt2 = 1.0 / t0\nt3 = math.sqrt(max(0, t2))\nt4 = t3**min(2.0, 5)\nanswer = t1 / t4\nprint(answer)" + ], + "Output Answer": [ + "1.9999999999999996" + ], + "split": "train" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 210 sq . feet , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 20.0\nn1 = 210.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "41" + ], + "split": "train" + }, + { + "Input": "the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each . the radius of the sphere is :", + "Output Program": [ + "import math\nn0 = 12.0\nt0 = n0 / 2.0\nt1 = 4.0 * 3.141592653589793\nt2 = n0 * t0\nt3 = t2 * 3.141592653589793\nt4 = t3 * 2.0\nt5 = t4 / t1\nanswer = math.sqrt(max(0, t5))\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the perimeter of a square is equal to the radius of a circle having area 39424 sq cm , what is the area of square ?", + "Output Program": [ + "import math\nn0 = 39424.0\nt0 = n0 / 3.141592653589793\nt1 = math.sqrt(max(0, t0))\nt2 = t1 / 4. # square edge given perimeter\nanswer = t2**2\nprint(answer)" + ], + "Output Answer": [ + "784.3155595568603" + ], + "split": "train" + }, + { + "Input": "calculate the effect changes in dimension of a rectangle will have on its area , if length is increased by 15 % and its breadth is decreased by 10 % ?", + "Output Program": [ + "n0 = 15.0\nn1 = 10.0\nt0 = n0 + 100.0\nt1 = 100.0 * 100.0\nt2 = 100.0 - n1\nt3 = t0 * t2\nt4 = t3 - t1\nt5 = t4 / t1\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "3.5000000000000004" + ], + "split": "train" + }, + { + "Input": "the area of a rectangular plot is 20 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the slant height of a cone is 21 cm and radius of the base is 10 cm , find the curved surface of the cone .", + "Output Program": [ + "n0 = 21.0\nn1 = 10.0\nt0 = n1 * 3.141592653589793\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "659.7344572538566" + ], + "split": "train" + }, + { + "Input": "the roof of an apartment building is rectangular and its length is 4 times longer than its width . if the area of the roof is 1024 feet squared , what is the difference between the length and the width of the roof ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 1024.0\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * n0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "in a rectangular coordinate system , what is the area of a rectangle whose vertices have the coordinates ( - 8 , 1 ) , ( 1 , 1 ) , ( 1 , - 7 and ( - 8 , - 7 ) ?", + "Output Program": [ + "n0 = 8.0\nn1 = 1.0\nn2 = 1.0\nn3 = 1.0\nn4 = 1.0\nn5 = 7.0\nn6 = 8.0\nn7 = 7.0\nt0 = n0 + n1\nt1 = n1 + n5\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "train" + }, + { + "Input": "if circles x and y have the same area and circle x has a circumference of 12 \u03c0 , half of the radius of circle y is :", + "Output Program": [ + "n0 = 12.0\nt0 = n0 / 2.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "in measuring the sides of a rectangle , one side is taken 9 % in excess , and the other 8 % in deficit . find the error percent in the area calculated from these measurements .", + "Output Program": [ + "n0 = 9.0\nn1 = 8.0\nt0 = n0 * n1\nt1 = n0 - n1\nt2 = t0 / 100.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.28" + ], + "split": "train" + }, + { + "Input": "the mass of 1 cubic meter of a substance is 300 kilograms under certain conditions . what is the volume , in cubic centimeters , of 1 gram of this substance under these conditions ? ( 1 kilogram = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )", + "Output Program": [ + "n0 = 1.0\nn1 = 300.0\nn2 = 1.0\nn3 = 1.0\nn4 = 1000.0\nn5 = 1.0\nn6 = 1.0\nn7 = 0.0\nt0 = n1 * 1000.0\nt1 = 100.0**min(3.0, 5)\nt2 = t1 / t0\nanswer = t2 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "1.3333333333333335" + ], + "split": "train" + }, + { + "Input": "if length of rectangle is increased by 10 % , and breadth is decreased by 10 % . what will it effect on area of rectangle ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nt0 = n0 * n0\nt1 = t0 / 100.0\nt2 = n0 + t1\nanswer = t2 - n0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "the parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 12 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )", + "Output Program": [ + "import math\nn0 = 16.0\nn1 = 12.0\nt0 = 2 * (n0 + n1) # perimetere of rectangle\nt1 = t0 / 4. # square edge given perimeter\nt2 = t1 / 2.0\nt3 = 2 * math.pi * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "21.991148575128552" + ], + "split": "train" + }, + { + "Input": "what is the % change in the area of a rectangle when its length increases by 60 % and its width decreases by 60 % ?", + "Output Program": [ + "n0 = 60.0\nn1 = 60.0\nt0 = n0 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular garden is three times its width . if the area of the rectangular garden is 588 square meters , then what is the width of the rectangular garden ?", + "Output Program": [ + "import math\nn0 = 588.0\nt0 = n0 / 3.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "a certain farmer pays $ 30 per acre per month to rent farmland . how much does the farmer pay per month to rent a rectangular plot of farmland that is 360 feet by 1210 feet ? ( 43,560 square feet = 1 acre )", + "Output Program": [ + "n0 = 30.0\nn1 = 360.0\nn2 = 1210.0\nn3 = 43560.0\nn4 = 1.0\nt0 = n1 * n2\nt1 = t0 / 10.0\nt2 = t0 / t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "the breadth of a rectangular hall is two - thirds of its length . if the area of the hall is 2400 sq metres , what is the length in metres ?", + "Output Program": [ + "import math\nn0 = 2400.0\nt0 = 2.0 / 3.0\nt1 = n0 / t0\nanswer = math.sqrt(max(0, t1))\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "if the difference between the length and breadth of a rectangle is 23 m and its perimeter is 166 m , what is its area ?", + "Output Program": [ + "n0 = 23.0\nn1 = 166.0\nt0 = n0 * 2.0\nt1 = n1 - t0\nt2 = t1 / 4.0\nt3 = n0 + t2\nanswer = t3 * t2 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "1590" + ], + "split": "train" + }, + { + "Input": "the radius of the base of cone is 3 cm and height is 4 cm . find the volume of the cone ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\n\nanswer = n0 * n1 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "what is the area of a square with perimeter 12 p ?", + "Output Program": [ + "n0 = 12.0\nt0 = n0 / 4. # square edge given perimeter\nanswer = t0**2\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 900 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?", + "Output Program": [ + "import math\nn0 = 900.0\nn1 = 10.0\nt0 = n1 / 2.0\nt1 = math.sqrt(max(0, n0))\nt2 = t1 / t0\nt3 = t2 * 2.0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "a rectangular grass field is 60 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?", + "Output Program": [ + "n0 = 60.0\nn1 = 55.0\nn2 = 2.5\nn3 = 2.0\nt0 = n2 * n3\nt1 = n0 * n1 # area of rectangle\nt2 = n0 + t0\nt3 = n1 + t0\nt4 = t2 * t3 # area of rectangle\nt5 = t4 - t1\nanswer = n3 * t5\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 625 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?", + "Output Program": [ + "import math\nn0 = 625.0\nn1 = 10.0\nt0 = n1 / 2.0\nt1 = math.sqrt(max(0, n0))\nt2 = t1 / t0\nt3 = t2 * 2.0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "the area of an isosceles trapezoid with sides of length 5 and bases of length 10 and 16 is ?", + "Output Program": [ + "n0 = 5.0\nn1 = 10.0\nn2 = 16.0\n\nanswer = 4.0 * (n2 + n1) / 2 # quadrilateral area\nprint(answer)" + ], + "Output Answer": [ + "52" + ], + "split": "train" + }, + { + "Input": "the following questions are based on the information given . choose the appropriate answer that suits the question based on the information . a cube is cut in two equal parts along a plane parallel to one of its faces . one piece is then colored red on the two larger faces and green on remaining . while the other is colored green on two smaller adjacent faces and red on the remaining . each is then cut into 32 cubes of same size and mixed up . 21 . how many cubes have only one colored face each ?", + "Output Program": [ + "n0 = 32.0\nn1 = 21.0\nt0 = n0 / 4.0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the breadth of a rectangular field is 60 % of its length . if the perimeter of the field is 800 m , find out the area of the field .", + "Output Program": [ + "n0 = 60.0\nn1 = 800.0\nt0 = n1 / 2.0\nt1 = n0 / 100.0\nt2 = t1 + 1.0\nt3 = t0 / t2\nt4 = t0 - t3\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "37500" + ], + "split": "train" + }, + { + "Input": "the width of a rectangle is 10 meter and its area is 150 square meter . if length of the rectangle is increased then its new area is 4 / 3 times of the original area . what is the new perimeter of the rectangle ?", + "Output Program": [ + "n0 = 10.0\nn1 = 150.0\nn2 = 4.0\nn3 = 3.0\nt0 = n1 * n2\nt1 = t0 / n3\nt2 = t1 / n0\nanswer = 2 * (n0 + t2) # perimetere of rectangle\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "if the area of a square with sides of length 4 centimeters is equal to the area of a rectangle with a width of 8 centimeters , what is the length of the rectangle , in centimeters ?", + "Output Program": [ + "n0 = 4.0\nn1 = 8.0\nt0 = n0**min(2.0, 5)\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the perimeter of a triangle is 32 cm and the inradius of the triangle is 3.5 cm . what is the area of the triangle ?", + "Output Program": [ + "n0 = 32.0\nn1 = 3.5\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "if circles x and y have the same area and circle x has a circumference of 10 \u03c0 , half of the radius of circle y is :", + "Output Program": [ + "n0 = 10.0\nt0 = n0 / 2.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "2.5" + ], + "split": "train" + }, + { + "Input": "the area of a parallelogram is 450 sq m and its altitude is twice the corresponding base . then the length of the base is ?", + "Output Program": [ + "import math\nn0 = 450.0\nt0 = n0 / 2.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "108 . triangle a \u2019 s base is 12 % greater than the base of triangle b , and a \u2019 s height is 12 % less than the height of triangle b . the area of triangle a is what percent less or more than the area of triangle b ?", + "Output Program": [ + "n0 = 108.0\nn1 = 12.0\nn2 = 12.0\nt0 = n1 + 100.0\nt1 = 100.0 * 100.0\nt2 = 100.0 - n1\nt3 = t0 * t2\nt4 = t1 - t3\nanswer = 100.0 / t4\nprint(answer)" + ], + "Output Answer": [ + "0.6944444444444444" + ], + "split": "train" + }, + { + "Input": "a diagonal of a polygon is an segment between two non - adjacent vertices of the polygon . how many diagonals does a regular 30 - sided polygon have ?", + "Output Program": [ + "n0 = 30.0\nt0 = n0 - 3.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "405" + ], + "split": "train" + }, + { + "Input": "the length of the rectangular field is double its width . inside the field there is square shaped pond 4 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 1.0\nn2 = 8.0\nt0 = 1 / 2.0\nt1 = n0**2\nt2 = n2 * t1\nt3 = t2 / t0\nanswer = math.sqrt(max(0, t3))\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "two isosceles triangles have equal vertical angles and their areas are in the ratio 16 : 49 . find the ratio of their corresponding heights .", + "Output Program": [ + "import math\nn0 = 16.0\nn1 = 49.0\nt0 = math.sqrt(max(0, n0))\nt1 = math.sqrt(max(0, n1))\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.5714285714285714" + ], + "split": "train" + }, + { + "Input": "the perimeter of an equilateral triangle is 60 . if one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 55 , then how long is the base of isosceles triangle ?", + "Output Program": [ + "n0 = 60.0\nn1 = 55.0\nt0 = n0 / 3.0\nt1 = n1 - t0\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "how many 1 x 1 x 1 cubes can you fit in a 15 x 16 x 13 box ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 1.0\nn3 = 15.0\nn4 = 16.0\nn5 = 13.0\n\nanswer = n3 * n4 * n5\nprint(answer)" + ], + "Output Answer": [ + "3120" + ], + "split": "train" + }, + { + "Input": "the edges of cuboid are 4 cm ; 5 cm and 6 cm . find its surface area ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 6.0\nt0 = n2 * 2.0\nt1 = n1 * 2.0\nt2 = 2.0 * 4.0\nt3 = t0 * 4.0\nt4 = n2 * t1\nt5 = n1 * t2\nt6 = t3 + t4\nanswer = t6 + t5\nprint(answer)" + ], + "Output Answer": [ + "148" + ], + "split": "train" + }, + { + "Input": "what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 60 % ?", + "Output Program": [ + "n0 = 60.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = t1**min(2.0, 5)\nt3 = t2 - 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "156.00000000000006" + ], + "split": "train" + }, + { + "Input": "five equal cubes , each of side 5 cm , are placed adjacent to each other . the volume of the new solid formed will be", + "Output Program": [ + "n0 = 5.0\nt0 = 1.0 + 4.0\nt1 = n0**3\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "625" + ], + "split": "train" + }, + { + "Input": "a wooden cube whose edge length is 6 inches is composed of smaller cubes with edge lengths of one inch . the outside surface of the large cube is painted red and then it is split up into its smaller cubes . if one cube is randomly selected from the small cubes , what is the probability that the cube will have at least one red face ?", + "Output Program": [ + "n0 = 6.0\nt0 = 1.0 * 4.0\nt1 = n0**3\nt2 = t0**3\nt3 = t2 / t1\nt4 = 1.0 - t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "70.37037037037037" + ], + "split": "train" + }, + { + "Input": "all the faces of cubes are painted with red colour . it is then cut into 64 equal small cubes . find how many small cubes are there whose three faces are coloured ?", + "Output Program": [ + "n0 = 64.0\nt0 = n0 / 4.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "if the sides of a square are doubled in length , the area of the original square is now how many times as large as the area of the resultant square ?", + "Output Program": [ + "t0 = 1.0 / 2.0\nt1 = t0**min(2.0, 5)\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "the floor of a rectangular room is 17 m long and 12 m wide . the room is surrounded by a veranda of width 2 m on all its sides . the area of the veranda is :", + "Output Program": [ + "n0 = 17.0\nn1 = 12.0\nn2 = 2.0\nt0 = n2 * n2\nt1 = n0 * n1 # area of rectangle\nt2 = n0 + t0\nt3 = n1 + t0\nt4 = t2 * t3 # area of rectangle\nanswer = t4 - t1\nprint(answer)" + ], + "Output Answer": [ + "132" + ], + "split": "train" + }, + { + "Input": "calculate the effect changes in dimension of a rectangle will have on its area , if length is increased by 20 % and its breadth is decreased by 5 % ?", + "Output Program": [ + "n0 = 20.0\nn1 = 5.0\nt0 = n0 + 100.0\nt1 = 100.0 * 100.0\nt2 = 100.0 - n1\nt3 = t0 * t2\nt4 = t3 - t1\nt5 = t4 / t1\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "14.000000000000002" + ], + "split": "train" + }, + { + "Input": "how many differently shaped triangles exist in which no two sides are of the same length , each side is of integral unit length and the perimeter of the triangle is less than 14 units ?", + "Output Program": [ + "n0 = 14.0\nt0 = 3.0**min(2.0, 5)\nanswer = n0 - t0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the cost of the paint is rs . 40 per kg . if 1 kg of paint covers 20 sq . ft , how much will it cost to paint outside of a cube having 30 feet each side", + "Output Program": [ + "n0 = 40.0\nn1 = 1.0\nn2 = 20.0\nn3 = 30.0\nt0 = 6 * n3**2 # surface of a cube\nt1 = t0 / n2\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "10800" + ], + "split": "train" + }, + { + "Input": "huey ' s hip pizza sells two sizes of square pizzas : a small pizza that measures 6 inches on a side and costs $ 10 , and a large pizza that measures 9 inches on a side and costs $ 20 . if two friends go to huey ' s with $ 30 apiece , how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone ?", + "Output Program": [ + "n0 = 6.0\nn1 = 10.0\nn2 = 9.0\nn3 = 20.0\nn4 = 30.0\nt0 = n2**min(2.0, 5)\nt1 = n0**min(2.0, 5)\nt2 = t1 + t0\nt3 = t0 * 3.0\nt4 = t2 + t2\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the area of a square field is 1600 km 2 . how long will it take for a horse to run around at the speed of 16 km / h ?", + "Output Program": [ + "import math\nn0 = 1600.0\nn1 = 2.0\nn2 = 16.0\nt0 = math.sqrt(max(0, n0))\nt1 = t0 * 4.0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "rectangular tile each of size 60 cm by 56 cm must be laid horizontally on a rectangular floor of size 560 cm by 240 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :", + "Output Program": [ + "n0 = 60.0\nn1 = 56.0\nn2 = 560.0\nn3 = 240.0\nt0 = n2 * n3\nt1 = n0 * n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "the length of the diagonal of a square is 12 cm . find its area and perimeter .", + "Output Program": [ + "import math\nn0 = 12.0\nt0 = math.sqrt(max(0, 2.0))\nt1 = n0 / t0\nanswer = 4 * t1\nprint(answer)" + ], + "Output Answer": [ + "33.94112549695428" + ], + "split": "train" + }, + { + "Input": "a cube of edge 15 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 14 cm , find the rise in water level ?", + "Output Program": [ + "n0 = 15.0\nn1 = 20.0\nn2 = 14.0\nt0 = n1 * n2\nt1 = n0**3\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "12.053571428571429" + ], + "split": "train" + }, + { + "Input": "if the sides of a triangle are 91 cm , 84 cm and 35 cm , what is its area ?", + "Output Program": [ + "n0 = 91.0\nn1 = 84.0\nn2 = 35.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "1470" + ], + "split": "train" + }, + { + "Input": "32 meters of wire is available to fence off a flower bed in the form of a circular sector . what must the radius of the circle in meters be , if we wish to have a flower bed with the greatest possible surface area ?", + "Output Program": [ + "n0 = 32.0\n\nanswer = n0 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "compute the perimeter of a square with area 36 .", + "Output Program": [ + "import math\nn0 = 36.0\nt0 = math.sqrt(max(0, n0))\nanswer = t0 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": ". if the sides of two cubes are in the ratio 3 : 1 the ratio of their total surface area is ?", + "Output Program": [ + "n0 = 3.0\nn1 = 1.0\nt0 = 6 * n0**2 # surface of a cube\nt1 = 6 * n1**2 # surface of a cube\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the area of a rectangular field is equal to 300 square meters . its perimeter is equal to 70 meters . find the length of this rectangle .", + "Output Program": [ + "import math\nn0 = 300.0\nn1 = 70.0\nt0 = n1 / 2.0\nt1 = n0 * 4.0\nt2 = t0 * t0\nt3 = t2 - t1\nt4 = math.sqrt(max(0, t3))\nt5 = t0 - t4\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "find the perimeter and area of a square of side 13 cm .", + "Output Program": [ + "n0 = 13.0\n\nanswer = n0**2\nprint(answer)" + ], + "Output Answer": [ + "169" + ], + "split": "train" + }, + { + "Input": "find the area of a right - angled triangle whose base is 12 cm and hypotenuse is 13 cm .", + "Output Program": [ + "import math\nn0 = 12.0\nn1 = 13.0\nt0 = n1**min(2.0, 5)\nt1 = n0**min(2.0, 5)\nt2 = t0 - t1\nt3 = math.sqrt(max(0, t2))\nanswer = n0 * t3 / 2\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "in a rectangular coordinate system , what is the area of a rectangle whose vertices have the coordinates ( - 9 , 1 ) , ( 1 , 1 ) , ( 1 , - 8 ) and ( - 9 , - 8 ) ?", + "Output Program": [ + "n0 = 9.0\nn1 = 1.0\nn2 = 1.0\nn3 = 1.0\nn4 = 1.0\nn5 = 8.0\nn6 = 9.0\nn7 = 8.0\nt0 = n0 + n1\nt1 = n1 + n5\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "what is the volume of an tetrahedron with edge length of 1 ?", + "Output Program": [ + "import math\nn0 = 1.0\nt0 = 10.0 + 2.0\nt1 = math.sqrt(max(0, 2.0))\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.11785113019775793" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is 3 times its width . if the width of the rectangle is 5 inches , what is the rectangle ' s area , in square inches ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nt0 = n0 * n1\nanswer = n1 * t0 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "a rectangular swimming pool is 20 feet by 22 feet . a deck that has uniform width surrounds the pool . the total area of the pool and deck is 728 square feet . what is the width of the deck ?", + "Output Program": [ + "import math\nn0 = 20.0\nn1 = 22.0\nn2 = 728.0\nt0 = n0 * n1 # area of rectangle\nt1 = n1 - 1.0\nt2 = t1**min(2.0, 5)\nt3 = n2 - t0\nt4 = t2 + t3\nt5 = math.sqrt(max(0, t4))\nt6 = t5 - t1\nanswer = t6 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a semicircle has a radius of 12 . what is the approximate perimeter of the semicircle ?", + "Output Program": [ + "import math\nn0 = 12.0\nt0 = 2 * math.pi * n0\nt1 = n0 * 2.0\nt2 = t0 / 2.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "61.69911184307752" + ], + "split": "train" + }, + { + "Input": "abce is an isosceles trapezoid and acde is a rectangle . ab = 10 and ec = 20 . what is the length of ae .", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 20.0\nt0 = n1**min(2.0, 5)\nt1 = n1 - n0\nt2 = t1 / 2.0\nt3 = t2**min(2.0, 5)\nt4 = n1 - t2\nt5 = t4**min(2.0, 5)\nt6 = t0 - t5\nt7 = t3 + t6\nt8 = t7 / 2.0\nanswer = math.sqrt(max(0, t8))\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the slant height of a right circular cone is 10 m and its height is 8 m . find the area of its curved surface .", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 8.0\nt0 = n0**min(2.0, 5)\nt1 = n1**min(2.0, 5)\nt2 = t0 - t1\nt3 = math.sqrt(max(0, t2))\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "what is the ratio between perimeters of two squares one having 1.5 times the diagonal then the other ?", + "Output Program": [ + "n0 = 1.5\nt0 = n0 / n0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "1.5" + ], + "split": "train" + }, + { + "Input": "a circular garden is surrounded by a fence of negligible width along the boundary . if the length of the fence is 1 / 6 of th area of the garden . what is the radius of the circular garden ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 6.0\nt0 = n1**min(2.0, 5)\nt1 = math.sqrt(max(0, t0))\nanswer = t1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a certain cube floating in a bucket of water has between 60 and 85 percent of its volume below the surface of the water . if between 9 and 26 cubic centimeters of the cube ' s volume is above the surface of the water , then the length of a side of the cube is approximately", + "Output Program": [ + "n0 = 60.0\nn1 = 85.0\nn2 = 9.0\nn3 = 26.0\nt0 = n3 * 100.0\nt1 = 100.0 - n0\nt2 = t0 / t1\nanswer = t2**(1 / 3)\nprint(answer)" + ], + "Output Answer": [ + "4.020725758589058" + ], + "split": "train" + }, + { + "Input": "the perimeter of an equilateral triangle is 60 . if one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 70 , then how long is the base of isosceles triangle ?", + "Output Program": [ + "n0 = 60.0\nn1 = 70.0\nt0 = n0 / 3.0\nt1 = n1 - t0\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "the ratio of male to female in a class is 2 : 7 . the career preference of the students in the class are to be represented in a circle graph . if the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one third of the males and two - third of the females in the class ?", + "Output Program": [ + "n0 = 2.0\nn1 = 7.0\nt0 = n0 + n1\nt1 = 2.0 / 3.0\nt2 = 2.0 / t0\nt3 = n1 / t0\nt4 = t2 / 3.0\nt5 = t3 * t1\nt6 = t4 * 360.0\nt7 = t5 * 360.0\nanswer = t6 + t7\nprint(answer)" + ], + "Output Answer": [ + "213.33333333333331" + ], + "split": "train" + }, + { + "Input": "which is the smallest number divides 2800 and gives a perfect square .", + "Output Program": [ + "n0 = 2800.0\nt0 = 2.0 + 3.0\nt1 = n0 / 2.0\nt2 = t1 / 2.0\nt3 = t2 / 2.0\nt4 = t3 / 2.0\nt5 = t4 / t0\nanswer = t5 / t0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "d and e are two points respectively on sides ab and ac of triangle abc such that de is parallel to bc . if the ratio of area of triangle ade to that of the trapezium decb is 144 : 25 and de = 13 cm , then find the length of bc .", + "Output Program": [ + "import math\nn0 = 144.0\nn1 = 25.0\nn2 = 13.0\nt0 = n0 + n1\nt1 = n1 / t0\nt2 = math.sqrt(max(0, t1))\nanswer = n2 * t2\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "a square mirror has exactly half the area of the rectangular wall on which it is hung . if each side of the mirror is 34 inches and the width of the wall is 54 inches , what is the length of the wall , in inches ?", + "Output Program": [ + "n0 = 34.0\nn1 = 54.0\nt0 = n0**2\nt1 = t0 * 2.0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "42.81481481481482" + ], + "split": "train" + }, + { + "Input": "three fifth of the square of a certain number is 126.15 . what is the number ?", + "Output Program": [ + "import math\nn0 = 126.15\nt0 = 1.0 + 4.0\nt1 = 3.0 / t0\nt2 = n0 / t1\nanswer = math.sqrt(max(0, t2))\nprint(answer)" + ], + "Output Answer": [ + "14.500000000000002" + ], + "split": "train" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 600 sq . ft , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 20.0\nn1 = 600.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "the perimeter of a triangle is 20 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ?", + "Output Program": [ + "n0 = 20.0\nn1 = 2.5\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "you buy a piece of land with an area of \u221a 900 , how long is one side of the land plot ?", + "Output Program": [ + "import math\nn0 = 900.0\n\nanswer = math.sqrt(max(0, n0))\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "in the coordinate plane , one of the vertices of a square is the point ( - 6 , - 4 ) . if the diagonals of that square intersect at point ( 3 , 2 ) , what is the area of that square ?", + "Output Program": [ + "n0 = 6.0\nn1 = 4.0\nn2 = 3.0\nn3 = 2.0\nt0 = n0 * n2\nanswer = t0 * t0\nprint(answer)" + ], + "Output Answer": [ + "324" + ], + "split": "train" + }, + { + "Input": "the cube root of . 000216 is :", + "Output Program": [ + "n0 = 216.0\nt0 = n0 / 1000.0\nt1 = 1.0 / 3.0\nt2 = t0 / 1000.0\nanswer = t2**min(t1, 5)\nprint(answer)" + ], + "Output Answer": [ + "0.06000000000000001" + ], + "split": "train" + }, + { + "Input": "what will be the cost of building a fence around a square plot with area equal to 49 sq ft , if the price per foot of building the fence is rs . 58 ?", + "Output Program": [ + "import math\nn0 = 49.0\nn1 = 58.0\nt0 = math.sqrt(max(0, n0))\nt1 = 4 * t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "1624" + ], + "split": "train" + }, + { + "Input": "the area of a parallelogram is 200 sq m and its altitude is twice the corresponding base . then the length of the base is ?", + "Output Program": [ + "import math\nn0 = 200.0\nt0 = n0 / 2.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the area of a square field is 900 km 2 . how long will it take for a horse to run around at the speed of 12 km / h ?", + "Output Program": [ + "import math\nn0 = 900.0\nn1 = 2.0\nn2 = 12.0\nt0 = math.sqrt(max(0, n0))\nt1 = t0 * 4.0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the edge of three cubes of metal is 3 dm , 4 dm and 5 dm . they are melted and formed into a single cube . find the edge of the new cube ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nn2 = 5.0\n\nanswer = 2.0 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck ' s tank is completely filled . if the truck ' s tank has a radius of 8 feet and a height of 10 feet , how far ( in feet ) did the oil level drop in the stationary tank ?", + "Output Program": [ + "import math\nn0 = 100.0\nn1 = 25.0\nn2 = 8.0\nn3 = 10.0\nt0 = math.pi * n0**2\nt1 = math.pi * n2**2 * n3\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.064" + ], + "split": "train" + }, + { + "Input": "the parameter of a square is equal to the perimeter of a rectangle of length 20 cm and breadth 16 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ?", + "Output Program": [ + "import math\nn0 = 20.0\nn1 = 16.0\nt0 = 2 * (n0 + n1) # perimetere of rectangle\nt1 = t0 / 4. # square edge given perimeter\nt2 = t1 / 2.0\nt3 = 2 * math.pi * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "28.274333882308138" + ], + "split": "train" + }, + { + "Input": "2 minute is taken to travel the diagonal of square field at 3 km / hour . calculate the area of field ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nt0 = n1 * 1000.0\nt1 = 10.0 * 180.0\nt2 = n0 * n1\nt3 = t1 * 2.0\nt4 = t2 * 10.0\nt5 = t0 / t3\nt6 = n0 * t4\nt7 = t5 * t6\nt8 = t7**min(2.0, 5)\nt9 = t8 / n0\nanswer = t9 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is 2 times its width . if the width of the rectangle is 5 inches , what is the rectangle ' s area , in square inches ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nt0 = n0 * n1\nanswer = n1 * t0 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "if a is the smallest positive integer such that 5880 multiplied by a is the square of an integer , then ya must be", + "Output Program": [ + "n0 = 5880.0\nt0 = 3.0 + 4.0\nt1 = 2.0**min(2.0, 5)\nt2 = t0**min(2.0, 5)\nt3 = t2 * t1\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "an error 2 % in excess is made while measuring the side ofa square . the % of error in the calculated area of the square is ?", + "Output Program": [ + "n0 = 2.0\nt0 = n0 + 100.0\nt1 = 100.0 * 100.0\nt2 = t0 * t0\nt3 = t2 - t1\nanswer = t3 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "4.04" + ], + "split": "train" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 400 sq . ft , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 20.0\nn1 = 400.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "a cube of edge 15 cm is imersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 15 cm , find the rise in waer level .", + "Output Program": [ + "n0 = 15.0\nn1 = 20.0\nn2 = 15.0\nt0 = n0 * n1\nt1 = n0**3\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "11.25" + ], + "split": "train" + }, + { + "Input": "the side of a rhombus is 28 m and length of one of its diagonals is 12 m . the area of the rhombus is ?", + "Output Program": [ + "import math\nn0 = 28.0\nn1 = 12.0\nt0 = n0 * 2.0\nt1 = n1**min(2.0, 5)\nt2 = t0**min(2.0, 5)\nt3 = t2 - t1\nt4 = math.sqrt(max(0, t3))\nt5 = n1 * t4\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "328.19506394825623" + ], + "split": "train" + }, + { + "Input": "a hall is 24 meters long and 12 meters wide . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , what is the volume of the hall ( in cubic meters ) ?", + "Output Program": [ + "n0 = 24.0\nn1 = 12.0\nt0 = n0 * n1 # area of rectangle\nt1 = 2 * (n0 + n1) # perimetere of rectangle\nt2 = t0 * 2.0\nt3 = t2 / t1\nanswer = n0 * n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "2304" + ], + "split": "train" + }, + { + "Input": "the perimeter of an equilateral triangle is 60 . if one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 50 , then how long is the base of isosceles triangle ?", + "Output Program": [ + "n0 = 60.0\nn1 = 50.0\nt0 = n0 / 3.0\nt1 = n1 - t0\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular field is 7 / 5 its width . if the perimeter of the field is 360 meters , what is the width of the field ?", + "Output Program": [ + "n0 = 7.0\nn1 = 5.0\nn2 = 360.0\nt0 = n0 / n1\nt1 = t0 + t0\nt2 = t1 + 2.0\nanswer = n2 / t2\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "there is a rectangular prism made of 1 in cubes that has been covered in tin foil . there are exactly 128 cubes that are not touching any tin foil on any of their sides . if the width of the figure created by these 128 cubes is twice the length and twice the height , what is the measure m in inches of the width of the foil covered prism ?", + "Output Program": [ + "n0 = 1.0\nn1 = 128.0\nn2 = 128.0\nt0 = 1 / 3.0\nt1 = n0 * 2.0\nt2 = n0 * t1\nt3 = n1 / t2\nt4 = t3**min(t0, 5)\nt5 = t1 * t4\nanswer = t5 + t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the perimeter of a triangle is 20 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle", + "Output Program": [ + "n0 = 20.0\nn1 = 2.5\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "find the area of the square , one of whose diagonals is 3.8 m long ?", + "Output Program": [ + "n0 = 3.8\nt0 = 1.0 / 2.0\nt1 = n0 * n0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "7.22" + ], + "split": "train" + }, + { + "Input": "what is the area of the square with the following coordinates : ( x , y ) , ( 20 , 20 ) , ( 20 , 9 ) , ( x , 9 ) ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 20.0\nn3 = 9.0\nn4 = 9.0\nt0 = n0 - n3\nanswer = t0**2\nprint(answer)" + ], + "Output Answer": [ + "121" + ], + "split": "train" + }, + { + "Input": "the width of a rectangular hall is \u00bd of its length . if the area of the hall is 450 sq . m , what is the difference between its length and breadth ?", + "Output Program": [ + "import math\nn0 = 450.0\nt0 = 1.0 / 2.0\nt1 = n0 / t0\nt2 = math.sqrt(max(0, t1))\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 8 , 0 ) , ( 0 , - 3.5 ) , ( - 8 , 0 ) ?", + "Output Program": [ + "n0 = 0.0\nn1 = 3.5\nn2 = 8.0\nn3 = 0.0\nn4 = 0.0\nn5 = 3.5\nn6 = 8.0\nn7 = 0.0\nt0 = n2 * 2.0\nt1 = n1 * 2.0\nanswer = t0 * t1 / 2\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "three table runners have a combined area of 208 square inches . by overlapping the runners to cover 80 % of a table of area 175 square inches , the area that is covered by exactly two layers of runner is 24 square inches . what is the area of the table that is covered with three layers of runner ?", + "Output Program": [ + "n0 = 208.0\nn1 = 80.0\nn2 = 175.0\nn3 = 24.0\nt0 = n1 / 100.0\nt1 = n0 - n3\nt2 = n2 * t0\nt3 = t1 - t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular garden is three times its width . if the area of the rectangular garden is 507 square meters , then what is the width of the rectangular garden ?", + "Output Program": [ + "import math\nn0 = 507.0\nt0 = n0 / 3.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is reduced by 15 % . by what % would the width have to be increased to maintain the original area ?", + "Output Program": [ + "n0 = 15.0\nt0 = 100.0 - n0\nt1 = t0 / 100.0\nt2 = 1.0 - t1\nt3 = t2 / t1\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "17.647058823529417" + ], + "split": "train" + }, + { + "Input": "when the oil from a circular cylinder leaked , the formula for the speed of the leak is v = kh ^ 2 , where h was the height of the remaining oil and k was constant . if the height of the cylinder is 4 , the speed of the leak is v \u00e2 \u20ac \u2122 , when the height of the oil remaining is 12 , what was the speed of the leak , in terms of v \u00e2 \u20ac \u2122 ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 12.0\nt0 = n2**min(2.0, 5)\nt1 = n1**min(2.0, 5)\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "in how many q ways can 5 people from a group of 6 people be seated around a circular table", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 6.0\nt0 = math.factorial(min(15, int(n1)))\nt1 = math.factorial(min(15, int(n0)))\nt2 = n0 - 1.0\nt3 = t0 / t1\nt4 = math.factorial(min(15, int(t2)))\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "train" + }, + { + "Input": "if the sum of a number and its square is 72 , what is the number ?", + "Output Program": [ + "import math\nn0 = 72.0\nt0 = math.sqrt(max(0, n0))\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 10 % ?", + "Output Program": [ + "n0 = 10.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = t1**min(2.0, 5)\nt3 = t2 - 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "21.000000000000018" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is 5 more than the width . what are the dimensions of the rectangle if the perimeter is 34 ?", + "Output Program": [ + "n0 = 5.0\nn1 = 34.0\nt0 = n1 / 2.0\nt1 = n0 + t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "the area of a base of a cone is 30 cm 2 . if the height of the cone is 6 cm , find its volume ?", + "Output Program": [ + "n0 = 30.0\nn1 = 2.0\nn2 = 6.0\nt0 = n0 * n2\nanswer = t0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is one - fourth of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1225 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?", + "Output Program": [ + "n0 = 1225.0\nn1 = 10.0\n\nanswer = n1 * n1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "the area of a square is equal to five times the area of a rectangle of dimensions 50 cm * 10 cm . what is the perimeter of the square ?", + "Output Program": [ + "import math\nn0 = 50.0\nn1 = 10.0\nt0 = n1 / 2.0\nt1 = n0 * n1 # area of rectangle\nt2 = t0 * t1\nt3 = math.sqrt(max(0, t2))\nanswer = t3 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "a took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m / min and b took the same time to cross the same field along its sides walking at the rate of 68 m / min . the area of the field is ?", + "Output Program": [ + "n0 = 15.0\nn1 = 52.0\nn2 = 68.0\nt0 = 2.0 * 4.0\nt1 = n2 - t0\nt2 = n0 / t1\nt3 = n2 * t2\nt4 = n1 * t2\nt5 = t3**min(2.0, 5)\nt6 = t4**min(2.0, 5)\nt7 = t5 - t6\nanswer = t7 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "a geometric shape is obtained by combining a square of side 8 cm and a semicircle of diameter 8 cm . what is the perimeter of the shape obtained ?", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 8.0\nt0 = n0 / 2.0\nt1 = 4 * n0\nt2 = 2 * math.pi * t0\nt3 = t1 - n0\nt4 = t2 / 2.0\nanswer = t4 + t3\nprint(answer)" + ], + "Output Answer": [ + "36.56637061435917" + ], + "split": "train" + }, + { + "Input": "a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 199 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ?", + "Output Program": [ + "n0 = 1.0\nn1 = 199.0\nt0 = 0.25 + 0.25\nt1 = n1 / 2.0\nt2 = t0 + t1\nanswer = t2**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "10000" + ], + "split": "train" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered . if the area of the field is 810 sq . feet , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 30.0\nn1 = 810.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "what will be the cost of building a fence around a square plot with area equal to 81 sq ft , if the price per foot of building the fence is rs . 58 ?", + "Output Program": [ + "import math\nn0 = 81.0\nn1 = 58.0\nt0 = math.sqrt(max(0, n0))\nt1 = 4 * t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "2088" + ], + "split": "train" + }, + { + "Input": "what is the area of a circle having the same perimeter as that of a square whose area is 121 .", + "Output Program": [ + "import math\nn0 = 121.0\nt0 = math.sqrt(max(0, n0))\nt1 = t0 * 4.0\nt2 = t1 / 3.141592653589793\nt3 = t2 / 2.0\nt4 = t3 * t3\nt5 = t4 * 3.141592653589793\nanswer = t5 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "308.1239698259094" + ], + "split": "train" + }, + { + "Input": "in measuring the sides of a rectangle , one side is taken 10 % in excess and other 5 % in deficit . find the error percentage in the area calculated from these measurements .", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nt0 = n0 * n1\nt1 = n0 - n1\nt2 = t0 / 100.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "4.5" + ], + "split": "train" + }, + { + "Input": "if the length of the longest chord of a certain circle is 20 , what is the radius of that certain circle ?", + "Output Program": [ + "n0 = 20.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "a piece of paper is in the shape of a right angled triangle and is cut along a line that is parallel to the hypotenuse , leaving a smaller triangle . there was a 35 % reduction in the length of the hypotenuse of the triangle . if the area of the original triangle was 34 square inches before the cut , what is the area ( in square inches ) of the smaller triangle ?", + "Output Program": [ + "n0 = 35.0\nn1 = 34.0\nt0 = n0 / 100.0\nt1 = 1.0 - t0\nt2 = t1**min(2.0, 5)\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "14.365000000000002" + ], + "split": "train" + }, + { + "Input": "how much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 19 inches than that of a rectangular sheet of paper measuring 9.5 inches by 11 inches ?", + "Output Program": [ + "n0 = 11.0\nn1 = 19.0\nn2 = 9.5\nn3 = 11.0\nt0 = n0 * n1 # area of rectangle\nt1 = n0 * n2 # area of rectangle\nt2 = t0 * 2.0\nt3 = t1 * 2.0\nt4 = t2 - t3\nt5 = t4 / t0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "a block of wood has dimensions 10 cm x 10 cm x 80 cm . the block is painted red and then cut evenly at the 40 cm mark , parallel to the sides , to form two rectangular solids of equal volume . what percentage of the surface area of each of the new solids is not painted red ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\nn2 = 80.0\nn3 = 40.0\nt0 = 100.0 * 4.0\nt1 = t0 * 4.0\nt2 = t1 + 100.0\nt3 = t2 + 100.0\nt4 = 100.0 / t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "5.555555555555555" + ], + "split": "train" + }, + { + "Input": "what is the perimeter , in meters , of a rectangular garden 4 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide ?", + "Output Program": [ + "n0 = 4.0\nn1 = 16.0\nn2 = 12.0\nt0 = n1 * n2 # area of rectangle\nt1 = t0 / 4.0\nanswer = 2 * (n0 + t1) # perimetere of rectangle\nprint(answer)" + ], + "Output Answer": [ + "104" + ], + "split": "train" + }, + { + "Input": "find the area of right angled triangle whose hypotenuse is 15 cm and one of the sides is 12 cm .", + "Output Program": [ + "import math\nn0 = 15.0\nn1 = 12.0\nt0 = n0**min(2.0, 5)\nt1 = n1**min(2.0, 5)\nt2 = t0 - t1\nt3 = math.sqrt(max(0, t2))\nt4 = n1 * t3\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "the sides of a square region , measured to the nearest centimeter , are 5 centimeters long . the least possible value of the actual area of the square region is", + "Output Program": [ + "n0 = 5.0\nt0 = n0 - 0.25\nt1 = t0 - 0.25\nanswer = t1**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "20.25" + ], + "split": "train" + }, + { + "Input": "if circles x and y have the same area and circle x has a circumference of 14 \u03c0 , half of the radius of circle y is :", + "Output Program": [ + "n0 = 14.0\nt0 = n0 / 2.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "3.5" + ], + "split": "train" + }, + { + "Input": "the lateral surface area of cube is 100 sq . units . find the volume of cube ?", + "Output Program": [ + "import math\nn0 = 100.0\nt0 = n0 / 4.0\nt1 = math.sqrt(max(0, t0))\nanswer = t1**min(3.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "36 people { a 1 , a 2 , . . . , a 36 } meet and shake hands in a circular fashion . in other words , there are totally 36 handshakes involving the pairs , { a 1 , a 2 } , { a 2 , a 3 } , . . . , { a 35 , a 36 } , { a 36 , a 1 } . then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is", + "Output Program": [ + "n0 = 36.0\nn1 = 1.0\nn2 = 2.0\nn3 = 36.0\nn4 = 36.0\nn5 = 1.0\nn6 = 2.0\nn7 = 2.0\nn8 = 3.0\nn9 = 35.0\nn10 = 36.0\nn11 = 36.0\nn12 = 1.0\nt0 = n1 + n2\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "if the sum of a number and its square is 306 , what is the number ?", + "Output Program": [ + "import math\nn0 = 306.0\nt0 = math.sqrt(max(0, n0))\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "a rectangular lawn of dimensions 70 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?", + "Output Program": [ + "n0 = 70.0\nn1 = 60.0\nn2 = 10.0\nn3 = 3.0\nt0 = n0 + n1\nt1 = t0 - n2\nt2 = n2 * t1\nanswer = n3 * t2\nprint(answer)" + ], + "Output Answer": [ + "3600" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 675 sq m , then what is the breadth of the rectangular plot ?", + "Output Program": [ + "import math\nn0 = 675.0\nt0 = n0 / 3.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "a rectangular grass field is 75 m * 55 m , it has a path of 3.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?", + "Output Program": [ + "n0 = 75.0\nn1 = 55.0\nn2 = 3.5\nn3 = 2.0\nt0 = n2 * n3\nt1 = n0 * n1 # area of rectangle\nt2 = n0 + t0\nt3 = n1 + t0\nt4 = t2 * t3 # area of rectangle\nt5 = t4 - t1\nanswer = n3 * t5\nprint(answer)" + ], + "Output Answer": [ + "1918" + ], + "split": "train" + }, + { + "Input": "the circumferences of two circles are 268 meters and 380 meters . find the difference between the areas of the larger and the smaller circles .", + "Output Program": [ + "import math\nn0 = 268.0\nn1 = 380.0\nt0 = 2.0 * 3.141592653589793\nt1 = n1 / t0\nt2 = n0 / t0\nt3 = math.pi * t1**2\nt4 = math.pi * t2**2\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "5775.414574918697" + ], + "split": "train" + }, + { + "Input": "the monthly rent of a shop of dimension 10 feet \u00d7 8 feet is rs . 2400 . what is the annual rent per square foot of the shop ?", + "Output Program": [ + "n0 = 10.0\nn1 = 8.0\nn2 = 2400.0\nt0 = 10.0 + 2.0\nt1 = n0 * n1 # area of rectangle\nt2 = n2 / t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "a cube has a volume of 216 cubic feet . if a similar cube is twice as long , twice as wide , and twice as high , then the volume , in cubic feet of such cube is ?", + "Output Program": [ + "n0 = 216.0\nt0 = n0**(1 / 3)\nt1 = t0 * 2.0\nanswer = t1**3\nprint(answer)" + ], + "Output Answer": [ + "1727.9999999999993" + ], + "split": "train" + }, + { + "Input": "a square of 2 unit is given and four circles are made on its corners having equal radius of each . and another circle of equal radius is made on the center of the square . find out the area of square which is not covered by circles ?", + "Output Program": [ + "import math\nn0 = 2.0\nt0 = n0 / 2.0\nt1 = n0**2\nt2 = t0 / 2.0\nt3 = math.pi * t2**2\nt4 = t3 * 4.0\nanswer = t1 - t4\nprint(answer)" + ], + "Output Answer": [ + "0.8584073464102069" + ], + "split": "train" + }, + { + "Input": "if y is the smallest positive integer such that 31,360 multiplied by y is the square of an integer , then y must be", + "Output Program": [ + "n0 = 31360.0\nt0 = 2.0 + 3.0\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the length and breadth of a rectangular floor are 16.25 metre and 12.75 metre respectively . find how many minimum number of square tiles would be required to cover it completely ?", + "Output Program": [ + "n0 = 16.25\nn1 = 12.75\nt0 = 10.0 + 10.0\nt1 = 2.0 + 3.0\nt2 = n0 * 100.0\nt3 = n1 * 100.0\nt4 = t0 + t1\nt5 = t2 * t3 # area of rectangle\nt6 = t4 * t4\nanswer = t5 / t6\nprint(answer)" + ], + "Output Answer": [ + "3315" + ], + "split": "train" + }, + { + "Input": "a voltage will influence current only if the circuit is :", + "Output Program": [ + "n0 = 65.0\nn1 = 2.0\nn2 = 29.0\nn3 = 5.0\nt0 = n2 * n3\nt1 = n0 - n2\nt2 = t0 / t1\nt3 = n0 * t2\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "train" + }, + { + "Input": "the red triangle is equilateral with a side of 23 centimetres . its perimeter is", + "Output Program": [ + "n0 = 23.0\n\nanswer = n0 + n0 + n0 # perimeter of a triangle\nprint(answer)" + ], + "Output Answer": [ + "69" + ], + "split": "train" + }, + { + "Input": "calculate the effect changes in dimension of a rectangle will have on its area , if length is increased by 35 % and its breadth is decreased by 21 % ?", + "Output Program": [ + "n0 = 35.0\nn1 = 21.0\nt0 = n0 + 100.0\nt1 = 100.0 * 100.0\nt2 = 100.0 - n1\nt3 = t0 * t2\nt4 = t3 - t1\nt5 = t4 / t1\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "6.65" + ], + "split": "train" + }, + { + "Input": "a hall is 15 m long and 12 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , the volume of the hall is :", + "Output Program": [ + "n0 = 15.0\nn1 = 12.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nt2 = n0 * n1 # area of rectangle\nt3 = t0 + t1\nt4 = t2 * 2.0\nt5 = t4 / t3\nanswer = n0 * n1 * t5\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "train" + }, + { + "Input": "two cubes each with side b are joined to form a cuboids . what is the surface area of this cuboids ?", + "Output Program": [ + "t0 = 1.0 * 2.0\nt1 = 1.0 * 1.0\nt2 = t0 * 2.0\nt3 = t2 + t1\nanswer = t3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the largest four - digit number which is a perfect cube , is", + "Output Program": [ + "t0 = 10.0 * 2.0\nt1 = t0 + 1.0\nanswer = t1**min(3.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "9261" + ], + "split": "train" + }, + { + "Input": "a number when divided by 6 leaves a remainder 3 . when the square of the same number is divided by 6 , the remainder is", + "Output Program": [ + "n0 = 6.0\nn1 = 3.0\nn2 = 6.0\nt0 = n0 * n1\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a square was given . inside the square there are white tiles and black tiles . black tiles was among the diagonal of the square and dimensions of both white as well as black tiles is 1 cm x 1 cm . if there are 81 black tiles in the square . then find the no of white tiles in it .", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 81.0\nt0 = n0 + n2\nt1 = t0 / 2.0\nt2 = t1**min(2.0, 5)\nanswer = t2 - n2\nprint(answer)" + ], + "Output Answer": [ + "1600" + ], + "split": "train" + }, + { + "Input": "if the sides of a triangle are 26 cm , 22 cm and 10 cm , what is its area ?", + "Output Program": [ + "n0 = 26.0\nn1 = 22.0\nn2 = 10.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "110" + ], + "split": "train" + }, + { + "Input": "if the length of the sides of two cubes are in the ratio 5 : 1 , what is the ratio of their total surface area ?", + "Output Program": [ + "n0 = 5.0\nn1 = 1.0\n\nanswer = n0 * n0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular field is 7 / 5 its width . if the perimeter of the field is 288 meters , what is the width of the field ?", + "Output Program": [ + "n0 = 7.0\nn1 = 5.0\nn2 = 288.0\nt0 = n0 / n1\nt1 = t0 + t0\nt2 = t1 + 2.0\nanswer = n2 / t2\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "three rugs have a combined area of 200 square meters . by overlapping the rugs to cover floor area of 138 square meters , the area that is covered by exactly two layers of rug is 24 square meters . what is the area that is covered with three layers of rug ?", + "Output Program": [ + "n0 = 200.0\nn1 = 138.0\nn2 = 24.0\nt0 = n0 - n1\nt1 = t0 - n2\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "if anangletis defined as 1 percent of 1 degree , then how many anglets are there in a sixth of a circle ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nt0 = 2.0 + 4.0\nt1 = 3600.0 / 10.0\nt2 = n0 / t0\nt3 = t1 * 100.0\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "6000" + ], + "split": "train" + }, + { + "Input": "in a rectangular coordinate system , what is the area of a quadrilateral whose vertices have the coordinates ( 4 , - 3 ) , ( 4 , 7 ) , ( 12 , 2 ) , ( 12 , - 7 ) ?", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nn2 = 4.0\nn3 = 7.0\nn4 = 12.0\nn5 = 2.0\nn6 = 12.0\nn7 = 7.0\nt0 = n1 + n3\nt1 = n3 + n5\nt2 = n4 - n0\nt3 = t0 + t1\nt4 = t3 * t2\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "76" + ], + "split": "train" + }, + { + "Input": "the length and breadth of a rectangle is increased by 30 % and 45 % respectively . what is the increase in the area ?", + "Output Program": [ + "n0 = 30.0\nn1 = 45.0\nt0 = n0 + 100.0\nt1 = n1 + 100.0\nt2 = 100.0 * 100.0 # area of rectangle\nt3 = t0 * t1 # area of rectangle\nt4 = t3 - t2\nt5 = t4 * 100.0\nanswer = t5 / t2\nprint(answer)" + ], + "Output Answer": [ + "88.5" + ], + "split": "train" + }, + { + "Input": "a cylindrical cube of radius 12 cm contains water upto a depth of 20 cm . a spherical iron ball is dropped into the tub and thus the level of water is raised by 6.75 cm . the radius of the ball is :", + "Output Program": [ + "import math\nn0 = 12.0\nn1 = 20.0\nn2 = 6.75\nt0 = 1.0 / 3.0\nt1 = 4.0 * 3.141592653589793\nt2 = math.pi * n0**2 * n2\nt3 = t2 * 3.0\nt4 = t3 / t1\nanswer = t4**min(t0, 5)\nprint(answer)" + ], + "Output Answer": [ + "8.999999999999998" + ], + "split": "train" + }, + { + "Input": "the side of a square is increased by 20 % then how much % does its area increases ?", + "Output Program": [ + "n0 = 20.0\nt0 = n0 + 100.0\nt1 = 100.0**2\nt2 = t0**2\nt3 = t2 - t1\nt4 = t3 * 100.0\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "the area of a rectangular plot is 23 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?", + "Output Program": [ + "n0 = 23.0\nn1 = 10.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "train" + }, + { + "Input": "a square is drawn by joining the mid points of the sides of a given square in the same way and this process continues indefinitely . if a side of the first square is 4 cm , determine the sum of the areas all the square .", + "Output Program": [ + "n0 = 4.0\nt0 = 1.0 / 2.0\nt1 = n0**min(2.0, 5)\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "the area of a square is equal to twice the area of a rectangle of dimensions 32 cm * 64 cm . what is the perimeter of the square ?", + "Output Program": [ + "n0 = 32.0\nn1 = 64.0\n\nanswer = 4 * n1\nprint(answer)" + ], + "Output Answer": [ + "256" + ], + "split": "train" + }, + { + "Input": "a circle graph shows how the budget of a certain company was spent : 15 percent for transportation , 9 percent for research and development , 5 percent for utilities , 4 percent for equipment , 2 percent for supplies , and the remainder for salaries . if the area of each sector of the graph is proportional to the percent of the budget it represents , how many degrees of the circle are used to represent salaries ?", + "Output Program": [ + "n0 = 15.0\nn1 = 9.0\nn2 = 5.0\nn3 = 4.0\nn4 = 2.0\nt0 = n0 + n1\nt1 = n2 + t0\nt2 = n3 + t1\nt3 = n4 + t2\nt4 = t3 * 360.0\nt5 = t4 / 100.0\nanswer = 360.0 - t5\nprint(answer)" + ], + "Output Answer": [ + "234" + ], + "split": "train" + }, + { + "Input": "the area of a rectangular field is equal to 750 square meters . its perimeter is equal to 110 meters . find the width of this rectangle .", + "Output Program": [ + "import math\nn0 = 750.0\nn1 = 110.0\nt0 = n1 / 2.0\nt1 = n0 * 4.0\nt2 = t0 * t0\nt3 = t2 - t1\nt4 = math.sqrt(max(0, t3))\nt5 = t0 - t4\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "find the area of a parallelogram with base 32 cm and height 14 cm ?", + "Output Program": [ + "n0 = 32.0\nn1 = 14.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "448" + ], + "split": "train" + }, + { + "Input": "the width of a rectangular hall is \u00bd of its length . if the area of the hall is 578 sq . m , what is the difference between its length and breadth ?", + "Output Program": [ + "import math\nn0 = 578.0\nt0 = 1.0 / 2.0\nt1 = n0 / t0\nt2 = math.sqrt(max(0, t1))\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "train" + }, + { + "Input": "the edge of a cube is 3 a cm . find its surface ?", + "Output Program": [ + "n0 = 3.0\n\nanswer = 6 * n0**2 # surface of a cube\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "train" + }, + { + "Input": "the sides of the triangle are in the ratio 5 : 6 : 7 and its perimeter is 720 cm . the length of the longest side is ?", + "Output Program": [ + "n0 = 5.0\nn1 = 6.0\nn2 = 7.0\nn3 = 720.0\nt0 = n0 + n1\nt1 = n2 * n3\nt2 = n2 + t0\nanswer = t1 / t2\nprint(answer)" + ], + "Output Answer": [ + "280" + ], + "split": "train" + }, + { + "Input": "amit and ian paint a wall in alternating shifts . first amit paints alone , then ian paints alone , then amit paints alone , etc . during each of his shifts , amit paints 1 / 2 of the remaining unpainted area of the wall , while ian paints 1 / 3 of the remaining unpainted area of the wall during each of his shifts . if amit goes first , what fraction of the wall ' s area will remain unpainted after amit has completed his 6 th shift ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 1.0\nn3 = 3.0\nn4 = 6.0\nt0 = n0 / n1\nt1 = n0 - t0\nt2 = t1 / n3\nt3 = t1 - t2\nt4 = t3 / n1\nt5 = t4 / n3\nt6 = t4 - t5\nt7 = t6 / n1\nt8 = t7 / n3\nt9 = t7 - t8\nt10 = t9 / n1\nt11 = t10 / n3\nt12 = t10 - t11\nt13 = t12 / n1\nt14 = t13 / n3\nt15 = t13 - t14\nanswer = t15 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.00205761316872428" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is halved , while its breadth is tripled . wa tis the % changein area ?", + "Output Program": [ + "t0 = 1.0 / 2.0\nt1 = t0 * 3.0\nt2 = t1 - 1.0\nt3 = t2 / 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 363 sq m , then what is the breadth of the rectangular plot ?", + "Output Program": [ + "import math\nn0 = 363.0\nt0 = n0 / 3.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "rectangular tile each of size 50 cm by 40 cm must be laid horizontally on a rectangular floor of size 120 cm by 150 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :", + "Output Program": [ + "n0 = 50.0\nn1 = 40.0\nn2 = 120.0\nn3 = 150.0\nt0 = n2 * n3\nt1 = n0 * n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "a certain farmer pays $ 60 per acre per month to rent farmland . how much does the farmer pay per month to rent a rectangular plot of farmland that is 360 feet by 1210 feet ? ( 43,560 square feet = 1 acre )", + "Output Program": [ + "n0 = 60.0\nn1 = 360.0\nn2 = 1210.0\nn3 = 43560.0\nn4 = 1.0\nt0 = n1 * n2\nt1 = t0 / 10.0\nt2 = t0 / t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "train" + }, + { + "Input": "the slant height of a cone is 18 cm and radius of the base is 8 cm , find the curved surface of the cone ?", + "Output Program": [ + "n0 = 18.0\nn1 = 8.0\nt0 = n1 * 3.141592653589793\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "452.3893421169302" + ], + "split": "train" + }, + { + "Input": "find the smallest number which should be multiplied with 1152 to make it a perfect square .", + "Output Program": [ + "n0 = 1152.0\nt0 = n0 / 3.0\nt1 = t0 / 3.0\nt2 = t1 / 4.0\nt3 = t2 / 4.0\nanswer = t3 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 30 cm , find the sum of the perimeters of all the triangles .", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 3.0\nn3 = 2.0\nn4 = 1.0\nn5 = 30.0\nt0 = n5 + n5 + n5 # perimeter of a triangle\nanswer = t0 + t0\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "train" + }, + { + "Input": "find the area of a parallelogram with base 32 cm and height 15 cm .", + "Output Program": [ + "n0 = 32.0\nn1 = 15.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "480" + ], + "split": "train" + }, + { + "Input": "in a triangle , one side is 6 cm and another side is 8 cm . which of the following can be the perimeter of the triangle ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 8.0\nt0 = n0**min(2.0, 5)\nt1 = n1**min(2.0, 5)\nt2 = t0 + t1\nt3 = math.sqrt(max(0, t2))\nt4 = n0 + n1 + t3 # perimeter of a triangle\nanswer = t4 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "find the area of the quadrilateral of one of its diagonals is 50 cm and its off sets 10 cm and 8 cm ?", + "Output Program": [ + "n0 = 50.0\nn1 = 10.0\nn2 = 8.0\nt0 = n1 + n2\nt1 = 1.0 / 2.0\nt2 = t0 * t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "450" + ], + "split": "train" + }, + { + "Input": "the circumference of a circle is equal to 72 pi . find the radius of this circle .", + "Output Program": [ + "n0 = 72.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "in triangle pqr , the angle q = 90 degree , pq = 7 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz", + "Output Program": [ + "n0 = 90.0\nn1 = 7.0\nn2 = 8.0\nt0 = n1 * n2\nanswer = t0 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "5.6" + ], + "split": "train" + }, + { + "Input": "the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 1.0\nn2 = 8.0\nt0 = 1 / 2.0\nt1 = n0**2\nt2 = n2 * t1\nt3 = t2 / t0\nanswer = math.sqrt(max(0, t3))\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is increased by 45 % and its breadth is decreased by 20 % . what is the effect on its area ?", + "Output Program": [ + "n0 = 45.0\nn1 = 20.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "11600" + ], + "split": "train" + }, + { + "Input": "the area of sector of a circle whose radius is 15 metro and whose angle at the center is 42 \u00e2 \u00b0 is ?", + "Output Program": [ + "n0 = 15.0\nn1 = 42.0\nt0 = 3.0 + 4.0\nt1 = 3600.0 / 10.0\nt2 = 10.0 * 2.0\nt3 = n0**min(2.0, 5)\nt4 = t2 + 2.0\nt5 = n1 / t1\nt6 = t4 / t0\nt7 = t6 * t3\nanswer = t5 * t7\nprint(answer)" + ], + "Output Answer": [ + "82.5" + ], + "split": "train" + }, + { + "Input": "34 . the side surface of a cylinder can is rolled with a rectangular plate . if the height of a cylinder tank is 8 feet and the perimeter of the circular base is 6 feet , what is the diagonal of the rectangular plate ?", + "Output Program": [ + "import math\nn0 = 34.0\nn1 = 8.0\nn2 = 6.0\nt0 = n1**min(2.0, 5)\nt1 = n2**min(2.0, 5)\nt2 = t0 + t1\nanswer = math.sqrt(max(0, t2))\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the diagonals of a rhombus are 22 cm and 30 cm . find its area ?", + "Output Program": [ + "n0 = 22.0\nn1 = 30.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "330" + ], + "split": "train" + }, + { + "Input": "find the circumference and area of radius 8 cm .", + "Output Program": [ + "import math\nn0 = 8.0\n\nanswer = math.pi * n0**2\nprint(answer)" + ], + "Output Answer": [ + "201.06192982974676" + ], + "split": "train" + }, + { + "Input": "a rectangular paper , when folded into two congruent parts had a perimeter of 34 cm for each part folded along one set of sides and the same is 38 cm when folded along the other set of sides . what is the area of the paper ?", + "Output Program": [ + "n0 = 34.0\nn1 = 38.0\nt0 = n1 * 2.0\nt1 = t0 - n0\nt2 = t1 / 3.0\nt3 = t2 * 2.0\nt4 = n1 - t3\nanswer = t2 * t4\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "train" + }, + { + "Input": "the water level in a rectangular swimming pool measuring 60 feet by 10 feet is to be lowered by 6 inches . how many gallons of water must be removed ? ( 1 cu ft = 7.5 gallons )", + "Output Program": [ + "n0 = 60.0\nn1 = 10.0\nn2 = 6.0\nn3 = 1.0\nn4 = 7.5\nt0 = 10.0 + 2.0\nt1 = n2 / t0\nt2 = n0 * n1 * t1\nanswer = n4 * t2\nprint(answer)" + ], + "Output Answer": [ + "2250" + ], + "split": "train" + }, + { + "Input": "what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 56 ?", + "Output Program": [ + "import math\nn0 = 289.0\nn1 = 56.0\nt0 = math.sqrt(max(0, n0))\nt1 = 4 * t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "3808" + ], + "split": "train" + }, + { + "Input": "in measuring the sides of a rectangle , one side is taken 20 % in excess and the other 10 % in deficit . find the error per cent in area calculated from the measurement ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nt0 = n0 * n1\nt1 = n0 - n1\nt2 = t0 / 100.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a triangle has sides 10 , 17 , and 21 . a square is inscribed in the triangle . one side of the square lies on the longest side of the triangle . the other two vertices of the square touch the two shorter sides of the triangle . what is the length of the side of the square ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 17.0\nn2 = 21.0\nt0 = (lambda s, a, b, c: math.sqrt(max(0, s * (s - a) * (s - b) * (s - c))))((n0 + n1 + n2) / 2, n0, n1, n2) # Heron's formula\nt1 = t0 * 2.0\nt2 = t1 / n2\nt3 = t2 / n2\nt4 = t3 + 1.0\nanswer = t2 / t4\nprint(answer)" + ], + "Output Answer": [ + "5.793103448275862" + ], + "split": "train" + }, + { + "Input": "a 25 cm wide path is to be made around a circular garden having a diameter of 4 meters . approximate area of the path is square meters is", + "Output Program": [ + "import math\nn0 = 25.0\nn1 = 4.0\nt0 = n1 / 2.0\nt1 = n0 / 100.0\nt2 = t0 + t1\nt3 = math.pi * t0**2\nt4 = math.pi * t2**2\nanswer = t4 - t3\nprint(answer)" + ], + "Output Answer": [ + "3.3379421944391545" + ], + "split": "train" + }, + { + "Input": "find the area of the quadrilateral of one of its diagonals is 40 cm and its off sets 11 cm and 9 cm ?", + "Output Program": [ + "n0 = 40.0\nn1 = 11.0\nn2 = 9.0\nt0 = n1 + n2\nt1 = 1.0 / 2.0\nt2 = t0 * t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "the area of a triangle will be when a = 1 m , b = 2 m , c = 5 m , a , b , c being lengths of respective sides ?", + "Output Program": [ + "n0 = 1.0\nn1 = 2.0\nn2 = 5.0\nt0 = n0 + n1\nt1 = n2 + t0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is 18 cm and its breadth is 10 cm . when the length is increased to 25 cm , what will be the breadth of the rectangle if the area remains the same ?", + "Output Program": [ + "n0 = 18.0\nn1 = 10.0\nn2 = 25.0\nt0 = n0 * n1\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "7.2" + ], + "split": "train" + }, + { + "Input": "the area of the maximum size of the circle described from the 10 inch square ?", + "Output Program": [ + "import math\nn0 = 10.0\nt0 = n0 / 2.0\nanswer = math.pi * t0**2\nprint(answer)" + ], + "Output Answer": [ + "78.53981633974483" + ], + "split": "train" + }, + { + "Input": "a polygon has 44 diagonals , then the number of its sides are", + "Output Program": [ + "import math\nn0 = 44.0\nt0 = n0 * 2.0\nt1 = 3.0**min(2.0, 5)\nt2 = t0 * 4.0\nt3 = t2 + t1\nt4 = math.sqrt(max(0, t3))\nt5 = t4 + 3.0\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "how much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 17 inches than that of a rectangular sheet of paper measuring 8.5 inches by 11 inches ?", + "Output Program": [ + "n0 = 11.0\nn1 = 17.0\nn2 = 8.5\nn3 = 11.0\nt0 = n0 * n1 # area of rectangle\nt1 = n0 * n2 # area of rectangle\nt2 = t0 * 2.0\nt3 = t1 * 2.0\nt4 = t2 - t3\nt5 = t4 / t0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "three circles of radius 3.5 cm are placed in such a way that each circle touches the other two . the area of the portion enclosed by the circles is", + "Output Program": [ + "import math\nn0 = 3.5\nt0 = math.pi * n0**2\nt1 = n0 * 2.0\nt2 = t0 / 2.0\nt3 = (lambda s, a, b, c: math.sqrt(max(0, s * (s - a) * (s - b) * (s - c))))((t1 + t1 + t1) / 2, t1, t1, t1) # Heron's formula\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "1.975367389481267" + ], + "split": "train" + }, + { + "Input": "what is the ratio between perimeters of two squares one having 2 times the diagonal then the other ?", + "Output Program": [ + "n0 = 2.0\nt0 = n0 / n0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the volume of a certain substance is always directly proportional to its weight . if 48 cubic inches of the substance weigh 112 ounces , what is the volume , in cubic inches , of 56 ounces of this substance ?", + "Output Program": [ + "n0 = 48.0\nn1 = 112.0\nn2 = 56.0\nt0 = n0 / n1\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "what is the ratio g of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled ?", + "Output Program": [ + "t0 = 2.0 * 3.0\nt1 = 1.0 * 2.0\nt2 = 1.0 * 1.0\nt3 = t1 * 2.0\nt4 = t3 + t2\nt5 = t4 * 2.0\nanswer = t0 / t5\nprint(answer)" + ], + "Output Answer": [ + "0.6" + ], + "split": "train" + }, + { + "Input": "a box measuring 24 inches long by 40 inches wide by 16 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?", + "Output Program": [ + "n0 = 24.0\nn1 = 40.0\nn2 = 16.0\nt0 = n2 / 2.0\nt1 = n0 * n1\nt2 = n2 * t1\nt3 = t0**3\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "one side of a rectangular field is 15 m and one of its diagonal is 17 m . find the area of field ?", + "Output Program": [ + "import math\nn0 = 15.0\nn1 = 17.0\nt0 = n1**min(2.0, 5)\nt1 = n0**min(2.0, 5)\nt2 = t0 - t1\nt3 = math.sqrt(max(0, t2))\nanswer = n0 * t3 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "the area of circle o is added to its diameter . if the circumference of circle o is then subtracted from this total , the result is 12 . what is the radius of circle o ?", + "Output Program": [ + "n0 = 12.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the length and breadth of a square are increased by 40 % and 30 % respectively . the area of the rectangle so formed exceeds the area of the square by ?", + "Output Program": [ + "n0 = 40.0\nn1 = 30.0\nt0 = n0 / 100.0\nt1 = n1 / 100.0\nt2 = t0 + 1.0\nt3 = t1 + 1.0\nt4 = t2 * t3\nt5 = t4 - 1.0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "81.99999999999999" + ], + "split": "train" + }, + { + "Input": "the length of a rectangualr hll is 5 m more than its breadth . the area of the hall is 750 m . the length of the hall is", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 750.0\nt0 = n1 * 4.0\nt1 = n0**min(2.0, 5)\nt2 = t0 + t1\nt3 = math.sqrt(max(0, t2))\nt4 = n0 + t3\nt5 = t4 / 2.0\nanswer = t5 - n0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "a semicircle has a radius of 20 . what is the approximate perimeter of the semicircle ?", + "Output Program": [ + "import math\nn0 = 20.0\nt0 = 2 * math.pi * n0\nt1 = n0 * 2.0\nt2 = t0 / 2.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "102.83185307179586" + ], + "split": "train" + }, + { + "Input": "a lady builds 9 cm length , 12 cm width , and 3 cm height box using 3 cubic cm cubes . what is the minimum number of cubes required to build the box ?", + "Output Program": [ + "n0 = 9.0\nn1 = 12.0\nn2 = 3.0\nn3 = 3.0\nt0 = n0 * n1\nt1 = n2 * t0\nanswer = t1 / n3\nprint(answer)" + ], + "Output Answer": [ + "108" + ], + "split": "train" + }, + { + "Input": "the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 \u03c0 \u00b7 r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams w ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 0.15\nn3 = 8.0\nn4 = 0.3\n\nanswer = n0 * n3\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "rectangular tile each of size 35 cm by 30 cm must be laid horizontally on a rectangular floor of size 1000 cm by 210 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :", + "Output Program": [ + "n0 = 35.0\nn1 = 30.0\nn2 = 1000.0\nn3 = 210.0\nt0 = n2 * n3\nt1 = n0 * n1\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "there is a right angle triangle inside a circle of diameter 18 cm . inside this triangle , there is another circle of diameter 6 cm . find the perimeter of the triangle .", + "Output Program": [ + "n0 = 18.0\nn1 = 6.0\nt0 = n0 + n1\nanswer = n0 + t0\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "there are two circles of different radii . the are of a square is 784 sq cm and its side is twice the radius of the larger circle . the radius of the larger circle is seven - third that of the smaller circle . find the circumference of the smaller circle ?", + "Output Program": [ + "import math\nn0 = 784.0\nt0 = 3.0 + 4.0\nt1 = math.sqrt(n0) # square edge given area\nt2 = t1 / 2.0\nt3 = t0 / 3.0\nt4 = t2 / t3\nanswer = t4 + 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "if a 7 cm cube is cut into 1 cm cubes , then what is the percentage increase in the surface area of the resulting cubes ?", + "Output Program": [ + "n0 = 7.0\nn1 = 1.0\nt0 = 6 * n1**2 # surface of a cube\nt1 = 6 * n0**2 # surface of a cube\nt2 = t0 * t1\nt3 = t2 / t1\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "train" + }, + { + "Input": "if the radius of a circle that centers at the origin is 5 , how many k points on the circle have integer coordinates ?", + "Output Program": [ + "n0 = 5.0\nt0 = n0 + 4.0\nt1 = n0 * n0\nt2 = 2.0**min(2.0, 5)\nt3 = t1 - t0\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a circle in the coordinate plane passes through points ( - 3 , - 2 ) and ( 2 , 4 ) . what is the smallest possible area of that circle ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 2.0\nn2 = 2.0\nn3 = 4.0\nt0 = n0 + n2\nt1 = n1 + n3\nt2 = t0 * t0\nt3 = t1 * t1\nt4 = t2 + t3\nt5 = math.sqrt(max(0, t4))\nt6 = t5 / n1\nanswer = t6**2\nprint(answer)" + ], + "Output Answer": [ + "15.249999999999998" + ], + "split": "train" + }, + { + "Input": "spheres a and b have their radil 40 cm and 10 cm respectively . the ratio of the surface area of a to the surface area of b is", + "Output Program": [ + "import math\nn0 = 40.0\nn1 = 10.0\nt0 = 4 * math.pi * n0**2\nt1 = 4 * math.pi * n1**2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "a hall is 15 m long and 12 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , the volume of the hall is", + "Output Program": [ + "n0 = 15.0\nn1 = 12.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nt2 = n0 * n1 # area of rectangle\nt3 = t0 + t1\nt4 = t2 * 2.0\nt5 = t4 / t3\nanswer = n0 * n1 * t5\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "train" + }, + { + "Input": "the surface of a cube is 54 sq cm . find its volume ?", + "Output Program": [ + "import math\nn0 = 54.0\nt0 = 2.0 + 4.0\nt1 = n0 / t0\nt2 = math.sqrt(max(0, t1))\nanswer = t2**3\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "the parameter of a square is equal to the perimeter of a rectangle of length 14 cm and breadth 10 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ?", + "Output Program": [ + "import math\nn0 = 14.0\nn1 = 10.0\nt0 = 2 * (n0 + n1) # perimetere of rectangle\nt1 = t0 / 4. # square edge given perimeter\nt2 = t1 / 2.0\nt3 = 2 * math.pi * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "18.84955592153876" + ], + "split": "train" + }, + { + "Input": "a rectangular lawn of dimensions 90 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?", + "Output Program": [ + "n0 = 90.0\nn1 = 60.0\nn2 = 10.0\nn3 = 3.0\nt0 = n0 + n1\nt1 = t0 - n2\nt2 = n2 * t1\nanswer = n3 * t2\nprint(answer)" + ], + "Output Answer": [ + "4200" + ], + "split": "train" + }, + { + "Input": "what is the area of a square field whose diagonal of length 20 m ?", + "Output Program": [ + "n0 = 20.0\nt0 = n0**2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "rectangle a has sides a and b , and rectangle b has sides c and d . if a / c = b / d = 2 / 3 , what is the ratio of rectangle a \u2019 s area to rectangle b \u2019 s area ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nt0 = n0**min(2.0, 5)\nt1 = n1**min(2.0, 5)\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.4444444444444444" + ], + "split": "train" + }, + { + "Input": "square a has an area of 121 square centimeters . square b has a perimeter of 16 centimeters . if square b is placed within square a and a random point is chosen within square a , what is the probability the point is not within square b ?", + "Output Program": [ + "n0 = 121.0\nn1 = 16.0\nt0 = n1 / 4.0\nt1 = t0**min(2.0, 5)\nt2 = n0 - t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.8677685950413223" + ], + "split": "train" + }, + { + "Input": "a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is", + "Output Program": [ + "n0 = 48.0\nn1 = 36.0\nn2 = 8.0\nn3 = 3.0\nt0 = n2 * 2.0\nt1 = n0 - t0\nt2 = n1 - t0\nanswer = n2 * t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "5120" + ], + "split": "train" + }, + { + "Input": "when magnified 1,000 times by an electron microscope , the image of a certain circular piece of tissue has a diameter of 0.3 centimeter . the actual diameter of the tissue , in centimeters , is", + "Output Program": [ + "n0 = 1000.0\nn1 = 0.3\n\nanswer = n1 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.0003" + ], + "split": "train" + }, + { + "Input": "square a has an area of 25 square centimeters . square b has a perimeter of 12 centimeters . if square b is placed within square a and a random point is chosen within square a , what is the probability the point is not within square b ?", + "Output Program": [ + "n0 = 25.0\nn1 = 12.0\nt0 = n1 / 4.0\nt1 = t0**min(2.0, 5)\nt2 = n0 - t1\nanswer = t2 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.64" + ], + "split": "train" + }, + { + "Input": ") a cube is painted blue on all of its surfaces . it is then cut in to 27 smaller cubes of equal size . find how many smaller cubes have no color ?", + "Output Program": [ + "n0 = 27.0\nt0 = n0 / 3.0\nt1 = t0 / 3.0\nt2 = t1 - 2.0\nanswer = t2**3\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "a rectangular field has to be fenced on three sides leaving a side of 25 feet uncovered . if the area of the field is 880 sq . feet , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 25.0\nn1 = 880.0\nt0 = n1 / n0\nt1 = 2 * (n0 + t0) # perimetere of rectangle\nanswer = t1 - n0\nprint(answer)" + ], + "Output Answer": [ + "95.4" + ], + "split": "train" + }, + { + "Input": "a cube of edge 15 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 15 cm , find the rise in water level ?", + "Output Program": [ + "n0 = 15.0\nn1 = 20.0\nn2 = 15.0\nt0 = n1 * n2\nt1 = n0**3\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "11.25" + ], + "split": "train" + }, + { + "Input": "the area of a rectangular plot is 21 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?", + "Output Program": [ + "n0 = 21.0\nn1 = 10.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "the length of the rectangular field is double its width . inside the field there is square shaped pond 5 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 1.0\nn2 = 8.0\nt0 = 1 / 2.0\nt1 = n0**2\nt2 = n2 * t1\nt3 = t2 / t0\nanswer = math.sqrt(max(0, t3))\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "if the length of a rectangle is halved and its breadth is tripled , what is the percentage change in its area ?", + "Output Program": [ + "t0 = 3.0 / 2.0\nt1 = t0 - 1.0\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 720 sq . feet , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 20.0\nn1 = 720.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "92" + ], + "split": "train" + }, + { + "Input": "in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 9 , 0 ) , ( 0 , - 3.5 ) , ( - 9 , 0 ) ?", + "Output Program": [ + "n0 = 0.0\nn1 = 3.5\nn2 = 9.0\nn3 = 0.0\nn4 = 0.0\nn5 = 3.5\nn6 = 9.0\nn7 = 0.0\nt0 = n2 * 2.0\nt1 = n1 * 2.0\nanswer = t0 * t1 / 2\nprint(answer)" + ], + "Output Answer": [ + "63" + ], + "split": "train" + }, + { + "Input": "three rugs have a combined area of 200 square meters . by overlapping the rugs to cover floor area of 140 square meters , the area that is covered by exactly two layers of rug is 22 square meters . what is the area that is covered with three layers of rug ?", + "Output Program": [ + "n0 = 200.0\nn1 = 140.0\nn2 = 22.0\nt0 = n0 - n1\nt1 = t0 - n2\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "19" + ], + "split": "train" + }, + { + "Input": "find the surface area of a 10 cm x 4 cm x 2 cm brick .", + "Output Program": [ + "n0 = 10.0\nn1 = 4.0\nn2 = 2.0\n\nanswer = 2 * (n0 * n1 + n0 * n2 + n1 * n2) # surface of a rectangular prism\nprint(answer)" + ], + "Output Answer": [ + "136" + ], + "split": "train" + }, + { + "Input": "a rectangular field has a length 10 meters more than it is width . if the area of the field is 171 , what is the length ( in meters ) of the rectangular field ?", + "Output Program": [ + "n0 = 10.0\nn1 = 171.0\nt0 = n1 / n0\nt1 = t0 / 2.0\nt2 = t1 + 0.33\nt3 = t2 + 0.25\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "19.130000000000003" + ], + "split": "train" + }, + { + "Input": "three walls have wallpaper covering a combined area of 300 square meters . by overlapping the wallpaper to cover a wall with an area of 180 square meters , the area that is covered by exactly two layers of wallpaper is 38 square meters . what is the area that is covered with three layers of wallpaper ?", + "Output Program": [ + "n0 = 300.0\nn1 = 180.0\nn2 = 38.0\nt0 = n0 - n1\nt1 = t0 - n2\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "41" + ], + "split": "train" + }, + { + "Input": "if the length of a rectangular field is 30 metres more than its breadth and the perimeter of the field is 540 metres , what is the area of the field in square metres ?", + "Output Program": [ + "n0 = 30.0\nn1 = 540.0\nt0 = n0 * 2.0\nt1 = n1 - t0\nt2 = t1 / 4. # square edge given perimeter\nt3 = n0 + t2\nanswer = t3 * t2 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "18000" + ], + "split": "train" + }, + { + "Input": "what will be the cost of building a fence around a circular plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 58 ?", + "Output Program": [ + "import math\nn0 = 289.0\nn1 = 58.0\nt0 = n0 / 3.141592653589793\nt1 = math.sqrt(max(0, t0))\nt2 = 2 * math.pi * t1\nanswer = n1 * t2\nprint(answer)" + ], + "Output Answer": [ + "3495.2789939856775" + ], + "split": "train" + }, + { + "Input": "twenty eight meters of wire is available to fence off a flower bed in the form of a circular sector . what must the radius of the circle in meters be , if we wish to have a flower bed with the greatest possible surface area ?", + "Output Program": [ + "t0 = 10.0 + 4.0\nt1 = t0 * 2.0\nt2 = t1 / 2.0\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m cube ) is :", + "Output Program": [ + "n0 = 48.0\nn1 = 36.0\nn2 = 8.0\nt0 = n2 * 2.0\nt1 = n0 - t0\nt2 = n1 - t0\nanswer = n2 * t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "5120" + ], + "split": "train" + }, + { + "Input": "while calculating the edge of a square , a worker makes an error of 2 % in excess . what % error does he make in calculating area ? ( % )", + "Output Program": [ + "n0 = 2.0\nt0 = n0 + 100.0\nt1 = 100.0**2\nt2 = t0**2\nt3 = t2 - t1\nanswer = t3 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "4.04" + ], + "split": "train" + }, + { + "Input": "the perimeter of one face of a cube is 40 cm . its volume will be :", + "Output Program": [ + "n0 = 40.0\nt0 = n0 / 4. # square edge given perimeter\nanswer = t0**3\nprint(answer)" + ], + "Output Answer": [ + "1000" + ], + "split": "train" + }, + { + "Input": "a semicircle has a radius of 11 . what is the approximate perimeter of the semicircle ?", + "Output Program": [ + "import math\nn0 = 11.0\nt0 = 2 * math.pi * n0\nt1 = n0 * 2.0\nt2 = t0 / 2.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "56.55751918948772" + ], + "split": "train" + }, + { + "Input": "three table runners have a combined area of 204 square inches . by overlapping the runners to cover 80 % of a table of area 175 square inches , the area that is covered by exactly two layers of runner is 24 square inches . what is the area of the table that is covered with three layers of runner ?", + "Output Program": [ + "n0 = 204.0\nn1 = 80.0\nn2 = 175.0\nn3 = 24.0\nt0 = n1 / 100.0\nt1 = n0 - n3\nt2 = n2 * t0\nt3 = t1 - t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 9 , what is the measure of side xy ?", + "Output Program": [ + "import math\nn0 = 9.0\nt0 = math.sqrt(max(0, n0))\nt1 = math.sqrt(max(0, 2.0))\nt2 = t0 * t1\nt3 = t2**min(2.0, 5)\nt4 = t3 + t3\nanswer = math.sqrt(max(0, t4))\nprint(answer)" + ], + "Output Answer": [ + "6.000000000000001" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle hall is 5 m more than its breadth . the area of the hall is 750 m 2 . the length of the hall is :", + "Output Program": [ + "n0 = 5.0\nn1 = 750.0\nn2 = 2.0\nt0 = n1 / n0\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "a tailor trims 6 feet from opposite edges of a square piece of cloth , and 5 feet from the other two edges . if 120 square feet of cloth remain , what was the length of a side of the original piece of cloth ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 5.0\nn2 = 120.0\nt0 = n0 * 2.0\nt1 = n1 * 2.0\nt2 = t0 + t1\nt3 = t1 * t0\nt4 = t2**min(2.0, 5)\nt5 = n2 - t3\nt6 = t5 * n0\nt7 = t6 + t4\nt8 = math.sqrt(max(0, t7))\nt9 = t2 + t8\nanswer = t9 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "22" + ], + "split": "train" + }, + { + "Input": "find the area of a parallelogram with base 14 cm and height 24 cm .", + "Output Program": [ + "n0 = 14.0\nn1 = 24.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "336" + ], + "split": "train" + }, + { + "Input": "34 . the side surface of a cylinder is rolled with a rectangular plate . if the perimeter of the circular base is 6 feet , and the diagonal of the rectangular plate was 10 ft . what is height of the of the cylinder ?", + "Output Program": [ + "import math\nn0 = 34.0\nn1 = 6.0\nn2 = 10.0\nt0 = n2**min(2.0, 5)\nt1 = n1**min(2.0, 5)\nt2 = t0 - t1\nanswer = math.sqrt(max(0, t2))\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "what is the area of square field whose side of length 16 m ?", + "Output Program": [ + "n0 = 16.0\n\nanswer = n0**2\nprint(answer)" + ], + "Output Answer": [ + "256" + ], + "split": "train" + }, + { + "Input": "the percentage increase in the area of rectangle , if each of its side is increased by 10 % is ?", + "Output Program": [ + "n0 = 10.0\nt0 = n0 + 100.0\nt1 = t0 / 100.0\nt2 = t1 * t1\nt3 = t2 - 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "21.000000000000018" + ], + "split": "train" + }, + { + "Input": "the diameter of a cylindrical tin is 6 cm and height is 5 cm . find the volume of the cylinder ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 5.0\nt0 = n0 / 2.0\nt1 = math.pi * t0**2 * n1\nanswer = t1 / 3.141592653589793\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "a circle is inscribed in a triangle of side 6 cm . and a square is inscribed in the circle . what is the area of square ?", + "Output Program": [ + "import math\nn0 = 6.0\nt0 = n0 * n0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "if the area of a triangle with base 6 cm is equal to the area of a square with side 6 cm , then the altitude of the triangle is", + "Output Program": [ + "n0 = 6.0\nn1 = 6.0\nt0 = n0**2\nt1 = t0 * 2.0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "abcd is a square where ab = \u00e2 \u02c6 \u0161 4004 . let x be a point on ab and y be a point on cd such that ax = cy . compute the area of trapezoid axyd .", + "Output Program": [ + "n0 = 4004.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "2002" + ], + "split": "train" + }, + { + "Input": "if circles x and y have the same area and circle x has a circumference of 20 \u03c0 , half of the radius of circle y is :", + "Output Program": [ + "n0 = 20.0\nt0 = n0 / 2.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 9 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?", + "Output Program": [ + "n0 = 25.0\nn1 = 15.0\nn2 = 12.0\nn3 = 9.0\nn4 = 6.0\nn5 = 3.0\nn6 = 4.0\nn7 = 3.0\nt0 = n0 + n1\nt1 = n2 * 2.0\nt2 = n4 * n5\nt3 = n5 * n6\nt4 = t0 * t1\nt5 = n5 * t3\nt6 = t4 - t2\nt7 = t6 - t5\nanswer = n3 * t7\nprint(answer)" + ], + "Output Answer": [ + "8154" + ], + "split": "train" + }, + { + "Input": "a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck ' s tank is completely filled . if the truck ' s tank has a radius of 5 feet and a height of 10 feet , how far did the oil level drop in the stationary tank ?", + "Output Program": [ + "import math\nn0 = 100.0\nn1 = 25.0\nn2 = 5.0\nn3 = 10.0\nt0 = math.pi * n0**2\nt1 = math.pi * n2**2 * n3\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.025" + ], + "split": "train" + }, + { + "Input": "the surface of a cube is 150 sq cm . find its volume ?", + "Output Program": [ + "import math\nn0 = 150.0\nt0 = 2.0 + 4.0\nt1 = n0 / t0\nt2 = math.sqrt(max(0, t1))\nanswer = t2**3\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "a diagonal of a polygon is an segment between two non - adjacent vertices of the polygon . how many diagonals does a regular 40 - sided polygon have ?", + "Output Program": [ + "n0 = 40.0\nt0 = n0 - 3.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "740" + ], + "split": "train" + }, + { + "Input": "in a company of 160 employees , 90 are females . a total of 80 employees have advanced degrees and the rest have a college degree only . if 40 employees are males with college degree only , how many employees are females with advanced degrees ?", + "Output Program": [ + "n0 = 160.0\nn1 = 90.0\nn2 = 80.0\nn3 = 40.0\nt0 = n0 - n1\nt1 = t0 - n3\nanswer = n2 - t1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "the edge of a cube is 6 a cm . find its surface ?", + "Output Program": [ + "n0 = 6.0\n\nanswer = 6 * n0**2 # surface of a cube\nprint(answer)" + ], + "Output Answer": [ + "216" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is reduced by 30 % . by what % would the width have to be increased to maintain the original area ?", + "Output Program": [ + "n0 = 30.0\nt0 = 100.0 - n0\nt1 = t0 / 100.0\nt2 = 1.0 - t1\nt3 = t2 / t1\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "42.85714285714287" + ], + "split": "train" + }, + { + "Input": "line l passes through the points ( - 2,0 ) and ( 0 , a ) . line ll passes through the points ( 4,0 ) and ( 6,2 ) . what value of a makes the two lines parallel ?", + "Output Program": [ + "n0 = 2.0\nn1 = 0.0\nn2 = 0.0\nn3 = 4.0\nn4 = 0.0\nn5 = 6.0\nn6 = 2.0\n\nanswer = 2.0 - n1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "the perimeter of one face a of cube is 20 cm . its volume must be", + "Output Program": [ + "n0 = 20.0\nt0 = n0 / 4. # square edge given perimeter\nanswer = t0**3\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "the area of a rectangle is 460 square metres . if the length is 15 % more than the breadth , what is the breadth of the rectangular field ?", + "Output Program": [ + "import math\nn0 = 460.0\nn1 = 15.0\nt0 = n1 / 100.0\nt1 = t0 + 1.0\nt2 = n0 / t1\nanswer = math.sqrt(max(0, t2))\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 5 inches by 24 inches and jordan ' s rectangle is 12 inches long , how wide is jordan ' s rectangle , in inches ?", + "Output Program": [ + "n0 = 5.0\nn1 = 24.0\nn2 = 12.0\nt0 = n0 * n1 # area of rectangle\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "a rectangular field has to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 680 sq . feet , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 20.0\nn1 = 680.0\nt0 = n1 / n0\nt1 = 2 * (n0 + t0) # perimetere of rectangle\nanswer = t1 - n0\nprint(answer)" + ], + "Output Answer": [ + "88" + ], + "split": "train" + }, + { + "Input": "each side of a rectangle is increased by 100 % . by what percentage does the area increase ?", + "Output Program": [ + "n0 = 100.0\nt0 = 2.0 * 2.0\nt1 = t0 - 1.0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "what is the area of a triangle with the following vertices l ( 2 , 3 ) , m ( 5 , 1 ) , and n ( 3 , 5 ) ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 3.0\nn2 = 5.0\nn3 = 1.0\nn4 = 3.0\nn5 = 5.0\nt0 = n2 - n0\nt1 = n3 - n1\nt2 = n0 - n1\nt3 = n1 - n2\nt4 = n3 - n2\nt5 = t0**min(2.0, 5)\nt6 = t1**min(2.0, 5)\nt7 = t2**min(2.0, 5)\nt8 = t3**min(2.0, 5)\nt9 = t4**min(2.0, 5)\nt10 = t5 + t6\nt11 = t7 + t8\nt12 = t9 + t8\nt13 = math.sqrt(max(0, t10))\nt14 = math.sqrt(max(0, t11))\nt15 = math.sqrt(max(0, t12))\nanswer = (lambda s, a, b, c: math.sqrt(max(0, s * (s - a) * (s - b) * (s - c))))((t13 + t14 + t15) / 2, t13, t14, t15) # Heron's formula\nprint(answer)" + ], + "Output Answer": [ + "4.000000000000001" + ], + "split": "train" + }, + { + "Input": "the perimeter of an isosceles right triangle is 4 + 4 sq rt 2 . what is the length of the hypotenuse of the triangle ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 4.0\nn2 = 2.0\nt0 = math.sqrt(max(0, n2))\nt1 = n0 * t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "2.8284271247461903" + ], + "split": "train" + }, + { + "Input": "an 11 - meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point ?", + "Output Program": [ + "import math\nn0 = 11.0\nn1 = 4.0\nt0 = math.sqrt(max(0, n1))\nt1 = 4 * t0\nt2 = n0 - t1\nt3 = t2 / n0\nanswer = t3 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "0.5454545454545454" + ], + "split": "train" + }, + { + "Input": "the supplementary of an angle is thrice its complimentary . find the angle .", + "Output Program": [ + "t0 = 100.0 - 10.0\nt1 = t0 * 3.0\nt2 = t0 * 2.0\nt3 = t1 - t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "a cheese factory sells its cheese in rectangular blocks . a normal block has a volume of three cubic feet . if a large block has twice the width , twice the depth , and three times the length of a normal block , what is the volume of cheese in a large block in cubic feet ?", + "Output Program": [ + "t0 = 2.0 * 2.0\nt1 = t0 * 3.0\nanswer = t1 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "a rectangular tiled patio is composed of 126 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 126 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?", + "Output Program": [ + "import math\nn0 = 126.0\nn1 = 2.0\nn2 = 4.0\nn3 = 126.0\nt0 = n0 * n1\nt1 = -n2\nt2 = n2**min(2.0, 5)\nt3 = n2 * t0\nt4 = t3 + t2\nt5 = math.sqrt(max(0, t4))\nt6 = t1 + t5\nt7 = t6 / 2.0\nanswer = n0 / t7\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "a rectangular floor is covered by a rug except for a strip 2 meters wide along each of the four edge . if the floor is 10 meters by 8 meters , what is the area of the rug in square meters ?", + "Output Program": [ + "n0 = 2.0\nn1 = 10.0\nn2 = 8.0\nt0 = n0 * 2.0\nt1 = n1 - t0\nt2 = n2 - t0\nanswer = t1 * t2 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "the area of a parallelogram is 98 sq m and its altitude is twice the corresponding base . then the length of the base is ?", + "Output Program": [ + "import math\nn0 = 98.0\nt0 = n0 / 2.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a small , rectangular park has a perimeter of 560 feet and a diagonal measurement of 100 feet . what is its area , in square feet ?", + "Output Program": [ + "n0 = 560.0\nn1 = 100.0\nt0 = 2.0 + 3.0\nt1 = n1 / t0\nt2 = t1 * 3.0\nt3 = t1 * 4.0\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "4800" + ], + "split": "train" + }, + { + "Input": "if the diagonal of a rectangle is 17 cm long and its perimeter is 46 cm , find the area of the rectangle .", + "Output Program": [ + "n0 = 17.0\nn1 = 46.0\nt0 = n1 / 2.0\nt1 = n0**min(2.0, 5)\nt2 = t0**min(2.0, 5)\nt3 = t2 - t1\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "if the length of the longest chord of a certain circle is 14 , what is the radius of that certain circle ?", + "Output Program": [ + "n0 = 14.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "the area of a rectangular field is equal to 800 square meters . its perimeter is equal to 120 meters . find the width of this rectangle .", + "Output Program": [ + "import math\nn0 = 800.0\nn1 = 120.0\nt0 = n1 / 2.0\nt1 = n0 * 4.0\nt2 = t0 * t0\nt3 = t2 - t1\nt4 = math.sqrt(max(0, t3))\nt5 = t0 - t4\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "find the area of the quadrilateral of one of its diagonals is 30 cm and its off sets 9 cm and 6 cm ?", + "Output Program": [ + "n0 = 30.0\nn1 = 9.0\nn2 = 6.0\nt0 = n1 + n2\nt1 = 1.0 / 2.0\nt2 = t0 * t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "225" + ], + "split": "train" + }, + { + "Input": "if the height of a triangle is decreased by 40 % , land its base is increased by 40 % , what will be the effect on its area ?", + "Output Program": [ + "n0 = 40.0\nn1 = 40.0\nt0 = n0 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = 100.0 - t3\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "find the surface area of a cuboid 12 m long , 14 m broad and 7 m high", + "Output Program": [ + "n0 = 12.0\nn1 = 14.0\nn2 = 7.0\nt0 = n0 * n1\nt1 = n0 * n2\nt2 = n1 * n2\nt3 = t0 + t1\nt4 = t3 + t2\nanswer = t4 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "700" + ], + "split": "train" + }, + { + "Input": "the size of a flat - screen tablet is given as the length of the screen \u2019 s diagonal . how many square inches greater is the screen of a square 6 - inch flat - screen tablet than a square 5 - inch flat - screen tablet ?", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nt0 = n0**min(2.0, 5)\nt1 = n1**min(2.0, 5)\nt2 = t0 / 2.0\nt3 = t1 / 2.0\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "5.5" + ], + "split": "train" + }, + { + "Input": "the monthly rent of a shop of dimension 18 feet \u00d7 20 feet is rs . 3600 . what is the annual rent per square foot of the shop ?", + "Output Program": [ + "n0 = 18.0\nn1 = 20.0\nn2 = 3600.0\nt0 = 10.0 + 2.0\nt1 = n0 * n1 # area of rectangle\nt2 = n2 / t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "the volume of a box with a square base is 128 cubic cm . the area of the base of the box is 8 inches more than the height . what is the length of the base of the box ?", + "Output Program": [ + "import math\nn0 = 128.0\nn1 = 8.0\nt0 = n0 * 4.0\nt1 = n1**min(2.0, 5)\nt2 = t0 + t1\nt3 = math.sqrt(max(0, t2))\nt4 = n1 + t3\nt5 = t4 / 2.0\nanswer = math.sqrt(max(0, t5))\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "how many diagonals does a polygon with 23 sides have , if one of its vertices does not connect to any diagonal ?", + "Output Program": [ + "n0 = 23.0\nt0 = n0 - 1.0\nt1 = t0 - 3.0\nt2 = t0 * t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "209" + ], + "split": "train" + }, + { + "Input": "the length of rectangle is thrice its breadth and its perimeter is 96 m , find the area of the rectangle ?", + "Output Program": [ + "n0 = 96.0\nt0 = 2.0 * 3.0\nt1 = 1.0 * 2.0\nt2 = t0 + t1\nt3 = n0 / t2\nt4 = t3 * 3.0\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "432" + ], + "split": "train" + }, + { + "Input": "find the volume , curved surface area and the total surface area of a cylinder with diameter of base 7 cm and height 40 cm .", + "Output Program": [ + "n0 = 7.0\nn1 = 40.0\nt0 = n0 / 2.0\nt1 = n0 * 3.141592653589793\nt2 = n1 * t1\nt3 = t0**min(2.0, 5)\nt4 = t3 * 3.141592653589793\nt5 = t4 * 2.0\nanswer = t5 + t2\nprint(answer)" + ], + "Output Answer": [ + "956.614963018092" + ], + "split": "train" + }, + { + "Input": "what is the smallest positive integer x , such that 1152 x is a perfect cube ?", + "Output Program": [ + "import math\nn0 = 1152.0\nt0 = 1.0 / 3.0\nt1 = n0**min(t0, 5)\nt2 = t1 + 2.0\nanswer = math.floor(t2)\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a 6 - meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 1 if the original wire was cut at an arbitrary point ?", + "Output Program": [ + "n0 = 6.0\nn1 = 1.0\nt0 = 4 * n1\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.6666666666666666" + ], + "split": "train" + }, + { + "Input": "the parameter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 10 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ?", + "Output Program": [ + "import math\nn0 = 18.0\nn1 = 10.0\nt0 = 2 * (n0 + n1) # perimetere of rectangle\nt1 = t0 / 4. # square edge given perimeter\nt2 = t1 / 2.0\nt3 = 2 * math.pi * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "21.991148575128552" + ], + "split": "train" + }, + { + "Input": "if paint costs $ 3.20 per quart , and a quart covers 120 square feet , how much will it cost to paint the outside of a cube 10 feet on each edge ?", + "Output Program": [ + "n0 = 3.2\nn1 = 120.0\nn2 = 10.0\nt0 = n0 / n1\nt1 = 6 * n2**2 # surface of a cube\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the parameter of a square is equal to the perimeter of a rectangle of length 20 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )", + "Output Program": [ + "import math\nn0 = 20.0\nn1 = 14.0\nt0 = 2 * (n0 + n1) # perimetere of rectangle\nt1 = t0 / 4. # square edge given perimeter\nt2 = t1 / 2.0\nt3 = 2 * math.pi * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "26.703537555513243" + ], + "split": "train" + }, + { + "Input": "the width of a rectangular hall is \u00bd of its length . if the area of the hall is 200 sq . m , what is the difference between its length and breadth ?", + "Output Program": [ + "import math\nn0 = 200.0\nt0 = 1.0 / 2.0\nt1 = n0 / t0\nt2 = math.sqrt(max(0, t1))\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "the area of sector of a circle whose radius is 12 metro and whose angle at the center is 41 \u00b0 is ?", + "Output Program": [ + "n0 = 12.0\nn1 = 41.0\nt0 = 3.0 + 4.0\nt1 = 3600.0 / 10.0\nt2 = 10.0 * 2.0\nt3 = n0**min(2.0, 5)\nt4 = t2 + 2.0\nt5 = n1 / t1\nt6 = t4 / t0\nt7 = t6 * t3\nanswer = t5 * t7\nprint(answer)" + ], + "Output Answer": [ + "51.54285714285714" + ], + "split": "train" + }, + { + "Input": "a rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?", + "Output Program": [ + "n0 = 80.0\nn1 = 60.0\nn2 = 10.0\nn3 = 3.0\nt0 = n0 + n1\nt1 = t0 - n2\nt2 = n2 * t1\nanswer = n3 * t2\nprint(answer)" + ], + "Output Answer": [ + "3900" + ], + "split": "train" + }, + { + "Input": "a equilateral triangle having one side 5 m . in this triangle there is a square of side 2 m . calculate the percentage of area outside square in that triangle .", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 2.0\nt0 = n0**min(2.0, 5)\nt1 = math.sqrt(max(0, 3.0))\nt2 = n1**2\nt3 = t1 / 4.0\nt4 = t3 * t0\nt5 = t4 - t2\nt6 = t5 / t4\nanswer = t6 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "63.04958277186395" + ], + "split": "train" + }, + { + "Input": "six dots are evenly spaced on the circumference of a circle . how many combinations of three dots can we make from these 6 dots that do not form an equilateral triangle ?", + "Output Program": [ + "import math\nn0 = 6.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(3.0)))\nt2 = t1 * t1\nt3 = t0 / t2\nanswer = t3 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck ' s tank is completely filled . if the truck ' s tank has a radius of 7 feet and a height of 10 feet , how far ( in feet ) did the oil level drop in the stationary tank ?", + "Output Program": [ + "import math\nn0 = 100.0\nn1 = 25.0\nn2 = 7.0\nn3 = 10.0\nt0 = math.pi * n0**2\nt1 = math.pi * n2**2 * n3\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.049" + ], + "split": "train" + }, + { + "Input": "three table runners have a combined area of 212 square inches . by overlapping the runners to cover 80 % of a table of area 175 square inches , the area that is covered by exactly two layers of runner is 24 square inches . what is the area of the table that is covered with three layers of runner ?", + "Output Program": [ + "n0 = 212.0\nn1 = 80.0\nn2 = 175.0\nn3 = 24.0\nt0 = n1 / 100.0\nt1 = n0 - n3\nt2 = n2 * t0\nt3 = t1 - t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "a sporting good store sells one type of baseball bat and one type of baseball . the cost for 2 bats and 4 balls is $ 200 . the cost for 1 bat and 6 balls is $ 220 , as well . if someone were to buy an equal number of bats and balls , at most how many bats can he purchase if he has a budget of $ 210 for the purchase ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 200.0\nn3 = 1.0\nn4 = 6.0\nn5 = 220.0\nn6 = 210.0\nt0 = n2 / 2.0\nt1 = n5 - t0\nt2 = t1 / n1\nt3 = n4 * t2\nt4 = n5 - t3\nt5 = t2 + t4\nanswer = n6 / t5\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "find the area of a parallelogram with base 12 cm and height 18 cm .", + "Output Program": [ + "n0 = 12.0\nn1 = 18.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "216" + ], + "split": "train" + }, + { + "Input": "the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 \u03c0 \u00b7 r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams e ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 0.15\nn3 = 8.0\nn4 = 0.3\n\nanswer = n0 * n3\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "if the sides of a triangle are 26 cm , 24 cm and 20 cm , what is its area ?", + "Output Program": [ + "n0 = 26.0\nn1 = 24.0\nn2 = 20.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "240" + ], + "split": "train" + }, + { + "Input": "a metallic sheet is of rectangular shape with dimensions 48 m x 38 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is :", + "Output Program": [ + "n0 = 48.0\nn1 = 38.0\nn2 = 8.0\nn3 = 3.0\nt0 = n2 * 2.0\nt1 = n0 - t0\nt2 = n1 - t0\nanswer = n2 * t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "5632" + ], + "split": "train" + }, + { + "Input": "what is the area of square field whose side of length 15 m ?", + "Output Program": [ + "n0 = 15.0\n\nanswer = n0**2\nprint(answer)" + ], + "Output Answer": [ + "225" + ], + "split": "train" + }, + { + "Input": "10 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?", + "Output Program": [ + "n0 = 10.0\nn1 = 7.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nt2 = n0 * t1\nt3 = t2 / 2.0\nanswer = t3 + t0\nprint(answer)" + ], + "Output Answer": [ + "115" + ], + "split": "train" + }, + { + "Input": "the slant height of a cone is 10 cm and radius of the base is 5 cm , find the curved surface of the cone .", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nt0 = n1 * 3.141592653589793\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "157.07963267948966" + ], + "split": "train" + }, + { + "Input": "find the area of a parallelogram with base 30 cm and height 12 cm ?", + "Output Program": [ + "n0 = 30.0\nn1 = 12.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "360" + ], + "split": "train" + }, + { + "Input": "the diagonals of a rhombus are 15 cm and 12 cm . find its area ?", + "Output Program": [ + "n0 = 15.0\nn1 = 12.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "what is the ratio between perimeters of two squares one having 3 times the diagonal then the other ?", + "Output Program": [ + "n0 = 3.0\nt0 = n0 / 3.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "find the area of the quadrilateral of one of its diagonals is 30 cm and its off sets 10 cm and 6 cm ?", + "Output Program": [ + "n0 = 30.0\nn1 = 10.0\nn2 = 6.0\nt0 = n1 + n2\nt1 = 1.0 / 2.0\nt2 = t0 * t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "240" + ], + "split": "train" + }, + { + "Input": "if the sides of a triangle are 26 cm , 24 cm and 12 cm , what is its area ?", + "Output Program": [ + "n0 = 26.0\nn1 = 24.0\nn2 = 12.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "train" + }, + { + "Input": "the volume of a certain substance is always directly proportional to its weight . if 48 cubic inches of the substance weigh 112 ounces , what is the volume , in cubic inches , of 84 ounces of this substance ?", + "Output Program": [ + "n0 = 48.0\nn1 = 112.0\nn2 = 84.0\nt0 = n0 / n1\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck ' s tank is completely filled . if the truck ' s tank has a radius of 5 feet and a height of 12 feet , how far ( in feet ) did the oil level drop in the stationary tank ?", + "Output Program": [ + "import math\nn0 = 100.0\nn1 = 25.0\nn2 = 5.0\nn3 = 12.0\nt0 = math.pi * n0**2\nt1 = math.pi * n2**2 * n3\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.03" + ], + "split": "train" + }, + { + "Input": "a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 5 feet . how many feet does the squirrel travels if the post is 25 feet tall and 3 feet in circumference ?", + "Output Program": [ + "n0 = 5.0\nn1 = 25.0\nn2 = 3.0\nt0 = n1 / n0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "a circular well with a diameter of 4 metres , is dug to a depth of 14 metres . what is the volume of the earth dug out ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 14.0\nt0 = n0 / 2.0\nanswer = math.pi * t0**2 * n1\nprint(answer)" + ], + "Output Answer": [ + "175.92918860102841" + ], + "split": "train" + }, + { + "Input": "what is the area of a square field whose diagonal of length 30 m ?", + "Output Program": [ + "n0 = 30.0\nt0 = n0**2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "450" + ], + "split": "train" + }, + { + "Input": "a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m ^ 3 ) is :", + "Output Program": [ + "n0 = 48.0\nn1 = 36.0\nn2 = 8.0\nn3 = 3.0\nt0 = n2 * 2.0\nt1 = n0 - t0\nt2 = n1 - t0\nanswer = n2 * t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "5120" + ], + "split": "train" + }, + { + "Input": "two circular frames are kept one above the other . frame x has a diameter of 16 cm and frame y has a diameter of 12 cm . what fraction of the surface of frame x is not covered by frame y ?", + "Output Program": [ + "import math\nn0 = 16.0\nn1 = 12.0\nt0 = n0 / 2.0\nt1 = n1 / 2.0\nt2 = math.pi * t0**2\nt3 = math.pi * t1**2\nt4 = t2 - t3\nanswer = t4 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.4375" + ], + "split": "train" + }, + { + "Input": "triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 64 , what is the measure of side xy ?", + "Output Program": [ + "import math\nn0 = 64.0\nt0 = math.sqrt(max(0, n0))\nt1 = math.sqrt(max(0, 2.0))\nt2 = t0 * t1\nt3 = t2**min(2.0, 5)\nt4 = t3 + t3\nanswer = math.sqrt(max(0, t4))\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "the surface area of a cube is 1734 sq . cm . find its volume", + "Output Program": [ + "import math\nn0 = 1734.0\nt0 = 2.0 * 3.0\nt1 = n0 / t0\nt2 = math.sqrt(max(0, t1))\nanswer = t2**3\nprint(answer)" + ], + "Output Answer": [ + "4913" + ], + "split": "train" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered . if the area of the field is 720 sq . feet , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 30.0\nn1 = 720.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "78" + ], + "split": "train" + }, + { + "Input": "you buy a piece of land with an area of \u00e2 \u02c6 \u0161 100 , how long is one side of the land plot ?", + "Output Program": [ + "import math\nn0 = 100.0\n\nanswer = math.sqrt(max(0, n0))\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "train" + }, + { + "Input": "if the perimeter of \u03b4 acd is 9 + 3 \u221a 3 , what is the perimeter of equilateral triangle \u03b4 abc ?", + "Output Program": [ + "import math\nn0 = 9.0\nn1 = 3.0\nn2 = 3.0\nt0 = n1 * 2.0\nt1 = math.sqrt(max(0, 3.0))\nt2 = 3.0 - t1\nt3 = t0 * t2\nt4 = t3 / t2\nanswer = n1 * t4\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 5 inches by 24 inches and jordan ' s rectangle is 3 inches long , how wide is jordan ' s rectangle , in inches ?", + "Output Program": [ + "n0 = 5.0\nn1 = 24.0\nn2 = 3.0\nt0 = n0 * n1 # area of rectangle\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "the surface area of a sphere is 4 \u03c0 r 2 , where r is the radius of the sphere . if the area of the base of a hemisphere is 3 , what is the surface area t of that hemisphere ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 3.0\nt0 = n2 / 3.141592653589793\nt1 = n0 * 3.141592653589793\nt2 = t0 * t1\nt3 = t0 * 3.141592653589793\nt4 = t2 / n1\nanswer = t4 + t3\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "a cylinder is inserted in a sphere d / h = 2 / 3 . find the surface area of the cylinder ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nt0 = n0 / 2.0\nt1 = 2.0 * 3.141592653589793\nt2 = n1 + t0\nanswer = t2 * t1\nprint(answer)" + ], + "Output Answer": [ + "25.132741228718345" + ], + "split": "train" + }, + { + "Input": "what will be the ratio between the area of a rectangle and the area of a triangle with one of the sides of the rectangle as base and a vertex on the opposite side of the rectangle ?", + "Output Program": [ + "t0 = 1.0 * 1.0 # area of rectangle\nt1 = t0 * t0 / 2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "30 square stone slabs of equal size were needed to cover a floor area of 120 sq . m . find the length of each stone slab ?", + "Output Program": [ + "import math\nn0 = 30.0\nn1 = 120.0\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "the area of a circular field is 13.86 hectares . find the cost of fencing it at the rate of rs . 4.90 per metre .", + "Output Program": [ + "import math\nn0 = 13.86\nn1 = 4.9\nt0 = n0 / 3.141592653589793\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * 100.0\nt3 = 2 * math.pi * t2\nanswer = t3 * n1\nprint(answer)" + ], + "Output Answer": [ + "6466.698709641254" + ], + "split": "train" + }, + { + "Input": "the sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 300 m , its area is ?", + "Output Program": [ + "n0 = 5.0\nn1 = 12.0\nn2 = 13.0\nn3 = 300.0\nt0 = n0 + n1\nt1 = n2 + t0\nt2 = n3 / t1\nanswer = n3 * t2\nprint(answer)" + ], + "Output Answer": [ + "3000" + ], + "split": "train" + }, + { + "Input": "approximately how many cubic feet of water are needed to fill a circular swimming pool that is 60 feet across and 6 feet deep ?", + "Output Program": [ + "import math\nn0 = 60.0\nn1 = 6.0\nt0 = n0 / 2.0\nanswer = math.pi * t0**2 * n1\nprint(answer)" + ], + "Output Answer": [ + "16964.600329384884" + ], + "split": "train" + }, + { + "Input": "a circular garden is surrounded by a fence of negligible width along the boundary . if the length of the fence is 1 / 4 of th area of the garden . what is the radius of the circular garden ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 4.0\nt0 = n1**min(2.0, 5)\nt1 = math.sqrt(max(0, t0))\nanswer = t1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a lady builds 7 cm length , 18 cm width , and 3 cm height box using 9 cubic cm cubes . what is the minimum number of cubes required to build the box ?", + "Output Program": [ + "n0 = 7.0\nn1 = 18.0\nn2 = 3.0\nn3 = 9.0\nt0 = n0 * n1\nt1 = n2 * t0\nanswer = t1 / n3\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "a lady grows cauliflower in her garden that is in the shape of a square . each cauliflower takes 1 square foot of area in her garden . this year , she has increased her output by 401 cauliflower when compared to last year . the shape of the area used for growing the cauliflower has remained a square in both these years . how many cauliflowers did she produce this year ?", + "Output Program": [ + "n0 = 1.0\nn1 = 401.0\nt0 = n1 - n0\nt1 = t0 / 2.0\nt2 = t1**min(2.0, 5)\nanswer = n1 + t2\nprint(answer)" + ], + "Output Answer": [ + "40401" + ], + "split": "train" + }, + { + "Input": "a box measuring 27 inches long by 15 inches wide by 6 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?", + "Output Program": [ + "n0 = 27.0\nn1 = 15.0\nn2 = 6.0\nt0 = n2 / 2.0\nt1 = n0 * n1\nt2 = n2 * t1\nt3 = t0**3\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "the number 130 can be written as the sum of the squares of 2 different positive integers . what is the sum of these 2 integers ?", + "Output Program": [ + "n0 = 130.0\nn1 = 2.0\nn2 = 2.0\nt0 = 3.0 + 4.0\nt1 = 2.0 + 3.0\nt2 = t0 + t1\nanswer = n1 + t2\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "the size of a flat - screen tablet is given as the length of the screen \u2019 s diagonal . how many square inches greater is the screen of a square 8 - inch flat - screen tablet than a square 7 - inch flat - screen tablet ?", + "Output Program": [ + "n0 = 8.0\nn1 = 7.0\nt0 = n0**min(2.0, 5)\nt1 = n1**min(2.0, 5)\nt2 = t0 / 2.0\nt3 = t1 / 2.0\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "7.5" + ], + "split": "train" + }, + { + "Input": "the radius of a sphere is increased by 10 % . the surface area increases by ?", + "Output Program": [ + "import math\nn0 = 10.0\nt0 = n0 / 100.0\nt1 = 4 * math.pi * 1.0**2\nt2 = t0 + 1.0\nt3 = 4 * math.pi * t2**2\nt4 = t3 - t1\nt5 = t4 / t1\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "21.00000000000002" + ], + "split": "train" + }, + { + "Input": "what is the area of a square field whose diagonal of length 28 m ?", + "Output Program": [ + "n0 = 28.0\nt0 = n0**2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "392" + ], + "split": "train" + }, + { + "Input": "the diameter of a cylindrical tin is 4 cm and height is 5 cm . find the volume of the cylinder ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 5.0\nt0 = n0 / 2.0\nt1 = math.pi * t0**2 * n1\nanswer = t1 / 3.141592653589793\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is halved , whileits breadth is tripled . wat is the % change in area ?", + "Output Program": [ + "t0 = 1.0 / 2.0\nt1 = t0 * 3.0\nt2 = t1 - 1.0\nt3 = t2 / 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "right triangle pqr is to be constructed in the xy - plane so that the right angle is at p and pr is parallel to the x - axis . the x and y coordinates of p , q and r are to be integers that satisfy the inequalitites - 4 \u2264 x \u2264 5 and 6 \u2264 y \u2264 16 . how many different triangles with these properties could be constructed ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 6.0\nn3 = 16.0\nt0 = n0 + n2\nt1 = n3 - n1\nt2 = 10.0 - 1.0\nt3 = t0 * t1\nt4 = t3 * t2\nanswer = t4 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "9900" + ], + "split": "train" + }, + { + "Input": "if the sum of a number and its square is 20 , what is the number ?", + "Output Program": [ + "import math\nn0 = 20.0\nt0 = math.sqrt(max(0, n0))\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 440 sq . feet , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 20.0\nn1 = 440.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "64" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 3600 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?", + "Output Program": [ + "import math\nn0 = 3600.0\nn1 = 10.0\nt0 = n1 / 2.0\nt1 = math.sqrt(max(0, n0))\nt2 = t1 / t0\nt3 = t2 * 2.0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "240" + ], + "split": "train" + }, + { + "Input": "in a certain parallelogram the degree measure of one angle exceeds that of the other by 50 what is the degree measure of the smaller angle ?", + "Output Program": [ + "n0 = 50.0\nt0 = 3600.0 / 10.0\nt1 = n0 * 2.0\nt2 = t0 - t1\nanswer = t2 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "train" + }, + { + "Input": "a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . how many feet does the squirrel travels if the post is 16 feet tall and 3 feet in circumference ?", + "Output Program": [ + "n0 = 4.0\nn1 = 16.0\nn2 = 3.0\nt0 = n1 / n0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a rectangular parking space is marked out by painting three of its sides . if the length of the unpainted side is 99 feet , and the sum of the lengths of the painted sides is 37 feet , find out the area of the parking space in square feet ?", + "Output Program": [ + "n0 = 99.0\nn1 = 37.0\nt0 = 3.0 * 3.0\nt1 = n1 - t0\nt2 = t1 / 2.0\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "126" + ], + "split": "train" + }, + { + "Input": "the perimeters of 2 squares are 60 cm and 48 cm . find the perimeter of a third square whose area is equal to the difference of the areas of the two squares ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 60.0\nn2 = 48.0\nt0 = n1 / 4.0\nt1 = n2 / 4.0\nt2 = t0**2\nt3 = t1**2\nt4 = t2 - t3\nt5 = math.sqrt(max(0, t4))\nanswer = 4 * t5\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "the edge of a cube is 2 a cm . find its surface ?", + "Output Program": [ + "n0 = 2.0\n\nanswer = 6 * n0**2 # surface of a cube\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "the perimeter of a triangle is 48 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ?", + "Output Program": [ + "n0 = 48.0\nn1 = 2.5\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "the slant height of a cone is 20 cm and radius of the base is 10 cm , find the curved surface of the cone .", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nt0 = n1 * 3.141592653589793\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "628.3185307179587" + ], + "split": "train" + }, + { + "Input": "a right triangle aec has to be constructed in the xy - plane so that the right angle is at a and ae is parallel to x axis . the coordinates of a , e and c are integers and satisfy the inequalities - 1 \u2264 x \u2264 7 and 1 \u2264 y \u2264 7 . how many different triangles can be constructed with these properties ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 7.0\nn2 = 1.0\nn3 = 7.0\nt0 = math.factorial(min(15, int(n1)))\nt1 = n1 * 2.0\nt2 = n1 - n0\nt3 = t2 * 4.0\nt4 = t3 * t2\nt5 = t4 * t1\nanswer = t0 - t5\nprint(answer)" + ], + "Output Answer": [ + "3024" + ], + "split": "train" + }, + { + "Input": "if the volume of the cube is 729 , then the surface area of the cube will be", + "Output Program": [ + "n0 = 729.0\nt0 = n0**(1 / 3)\nt1 = 2.0 * 3.0\nt2 = t0**min(2.0, 5)\nanswer = t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "485.99999999999983" + ], + "split": "train" + }, + { + "Input": "when the circumference and area of a circle are numerically equal , then the diameter is numerically equal to", + "Output Program": [ + "t0 = 2.0 * 3.141592653589793\nt1 = t0 / 3.141592653589793\nanswer = t1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "find the circumference and area of radius 6 cm .", + "Output Program": [ + "import math\nn0 = 6.0\n\nanswer = math.pi * n0**2\nprint(answer)" + ], + "Output Answer": [ + "113.09733552923255" + ], + "split": "train" + }, + { + "Input": "one side of a rectangular field is 15 m and one of its diagonals is 17 m . find the area of the field in meter square", + "Output Program": [ + "import math\nn0 = 15.0\nn1 = 17.0\nt0 = n1**min(2.0, 5)\nt1 = n0**min(2.0, 5)\nt2 = t0 - t1\nt3 = math.sqrt(max(0, t2))\nanswer = n0 * t3 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "a picture is copied onto a sheet of paper 8.5 inches by 10 inches . a 1.5 inch margin is left all around . what area in square inches does the picture cover ?", + "Output Program": [ + "n0 = 8.5\nn1 = 10.0\nn2 = 1.5\nt0 = n2 * 2.0\nt1 = n0 - t0\nt2 = n1 - t0\nanswer = t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "38.5" + ], + "split": "train" + }, + { + "Input": "a tailor trims 4 feet from opposite edges of a square piece of cloth , and 3 feet from the other two edges . if 120 square feet of cloth remain , what was the length of a side of the original piece of cloth ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 3.0\nn2 = 120.0\nt0 = n0 * 2.0\nt1 = n1 * 2.0\nt2 = t0 + t1\nt3 = t1 * t0\nt4 = t2**min(2.0, 5)\nt5 = n2 - t3\nt6 = t5 * 4.0\nt7 = t6 + t4\nt8 = math.sqrt(max(0, t7))\nt9 = t2 + t8\nanswer = t9 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "the size of a television screen is given as the length of the screen ' s diagonal . if the screens were flat , then the area of a square 20 - inch screen would be how many square inches greater than the area of a square 18 - inch screen ?", + "Output Program": [ + "n0 = 20.0\nn1 = 18.0\nt0 = n0**min(2.0, 5)\nt1 = n1**min(2.0, 5)\nt2 = t0 - t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "38" + ], + "split": "train" + }, + { + "Input": "a rectangle has a perimeter of 176 inches . the length of the rectangle is 8 inches more than its width . what is the area of the rectangle ?", + "Output Program": [ + "n0 = 176.0\nn1 = 8.0\nt0 = n0 / 2.0\nt1 = t0 - n1\nt2 = t1 / 2.0\nt3 = n1 + t2\nanswer = t3 * t2 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "1920" + ], + "split": "train" + }, + { + "Input": "what is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between the two sides is 150 o ?", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 12.0\nn2 = 150.0\nt0 = n0 / 2.0\nt1 = math.sqrt(max(0, 3.0))\nt2 = t1 / 2.0\nt3 = n0 * t2\nt4 = n1 + t3\nt5 = t0 * t3 / 2\nt6 = t4 * t0 / 2\nanswer = t6 - t5\nprint(answer)" + ], + "Output Answer": [ + "23.999999999999996" + ], + "split": "train" + }, + { + "Input": "if abc is a quarter circle and a smaller circle is inscribed in it ; if radius of quarter circle is 1.414 units . find the radius of smaller circle", + "Output Program": [ + "n0 = 1.414\n\nanswer = 2.0 - n0\nprint(answer)" + ], + "Output Answer": [ + "0.5860000000000001" + ], + "split": "train" + }, + { + "Input": "a rectangular paper when folded into two congruent parts had a perimeter of 34 cm foer each part folded along one set of sides and the same is 38 cm . when folded along the other set of sides . what is the area of the paper ?", + "Output Program": [ + "n0 = 34.0\nn1 = 38.0\nt0 = 10.0 * 2.0\nt1 = n0 - t0\nanswer = t1 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "train" + }, + { + "Input": "what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 30 % ?", + "Output Program": [ + "n0 = 30.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = t1**min(2.0, 5)\nt3 = t2 - 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "69.00000000000001" + ], + "split": "train" + }, + { + "Input": "the slant height of a cone is 13 cm and radius of the base is 9 cm , find the curved surface of the cone ?", + "Output Program": [ + "n0 = 13.0\nn1 = 9.0\nt0 = n1 * 3.141592653589793\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "367.5663404700058" + ], + "split": "train" + }, + { + "Input": "if the diameter of circle r is 60 % of the diameter of circle s , the area of circle r is what percent of the area of circle s ?", + "Output Program": [ + "import math\nn0 = 60.0\nt0 = math.pi * n0**2\nt1 = math.pi * 100.0**2\nt2 = t0 * 100.0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "if the volume and surface area of a sphere are numerically the same , then its radius is : ?", + "Output Program": [ + "t0 = 4.0 / 3.0\nt1 = 4.0 * 3.141592653589793\nt2 = t0 * 3.141592653589793\nt3 = t2 / t1\nanswer = 1.0 / t3\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is increased to 2 times its original size and its width is increased to 3 times its original size . if the area of the new rectangle is equal to 1800 square meters , what is the area of the original rectangle ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 1800.0\nt0 = 2.0 * 3.0\nanswer = n2 / t0\nprint(answer)" + ], + "Output Answer": [ + "300" + ], + "split": "train" + }, + { + "Input": "carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 12 inches by 15 inches and jordan ' s rectangle is 9 inches long , how wide is jordan ' s rectangle , in inches ?", + "Output Program": [ + "n0 = 12.0\nn1 = 15.0\nn2 = 9.0\nt0 = n0 * n1 # area of rectangle\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "find the surface area of a 10 cm * 4 cm * 3 cm brick .", + "Output Program": [ + "n0 = 10.0\nn1 = 4.0\nn2 = 3.0\n\nanswer = 2 * (n0 * n1 + n0 * n2 + n1 * n2) # surface of a rectangular prism\nprint(answer)" + ], + "Output Answer": [ + "164" + ], + "split": "train" + }, + { + "Input": "sides of a triangle are 13 cm . 14 cm . and 15 cm . respectively . calculate the area of triangle .", + "Output Program": [ + "import math\nn0 = 13.0\nn1 = 14.0\nn2 = 15.0\n\nanswer = (lambda s, a, b, c: math.sqrt(max(0, s * (s - a) * (s - b) * (s - c))))((n0 + n1 + n2) / 2, n0, n1, n2) # Heron's formula\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "train" + }, + { + "Input": "a cube of edge 10 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 15 cm , find the rise in water level ?", + "Output Program": [ + "n0 = 10.0\nn1 = 20.0\nn2 = 15.0\nt0 = n1 * n2\nt1 = n0**3\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "3.3333333333333335" + ], + "split": "train" + }, + { + "Input": "the size of a television screen is given as the length of the screen ' s diagonal . if the screens were flat , then the area of a square 22 - inch screen would be how many square inches greater than the area of a square 20 - inch screen ?", + "Output Program": [ + "n0 = 22.0\nn1 = 20.0\nt0 = n0**min(2.0, 5)\nt1 = n1**min(2.0, 5)\nt2 = t0 - t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "train" + }, + { + "Input": "the circumferences of two circles are 264 meters and 352 meters . find the difference between the areas of the larger and the smaller circles .", + "Output Program": [ + "import math\nn0 = 264.0\nn1 = 352.0\nt0 = 2.0 * 3.141592653589793\nt1 = n1 / t0\nt2 = n0 / t0\nt3 = math.pi * t1**2\nt4 = math.pi * t2**2\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "4313.735577562732" + ], + "split": "train" + }, + { + "Input": "in measuring the sides of a rectangle , one side is taken 6 % in excess and other 5 % in deficit . find the error percentage in the area calculated from these measurements .", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nt0 = n0 * n1\nt1 = n0 - n1\nt2 = t0 / 100.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.7" + ], + "split": "train" + }, + { + "Input": "if a is the smallest positive integer such that 3150 multiplied by a is the square of an integer , then a must be", + "Output Program": [ + "n0 = 3150.0\nt0 = 1.0 + 4.0\nt1 = t0 * t0\nt2 = n0 / t1\nt3 = t2 / 2.0\nt4 = t3 / 3.0\nt5 = t4 / 3.0\nanswer = t5 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "train" + }, + { + "Input": "the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 150 sq . cm , what is the length of the rectangle ?", + "Output Program": [ + "n0 = 5.0\nn1 = 1.0\nn2 = 150.0\n\nanswer = n2 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "in triangle pqr , the angle q = 90 degree , pq = 3 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz", + "Output Program": [ + "n0 = 90.0\nn1 = 3.0\nn2 = 8.0\nt0 = n1 * n2\nanswer = t0 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "2.4" + ], + "split": "train" + }, + { + "Input": "the area of sector of a circle whose radius is 12 metro and whose angle at the center is 36 \u00e2 \u00b0 is ?", + "Output Program": [ + "n0 = 12.0\nn1 = 36.0\nt0 = 3.0 + 4.0\nt1 = 3600.0 / 10.0\nt2 = 10.0 * 2.0\nt3 = n0**min(2.0, 5)\nt4 = t2 + 2.0\nt5 = n1 / t1\nt6 = t4 / t0\nt7 = t6 * t3\nanswer = t5 * t7\nprint(answer)" + ], + "Output Answer": [ + "45.25714285714286" + ], + "split": "train" + }, + { + "Input": "if the difference between the length and breadth of a rectangle is 23 m and its perimeter is 186 m , what is its area ?", + "Output Program": [ + "n0 = 23.0\nn1 = 186.0\nt0 = n0 * 2.0\nt1 = n1 - t0\nt2 = t1 / 4.0\nt3 = n0 + t2\nanswer = t3 * t2 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "2030" + ], + "split": "train" + }, + { + "Input": "a small , rectangular park has a perimeter of 560 feet and a diagonal measurement of 400 feet . what is its area , in square feet ?", + "Output Program": [ + "n0 = 560.0\nn1 = 400.0\nt0 = 2.0 + 3.0\nt1 = n1 / t0\nt2 = t1 * 3.0\nt3 = t1 * 4.0\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "76800" + ], + "split": "train" + }, + { + "Input": "the difference of the areas of two squares drawn on two line segments in 32 sq . cm . find the length of the greater line segment if one is longer than the other by 2 cm", + "Output Program": [ + "n0 = 32.0\nn1 = 2.0\nt0 = n1 * 2.0\nt1 = n0 - t0\nanswer = t1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 10 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 10.0\nn1 = 680.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "146" + ], + "split": "train" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 20.0\nn1 = 680.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "88" + ], + "split": "train" + }, + { + "Input": "the diagonals of a rhombus are 15 cm and 17 cm . find its area ?", + "Output Program": [ + "n0 = 15.0\nn1 = 17.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "127.5" + ], + "split": "train" + }, + { + "Input": "12 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?", + "Output Program": [ + "n0 = 12.0\nn1 = 7.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nt2 = n0 * t1\nt3 = t2 / 2.0\nanswer = t3 + t0\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular field is 7 / 5 its width . if the perimeter of the field is 384 meters , what is the width of the field ?", + "Output Program": [ + "n0 = 7.0\nn1 = 5.0\nn2 = 384.0\nt0 = n0 / n1\nt1 = t0 + t0\nt2 = t1 + 2.0\nanswer = n2 / t2\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "a rectangular garden is to be twice as long as it is wide . if 300 yards of fencing , including the gate , will completely enclose the garden , what will be the length of the garden , in yards ?", + "Output Program": [ + "n0 = 300.0\nt0 = 1.0 + 2.0\nt1 = t0 * 2.0\nt2 = n0 / t1\nanswer = t2 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "if each side of a right triangle is increased by 10 % and the base ( b ) is half of the height , find the percentage change in its area ?", + "Output Program": [ + "n0 = 10.0\nt0 = n0 + 100.0\nt1 = t0 / 100.0\nt2 = t1**min(2.0, 5)\nt3 = t2 - 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "21.000000000000018" + ], + "split": "train" + }, + { + "Input": "30 square stone slabs of equal size were needed to cover a floor area of 50.7 sq . m . find the length of each stone slab ?", + "Output Program": [ + "import math\nn0 = 30.0\nn1 = 50.7\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "130" + ], + "split": "train" + }, + { + "Input": "a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 80 cents . how many cents does a solution of 1 liter of spirit and 2 liters of water cost ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 80.0\nn3 = 1.0\nn4 = 2.0\nt0 = n0 + n4\nt1 = n0 / t0\nt2 = n2 * t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "what would be the length of the diagonal of a square plot whose area is equal to the area of a rectangular plot of 45 m length and 40 m width ?", + "Output Program": [ + "import math\nn0 = 45.0\nn1 = 40.0\nt0 = n0 * n1 # area of rectangle\nt1 = math.sqrt(t0) # square edge given area\nanswer = math.sqrt(t1**2 + t1**2)\nprint(answer)" + ], + "Output Answer": [ + "60.00000000000001" + ], + "split": "train" + }, + { + "Input": "if the radius of a circle that centers at the origin is 5 , how many w points on the circle have integer coordinates ?", + "Output Program": [ + "n0 = 5.0\nt0 = n0 + 4.0\nt1 = n0 * n0\nt2 = 2.0**min(2.0, 5)\nt3 = t1 - t0\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a wire can be bent in the form of a circle of radius 56 cm . if it is bent in the form of a square , then its area will be", + "Output Program": [ + "import math\nn0 = 56.0\nt0 = 2 * math.pi * n0\nt1 = t0 / 4.0\nanswer = t1**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "7737.769850454057" + ], + "split": "train" + }, + { + "Input": "the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 50 of the area of the field . what is the length of the field ?", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 1.0\nn2 = 50.0\nt0 = 1 / 2.0\nt1 = n0**2\nt2 = n2 * t1\nt3 = t2 / t0\nanswer = math.sqrt(max(0, t3))\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 12 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?", + "Output Program": [ + "import math\nn0 = 12.0\nn1 = 1200.0\nn2 = 2.0\nn3 = 30.0\nt0 = n1 / n3\nt1 = n3**min(n2, 5)\nt2 = n3 + t0\nt3 = t0**min(n2, 5)\nt4 = t1 + t3\nt5 = math.sqrt(max(0, t4))\nt6 = t2 + t5\nanswer = n0 * t6\nprint(answer)" + ], + "Output Answer": [ + "1440" + ], + "split": "train" + }, + { + "Input": "what is the smallest positive perfect square that is divisible by 4 , 10 , and 18 ?", + "Output Program": [ + "n0 = 4.0\nn1 = 10.0\nn2 = 18.0\nt0 = n1 * n2\nt1 = 3.0**min(2.0, 5)\nt2 = n0 * t1\nt3 = n1 * t2\nt4 = t3 * 2.0\nanswer = t4 + t0\nprint(answer)" + ], + "Output Answer": [ + "900" + ], + "split": "train" + }, + { + "Input": "if the radius of a circle that centers at the origin is 5 , how many j points on the circle have integer coordinates ?", + "Output Program": [ + "n0 = 5.0\nt0 = n0 + 4.0\nt1 = n0 * n0\nt2 = 2.0**min(2.0, 5)\nt3 = t1 - t0\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the area of sector of a circle whose radius is 10 metro and whose angle at the center is 42 \u00e2 \u00b0 is ?", + "Output Program": [ + "n0 = 10.0\nn1 = 42.0\nt0 = 3.0 + 4.0\nt1 = 3600.0 / 10.0\nt2 = 10.0 * 2.0\nt3 = n0**min(2.0, 5)\nt4 = t2 + 2.0\nt5 = n1 / t1\nt6 = t4 / t0\nt7 = t6 * t3\nanswer = t5 * t7\nprint(answer)" + ], + "Output Answer": [ + "36.666666666666664" + ], + "split": "train" + }, + { + "Input": "a lamp is put on one corner of a square plot of side 50 m . it ' s light reaches 21 m . find the area of that plot that is lit by that lamp ?", + "Output Program": [ + "import math\nn0 = 50.0\nn1 = 21.0\nt0 = math.pi * n1**2\nanswer = t0 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "346.3605900582747" + ], + "split": "train" + }, + { + "Input": "the parameter of a square is equal to the perimeter of a rectangle of length 36 cm and breadth 20 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ?", + "Output Program": [ + "import math\nn0 = 36.0\nn1 = 20.0\nt0 = 2 * (n0 + n1) # perimetere of rectangle\nt1 = t0 / 4. # square edge given perimeter\nt2 = t1 / 2.0\nt3 = 2 * math.pi * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "43.982297150257104" + ], + "split": "train" + }, + { + "Input": "a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck ' s tank is completely filled . if the truck ' s tank has a radius of 4 feet and a height of 10 feet , how far ( in feet ) did the oil level drop in the stationary tank ?", + "Output Program": [ + "import math\nn0 = 100.0\nn1 = 25.0\nn2 = 4.0\nn3 = 10.0\nt0 = math.pi * n0**2\nt1 = math.pi * n2**2 * n3\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.016" + ], + "split": "train" + }, + { + "Input": "what is the area of a square field whose diagonal of length 10 m ?", + "Output Program": [ + "n0 = 10.0\nt0 = n0**2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a number when divided by 6 leaves a remainder 3 . when the square of the same number is divided by 6 , the remainder is :", + "Output Program": [ + "n0 = 6.0\nn1 = 3.0\nn2 = 6.0\nt0 = n0 * n1\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "how many diagonals does a polygon with 15 sides have , if one of its vertices does not connect to any diagonal ?", + "Output Program": [ + "n0 = 15.0\nt0 = n0 - 1.0\nt1 = t0 - 3.0\nt2 = t0 * t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "77" + ], + "split": "train" + }, + { + "Input": "a hall is 18 meters long and 9 meters wide . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , what is the volume of the hall ( in cubic meters ) ?", + "Output Program": [ + "n0 = 18.0\nn1 = 9.0\nt0 = n0 * n1 # area of rectangle\nt1 = 2 * (n0 + n1) # perimetere of rectangle\nt2 = t0 * 2.0\nt3 = t2 / t1\nanswer = n0 * n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "972" + ], + "split": "train" + }, + { + "Input": "a football field is 7200 square yards . if 1200 pounds of fertilizer are spread evenly across the entire field , how many pounds of fertilizer were spread over an area of the field totaling 3600 square yards ?", + "Output Program": [ + "n0 = 7200.0\nn1 = 1200.0\nn2 = 3600.0\nt0 = n1 / n0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "train" + }, + { + "Input": "a rectangular grass field is 95 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?", + "Output Program": [ + "n0 = 95.0\nn1 = 55.0\nn2 = 2.5\nn3 = 2.0\nt0 = n2 * n3\nt1 = n0 * n1 # area of rectangle\nt2 = n0 + t0\nt3 = n1 + t0\nt4 = t2 * t3 # area of rectangle\nt5 = t4 - t1\nanswer = n3 * t5\nprint(answer)" + ], + "Output Answer": [ + "1550" + ], + "split": "train" + }, + { + "Input": "the perimeter of a triangle is 36 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ?", + "Output Program": [ + "n0 = 36.0\nn1 = 2.5\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "if the area of a square with sides of length 9 centimeters is equal to the area of a rectangle with a width of 3 centimeters , what is the length of the rectangle , in centimeters ?", + "Output Program": [ + "n0 = 9.0\nn1 = 3.0\nt0 = n0**min(2.0, 5)\nanswer = t0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is reduced by 25 % . by what % would the width have to be increased to maintainthe original area ?", + "Output Program": [ + "n0 = 25.0\nt0 = 100.0 - n0\nt1 = t0 / 100.0\nt2 = 1.0 - t1\nt3 = t2 / t1\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "33.33333333333333" + ], + "split": "train" + }, + { + "Input": "a cube 125 mt is colored pink on two opposite surfaces and then cut in to 125 smaller cubes then find how many number of cubes have pink color ?", + "Output Program": [ + "n0 = 65.0\nn1 = 2.0\nn2 = 29.0\nn3 = 5.0\nt0 = n2 * n3\nt1 = n0 - n2\nt2 = t0 / t1\nt3 = n0 * t2\nanswer = t3 / t2\nprint(answer)" + ], + "Output Answer": [ + "65" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular garden is three times its width . if the area of the rectangular garden is 768 square meters , then what is the width of the rectangular garden ?", + "Output Program": [ + "import math\nn0 = 768.0\nt0 = n0 / 3.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "train" + }, + { + "Input": "find the perimeter and area of a square of side 11 cm .", + "Output Program": [ + "n0 = 11.0\n\nanswer = n0**2\nprint(answer)" + ], + "Output Answer": [ + "121" + ], + "split": "train" + }, + { + "Input": "if the height of a cone is increased by 120 % then its volume is increased by ?", + "Output Program": [ + "n0 = 120.0\n\nanswer = n0 * 1.0 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "train" + }, + { + "Input": "if each edge of cube increased by 10 % , the percentage increase in surface area is :", + "Output Program": [ + "n0 = 10.0\nt0 = n0 + 100.0\nt1 = 100.0**min(3.0, 5)\nt2 = t0**min(3.0, 5)\nt3 = t2 - t1\nt4 = t3 / t1\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "33.1" + ], + "split": "train" + }, + { + "Input": "the length of each side of square a is increased by 100 percent to make square b . if the length of the side of square b is increased by 60 percent to make square c , by what percent is the area of square c greater than the sum of the areas of squares a and b ?", + "Output Program": [ + "n0 = 100.0\nn1 = 60.0\nt0 = n0 / n0\nt1 = t0 + 1.0\nt2 = n1 * t1\nt3 = t1**2\nt4 = t3 + 1.0\nt5 = t2 / n0\nt6 = t1 + t5\nt7 = t6**2\nt8 = t7 - 1.0\nt9 = t8 - 4.0\nt10 = t9 / t4\nanswer = n0 * t10\nprint(answer)" + ], + "Output Answer": [ + "104.80000000000005" + ], + "split": "train" + }, + { + "Input": "find the perimeter and area of a square of side 15 cm .", + "Output Program": [ + "n0 = 15.0\n\nanswer = n0**2\nprint(answer)" + ], + "Output Answer": [ + "225" + ], + "split": "train" + }, + { + "Input": "the perimeter of an isosceles right triangle is 10 + 10 sq rt 2 . what is the length of the hypotenuse of the triangle ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 10.0\nn2 = 2.0\nt0 = math.sqrt(max(0, n2))\nt1 = n0 * t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "7.0710678118654755" + ], + "split": "train" + }, + { + "Input": "a metallic sheet is of rectangular shape with dimensions 100 m x 50 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 10 m , the volume of the box ( in m cube ) is :", + "Output Program": [ + "n0 = 100.0\nn1 = 50.0\nn2 = 10.0\nt0 = n2 * 2.0\nt1 = n0 - t0\nt2 = n1 - t0\nanswer = n2 * t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "24000" + ], + "split": "train" + }, + { + "Input": "two equilateral triangles of side 12 cm are placed one on top of another , such that a 6 pointed star is formed . if the six verticals lie on a circle what is the area of the circle not enclosed by the star ?", + "Output Program": [ + "import math\nn0 = 12.0\nn1 = 6.0\nt0 = n0 / 3.0\nt1 = math.sqrt(max(0, 3.0))\nt2 = t1 / 2.0\nt3 = t0**min(2.0, 5)\nt4 = n0 * t2\nt5 = t3 * t1\nt6 = t5 / 4.0\nt7 = t4 * 2.0\nt8 = t7 / 3.0\nt9 = n0 * t6\nt10 = math.pi * t8**2\nanswer = t10 - t9\nprint(answer)" + ], + "Output Answer": [ + "67.65800860900399" + ], + "split": "train" + }, + { + "Input": "there are thirty - 4 lines that are tangent to a circle , and these lines create regions in the plane . can you tell how many of these regions are not enclosed ?", + "Output Program": [ + "n0 = 4.0\nt0 = n0 * 10.0\nt1 = 10.0 * 2.0\nt2 = n0 * 2.0\nt3 = t0 + t1\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "68" + ], + "split": "train" + }, + { + "Input": "the sides of a rectangle are in the ratio 4 : 3 and its area is 972 sq . m find the perimeter of rectangle", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 3.0\nn2 = 972.0\nt0 = n0 * n1\nt1 = n2 / t0\nt2 = math.sqrt(max(0, t1))\nt3 = n0 * t2\nt4 = n1 * t2\nanswer = 2 * (t3 + t4) # perimetere of rectangle\nprint(answer)" + ], + "Output Answer": [ + "126" + ], + "split": "train" + }, + { + "Input": "if the sum of a number and its square is 342 , what is the number ?", + "Output Program": [ + "import math\nn0 = 342.0\nt0 = math.sqrt(max(0, n0))\nanswer = math.floor(t0)\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "in how many w ways can 5 people from a group of 6 people be seated around a circular table", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 6.0\nt0 = math.factorial(min(15, int(n1)))\nanswer = t0 / n0\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "train" + }, + { + "Input": "the area of a circular field is 13.86 hectares . find the cost of fencing it at the rate of rs . 4.70 per metre .", + "Output Program": [ + "import math\nn0 = 13.86\nn1 = 4.7\nt0 = n0 / 3.141592653589793\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * 100.0\nt3 = 2 * math.pi * t2\nanswer = t3 * n1\nprint(answer)" + ], + "Output Answer": [ + "6202.751823533447" + ], + "split": "train" + }, + { + "Input": "what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 50 % ?", + "Output Program": [ + "n0 = 50.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = t1**min(2.0, 5)\nt3 = t2 - 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "find the area of a parallelogram with base 24 cm and height 10 cm ?", + "Output Program": [ + "n0 = 24.0\nn1 = 10.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "240" + ], + "split": "train" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 40 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 40.0\nn1 = 680.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "74" + ], + "split": "train" + }, + { + "Input": "oy started cycling along the boundaries of a square field from corner point a . after half an hour he reached the corner point c , diagonally opposite to a . if his speed was 8 km / hr , the area of the filed in square km is ?", + "Output Program": [ + "n0 = 8.0\nt0 = n0 / 2.0\nt1 = t0 / 2.0\nanswer = t1**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "each of the 9 squares shown is to contain one number chosen from 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , and 9 . no number is to be repeated . suppose the sum of the 5 squares aligned vertically on the right is 32 and that the sum of the 5 squares aligned horizontally on the bottom is 20 . what number goes in the shared corner square ?", + "Output Program": [ + "n0 = 9.0\nn1 = 1.0\nn2 = 2.0\nn3 = 3.0\nn4 = 4.0\nn5 = 5.0\nn6 = 6.0\nn7 = 7.0\nn8 = 8.0\nn9 = 9.0\nn10 = 5.0\nn11 = 32.0\nn12 = 5.0\nn13 = 20.0\nt0 = n1 + n2\nanswer = n4 + t0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "the breadth of a rectangular field is 60 % of its length . if the perimeter of the field is 800 m . what is the area of the field ?", + "Output Program": [ + "n0 = 60.0\nn1 = 800.0\nt0 = n1 / 2.0\nt1 = n0 / 100.0\nt2 = t1 + 1.0\nt3 = t0 / t2\nt4 = t0 - t3\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "37500" + ], + "split": "train" + }, + { + "Input": "the number 83 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?", + "Output Program": [ + "n0 = 83.0\nn1 = 3.0\nn2 = 3.0\nt0 = 3.0 + 4.0\nt1 = 2.0 + 3.0\nt2 = t0 + t1\nanswer = n1 + t2\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "the slant height of a cone is 10 cm and radius of the base is 5 cm , find the curved surface of the cone ?", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\nt0 = n1 * 3.141592653589793\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "157.07963267948966" + ], + "split": "train" + }, + { + "Input": "a rectangular region has a fence along three sides and a wall along the fourth side . the fenced side opposite the wall is twice the length of each of the other two fenced sides . if the area of the rectangular region is 200 square feet , what is the total length of the fence , in feet ?", + "Output Program": [ + "n0 = 200.0\nt0 = 1.0 + 1.0\nt1 = t0 * 2.0\nt2 = t1 + 1.0\nt3 = t2 * 2.0\nt4 = t3 + t3\nt5 = t2 + t3\nt6 = t4 + t3\nt7 = t5 + t2\nt8 = n0 / t7\nanswer = t6 + t8\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "if a triangle in the xy - coordinate system has vertices at ( - 2 , - 3 ) , ( 4 , - 3 ) and ( 28 , 7 ) , what is the area of the triangle ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 3.0\nn2 = 4.0\nn3 = 3.0\nn4 = 28.0\nn5 = 7.0\nt0 = n0 + n4\nt1 = n1 + n5\nt2 = n0 + n2\nt3 = n4 - n2\nt4 = t0**min(2.0, 5)\nt5 = t1**min(2.0, 5)\nt6 = t3**min(2.0, 5)\nt7 = t2**min(2.0, 5)\nt8 = t4 + t5\nt9 = t6 + t5\nt10 = math.sqrt(max(0, t7))\nt11 = math.sqrt(max(0, t8))\nt12 = math.sqrt(max(0, t9))\nanswer = (lambda s, a, b, c: math.sqrt(max(0, s * (s - a) * (s - b) * (s - c))))((t11 + t12 + t10) / 2, t11, t12, t10) # Heron's formula\nprint(answer)" + ], + "Output Answer": [ + "30.000000000000178" + ], + "split": "train" + }, + { + "Input": "a crate measures 7 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still fit in the crate ?", + "Output Program": [ + "n0 = 7.0\nn1 = 8.0\nn2 = 12.0\nt0 = n1 * n2\nt1 = n0 * t0\nt2 = t1 / n2\nanswer = t2 / n1\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "what is the ratio between perimeters of two squares one having 11 times the diagonal then the other ?", + "Output Program": [ + "n0 = 11.0\nt0 = n0 / n0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "train" + }, + { + "Input": "the breath of a rectangle is three - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 2025 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the length is 10 units ?", + "Output Program": [ + "import math\nn0 = 2025.0\nn1 = 10.0\nt0 = 1.0 + 4.0\nt1 = math.sqrt(n0) # square edge given area\nt2 = t1 * 3.0\nt3 = t2 / t0\nanswer = n1 * t3 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "270" + ], + "split": "train" + }, + { + "Input": "calculate the area of a triangle , if the sides are 30 cm , 21 cm and 10 cm , what is its area ?", + "Output Program": [ + "n0 = 30.0\nn1 = 21.0\nn2 = 10.0\nt0 = n1 / 2.0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "105" + ], + "split": "train" + }, + { + "Input": "one side of a rectangular field is 16 m and one of its diagonal is 17 m . find the area of the field .", + "Output Program": [ + "import math\nn0 = 16.0\nn1 = 17.0\nt0 = n1**min(2.0, 5)\nt1 = n0**min(2.0, 5)\nt2 = t0 - t1\nt3 = math.sqrt(max(0, t2))\nanswer = n0 * t3 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "91.91300234460846" + ], + "split": "train" + }, + { + "Input": "the side of a square is increased by 5 % then how much % does its area increases ?", + "Output Program": [ + "n0 = 5.0\nt0 = n0 + 100.0\nt1 = 100.0**2\nt2 = t0**2\nt3 = t2 - t1\nt4 = t3 * 100.0\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "10.25" + ], + "split": "train" + }, + { + "Input": "a circular mat with radius 10 inches is placed on a square tabletop , each of whose sides is 24 inches long . which of the following is closest to the fraction of the tabletop covered by the mat ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 24.0\nt0 = math.pi * n0**2\nt1 = n1**2\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.545415391248228" + ], + "split": "train" + }, + { + "Input": "two tracks are parallel . the first track has 6 checkpoints and the second one has 10 checkpoints . in how many ways can the 6 checkpoints of first track be joined with the 10 checkpoints of the second to form a triangle ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 10.0\nn2 = 6.0\nn3 = 10.0\nt0 = math.factorial(min(15, int(n1)))\nt1 = math.factorial(min(15, int(2.0)))\nt2 = math.factorial(min(15, int(n0)))\nt3 = n1 - 2.0\nt4 = n0 - 1.0\nt5 = 10.0 - 1.0\nt6 = n0 - 2.0\nt7 = t2 / 2.0\nt8 = math.factorial(min(15, int(t3)))\nt9 = math.factorial(min(15, int(t4)))\nt10 = math.factorial(min(15, int(t5)))\nt11 = math.factorial(min(15, int(t6)))\nt12 = t0 / t8\nt13 = t2 / t9\nt14 = t0 / t10\nt15 = t7 / t11\nt16 = t12 / t1\nt17 = t14 * t15\nt18 = t16 * t13\nanswer = t18 + t17\nprint(answer)" + ], + "Output Answer": [ + "420" + ], + "split": "train" + }, + { + "Input": "the size of a flat - screen television is given as the length of the screen \u2019 s diagonal . how many square inches greater is the screen of a square 21 - inch flat - screen television than a square 19 - inch flat - screen television ?", + "Output Program": [ + "n0 = 21.0\nn1 = 19.0\nt0 = n0**min(2.0, 5)\nt1 = n1**min(2.0, 5)\nt2 = t0 / 2.0\nt3 = t1 / 2.0\nanswer = t2 - t3\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "how many boxes do you need if you have to pack 240 pairs ornamental bangles into boxes that each hold 2 dozens of bangles ?", + "Output Program": [ + "n0 = 240.0\nn1 = 2.0\n\nanswer = n0 / 12.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "on dividing a number by 5 , we get 3 as remainder . what will be the remainder when the square of this number is divided by 5 ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 3.0\nn2 = 5.0\nt0 = n1**min(2.0, 5)\nt1 = t0 / n0\nt2 = math.floor(t1)\nt3 = t1 - t2\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 8 cm each . the radius of the sphere is", + "Output Program": [ + "import math\nn0 = 8.0\nt0 = n0 / 2.0\nt1 = 4.0 * 3.141592653589793\nt2 = n0 * t0\nt3 = t2 * 3.141592653589793\nt4 = t3 * 2.0\nt5 = t4 / t1\nanswer = math.sqrt(max(0, t5))\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a rectangular table , kept against a wall has a three sides free and the wall along the fourth side . the side opposite the wall is twice the length of each of the other two free sides . if the area of the rectangular table is 128 square feet , what is the total length of the table free sides , in feet ?", + "Output Program": [ + "import math\nn0 = 128.0\nt0 = n0 / 2.0\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * 2.0\nt3 = t2 + t1\nanswer = t3 + t1\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "what is the maximum number r of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?", + "Output Program": [ + "import math\nn0 = 27.0\nn1 = 8.0\nn2 = 9.0\nn3 = 12.0\nt0 = n0**(1 / 3)\nt1 = n2 / 3.0\nt2 = n1 / t0\nt3 = n3 / t0\nt4 = math.floor(t2)\nt5 = t1 * t3\nanswer = t4 * t5\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 10 , 0 ) , ( 0 , - 3.5 ) , ( - 10 , 0 ) ?", + "Output Program": [ + "n0 = 0.0\nn1 = 3.5\nn2 = 10.0\nn3 = 0.0\nn4 = 0.0\nn5 = 3.5\nn6 = 10.0\nn7 = 0.0\nt0 = n2 * 2.0\nt1 = n1 * 2.0\nanswer = t0 * t1 / 2\nprint(answer)" + ], + "Output Answer": [ + "70" + ], + "split": "train" + }, + { + "Input": "108 . triangle a \u2019 s base is 20 % greater than the base of triangle b , and a \u2019 s height is 20 % less than the height of triangle b . the area of triangle a is what percent less or more than the area of triangle b ?", + "Output Program": [ + "n0 = 108.0\nn1 = 20.0\nn2 = 20.0\nt0 = n1 + 100.0\nt1 = 100.0 * 100.0\nt2 = 100.0 - n1\nt3 = t0 * t2\nt4 = t1 - t3\nanswer = 100.0 / t4\nprint(answer)" + ], + "Output Answer": [ + "0.25" + ], + "split": "train" + }, + { + "Input": "the perimeter of one face of a cube is 28 cm . its volume will be :", + "Output Program": [ + "n0 = 28.0\nt0 = n0 / 4. # square edge given perimeter\nanswer = t0**3\nprint(answer)" + ], + "Output Answer": [ + "343" + ], + "split": "train" + }, + { + "Input": "a carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet . if the carpenter made instead a sandbox which was twice as long , twice as wide and twice as high as the original , what would the capacity be of the new larger sandbox ?", + "Output Program": [ + "n0 = 10.0\nt0 = 2.0**min(3.0, 5)\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "train" + }, + { + "Input": "the area of sector of a circle whose radius is 12 metro and whose angle at the center is 42 \u00b0 is ?", + "Output Program": [ + "n0 = 12.0\nn1 = 42.0\nt0 = 3.0 + 4.0\nt1 = 3600.0 / 10.0\nt2 = 10.0 * 2.0\nt3 = n0**min(2.0, 5)\nt4 = t2 + 2.0\nt5 = n1 / t1\nt6 = t4 / t0\nt7 = t6 * t3\nanswer = t5 * t7\nprint(answer)" + ], + "Output Answer": [ + "52.8" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular garden is three times its width . if the area of the rectangular garden is 675 square meters , then what is the width of the rectangular garden ?", + "Output Program": [ + "import math\nn0 = 675.0\nt0 = n0 / 3.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "train" + }, + { + "Input": "the area of an isosceles trapezoid with sides of length 5 and bases of length 6 and 12 is ?", + "Output Program": [ + "n0 = 5.0\nn1 = 6.0\nn2 = 12.0\n\nanswer = 4.0 * (n2 + n1) / 2 # quadrilateral area\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "the area of a circular place is 17.56 hectares . find the cost of fencing it at the rate of rs . 3 / meter approximately .", + "Output Program": [ + "import math\nn0 = 17.56\nn1 = 3.0\nt0 = 10.0 * 1000.0\nt1 = n0 * t0\nt2 = t1 / 3.141592653589793\nt3 = math.sqrt(max(0, t2))\nt4 = 2 * math.pi * t3\nanswer = t4 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "4456.443887106987" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is halved , while its breadth is tripled . wat isthe % change in area ?", + "Output Program": [ + "t0 = 1.0 / 2.0\nt1 = t0 * 3.0\nt2 = t1 - 1.0\nt3 = t2 / 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "find the circumference and area of radius 7 cm .", + "Output Program": [ + "import math\nn0 = 7.0\n\nanswer = math.pi * n0**2\nprint(answer)" + ], + "Output Answer": [ + "153.93804002589985" + ], + "split": "train" + }, + { + "Input": "a crate measures 3 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still fit in the crate ?", + "Output Program": [ + "n0 = 3.0\nn1 = 8.0\nn2 = 12.0\nt0 = n1 * n2\nt1 = n0 * t0\nt2 = t1 / n2\nanswer = t2 / n1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "what is the total surface area in square meters of a rectangular solid whose length is 6 meters , width is 5 meters , and depth is 2 meters ?", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nn2 = 2.0\n\nanswer = 2 * (n0 * n1 + n0 * n2 + n1 * n2) # surface of a rectangular prism\nprint(answer)" + ], + "Output Answer": [ + "104" + ], + "split": "train" + }, + { + "Input": "in a new housing development , trees are to be planted along the sidewalk of a certain street . each tree takes up one square foot of sidewalk space , and there are to be 20 feet between each tree . how many trees can be planted if the road is 148 feet long ?", + "Output Program": [ + "n0 = 20.0\nn1 = 148.0\nt0 = n0 + 1.0\nt1 = n1 - 1.0\nt2 = t1 / t0\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "when magnified 1,000 times by an electron microscope , the image of a certain circular piece of tissue has a diameter of 1 centimeter . the actual diameter of the tissue , in centimeters , is", + "Output Program": [ + "n0 = 1000.0\nn1 = 1.0\n\nanswer = n1 / n0\nprint(answer)" + ], + "Output Answer": [ + "0.001" + ], + "split": "train" + }, + { + "Input": "the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 16 cm each . the radius of the sphere is", + "Output Program": [ + "import math\nn0 = 16.0\nt0 = n0 / 2.0\nt1 = 4.0 * 3.141592653589793\nt2 = n0 * t0\nt3 = t2 * 3.141592653589793\nt4 = t3 * 2.0\nt5 = t4 / t1\nanswer = math.sqrt(max(0, t5))\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 2700 sq m , then what is the breadth of the rectangular plot ?", + "Output Program": [ + "import math\nn0 = 2700.0\nt0 = n0 / 3.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "frank the fencemaker needs to fence in a rectangular yard . he fences in the entire yard , except for one full side of the yard , which equals 40 feet . the yard has an area of 240 square feet . how many feet offence does frank use ?", + "Output Program": [ + "n0 = 40.0\nn1 = 240.0\nt0 = n1 / n0\nt1 = t0 + t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "52" + ], + "split": "train" + }, + { + "Input": "if the volume of two cubes are in the ratio 27 : 1 , the ratio of their edges is :", + "Output Program": [ + "n0 = 27.0\nn1 = 1.0\n\nanswer = n0**(1 / 3)\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "the points a ( 0 , 0 ) , b ( 0 , 4 a - 2 ) and c ( 2 a + 1 , 2 a + 6 ) form a triangle . if angle abc = 90 , what is the area of triangle abc ?", + "Output Program": [ + "n0 = 0.0\nn1 = 0.0\nn2 = 0.0\nn3 = 4.0\nn4 = 2.0\nn5 = 2.0\nn6 = 1.0\nn7 = 2.0\nn8 = 6.0\nn9 = 90.0\nt0 = n4 + n8\nt1 = n3 - n4\nt2 = t0 / n4\nt3 = t2 * t1\nt4 = n3 * t2\nt5 = t3 + 1.0\nt6 = t4 - n4\nt7 = t5 * t6\nanswer = t7 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "63" + ], + "split": "train" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 80 sq . feet , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 20.0\nn1 = 80.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "find the area of the quadrilateral of one of its diagonals is 10 cm and its off sets 7 cm and 3 cm ?", + "Output Program": [ + "n0 = 10.0\nn1 = 7.0\nn2 = 3.0\nt0 = n1 + n2\nt1 = 1.0 / 2.0\nt2 = t0 * t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 15 inches by 24 inches and jordan ' s rectangle is 8 inches long , how wide is jordan ' s rectangle , in inches ?", + "Output Program": [ + "n0 = 15.0\nn1 = 24.0\nn2 = 8.0\nt0 = n0 * n1 # area of rectangle\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is 2 cm more than the width of the rectangle . the perimeter of the rectangle is 20 cm . find the length and the width of the rectangle .", + "Output Program": [ + "n0 = 2.0\nn1 = 20.0\nt0 = n1 / 2.0\nt1 = t0 - n0\nt2 = t1 / 2.0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "a cube has a volume of 27 cubic feet . if a similar cube is twice as long , twice as wide , and twice as high , then the volume , in cubic feet of such cube is ?", + "Output Program": [ + "n0 = 27.0\nt0 = n0**(1 / 3)\nt1 = t0 * 2.0\nanswer = t1**3\nprint(answer)" + ], + "Output Answer": [ + "216" + ], + "split": "train" + }, + { + "Input": "find the area of a parallelogram with base 20 cm and height 16 cm ?", + "Output Program": [ + "n0 = 20.0\nn1 = 16.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "320" + ], + "split": "train" + }, + { + "Input": "the volume of the sphere q is ( 37 / 64 ) % less than the volume of sphere p and the volume of sphere r is ( 19 / 27 ) % less than that of sphere q . by what is the surface area of sphere r less than the surface area of sphere p ?", + "Output Program": [ + "n0 = 37.0\nn1 = 64.0\nn2 = 19.0\nn3 = 27.0\nt0 = 1.0 / 3.0\nt1 = n1**min(t0, 5)\nt2 = n1 / t1\nt3 = t2 - t1\nt4 = t3 / t2\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "find the area of circle whose radius is 7 m ?", + "Output Program": [ + "import math\nn0 = 7.0\n\nanswer = math.pi * n0**2\nprint(answer)" + ], + "Output Answer": [ + "153.93804002589985" + ], + "split": "train" + }, + { + "Input": "in the rectangle below , the line mn cuts the rectangle into two regions . find x the length of segment nb so that the area of the quadrilateral mnbc is 40 % of the total area of the rectangle .", + "Output Program": [ + "n0 = 40.0\nt0 = n0 / 12.0\nt1 = t0 - 0.33\nanswer = t1 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "1.0033333333333334" + ], + "split": "train" + }, + { + "Input": "the floor of a rectangular room is 20 m long and 12 m wide . the room is surrounded by a veranda of width 2 m on all its sides . the area of the veranda is :", + "Output Program": [ + "n0 = 20.0\nn1 = 12.0\nn2 = 2.0\nt0 = n2 * n2\nt1 = n0 * n1 # area of rectangle\nt2 = n0 + t0\nt3 = n1 + t0\nt4 = t2 * t3 # area of rectangle\nanswer = t4 - t1\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "train" + }, + { + "Input": "what is the area of square field whose side of length 12 m ?", + "Output Program": [ + "n0 = 12.0\n\nanswer = n0**2\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "train" + }, + { + "Input": "in an electric circuit , three resistors with resistances 2 ohms , 5 ohms and 6 ohms are connected in parallel . in this case , if r is the combined resistance of these three resistors , then the reciprocal of r is equal to the sum of the reciprocals resistors . what is r value ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\nn2 = 6.0\nt0 = 1.0 / n0\nt1 = 1.0 / n1\nt2 = 1.0 / n2\nt3 = t0 + t1\nanswer = t3 + t2\nprint(answer)" + ], + "Output Answer": [ + "0.8666666666666666" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is increased by 25 % and its breadth is decreased by 15 % . what is the effect on its area ?", + "Output Program": [ + "n0 = 25.0\nn1 = 15.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "10625" + ], + "split": "train" + }, + { + "Input": "the ratio between the perimeter and the breadth of a rectangle is 5 : 1 . if the area of the rectangle is 216 sq . cm , what is the length of the rectangle ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 1.0\nn2 = 216.0\nt0 = 3.0 / 2.0\nt1 = n2 * t0\nanswer = math.sqrt(max(0, t1))\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "train" + }, + { + "Input": "a rectangular tiled patio is composed of 48 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 48 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?", + "Output Program": [ + "import math\nn0 = 48.0\nn1 = 2.0\nn2 = 4.0\nn3 = 48.0\nt0 = n0 * n1\nt1 = -n2\nt2 = n2**min(n1, 5)\nt3 = n2 * t0\nt4 = t3 + t2\nt5 = math.sqrt(max(0, t4))\nt6 = t1 + t5\nt7 = t6 / n1\nanswer = n0 / t7\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the sides of a cube measures 6.5 cm . if the surface area of the cube is the same as a ball , what is the radius of the ball ? round to the nearest whole number .", + "Output Program": [ + "import math\nn0 = 6.5\nt0 = 6 * n0**2 # surface of a cube\nt1 = t0 / 4.0\nt2 = t1 / 3.141592653589793\nt3 = math.sqrt(max(0, t2))\nanswer = math.floor(t3)\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 54 ?", + "Output Program": [ + "import math\nn0 = 289.0\nn1 = 54.0\nt0 = math.sqrt(max(0, n0))\nt1 = 4 * t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "3672" + ], + "split": "train" + }, + { + "Input": "the area of a square field is 7201 sq m . how long will a lady take to cross the field diagonally at the rate of 1.2 km / hr ?", + "Output Program": [ + "n0 = 7201.0\nn1 = 1.2\nt0 = n1 * 1000.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "6.0008333333333335" + ], + "split": "train" + }, + { + "Input": "the area of a parallelogram is 128 sq m and its altitude is twice the corresponding base . then the length of the base is ?", + "Output Program": [ + "import math\nn0 = 128.0\nt0 = n0 / 2.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "three runners running around a circular track can complete one revolution in 2 , 4 and 5.5 respectively . when will they meet at starting point ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nn2 = 5.5\nt0 = n0 * n1\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "if the length of the diagonal of a square is 20 cm , then its perimeter must be", + "Output Program": [ + "import math\nn0 = 20.0\nt0 = n0**min(2.0, 5)\nt1 = math.sqrt(max(0, 2.0))\nt2 = t0 / 2.0\nt3 = math.sqrt(max(0, t2))\nt4 = t3 / t1\nanswer = 4 * t4\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "the length and breadth of a rectangle is increased by 10 % and 25 % respectively . what is the increase in the area ?. a . 27.5 %", + "Output Program": [ + "n0 = 10.0\nn1 = 25.0\nt0 = n0 + 100.0\nt1 = n1 + 100.0\nt2 = 100.0 * 100.0 # area of rectangle\nt3 = t0 * t1 # area of rectangle\nt4 = t3 - t2\nt5 = t4 * 100.0\nanswer = t5 / t2\nprint(answer)" + ], + "Output Answer": [ + "37.5" + ], + "split": "train" + }, + { + "Input": "a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 50 cents . how many cents does a solution of 1 liter of spirit and 2 liters of water cost ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 50.0\nn3 = 1.0\nn4 = 2.0\nt0 = n0 + n4\nt1 = n0 / t0\nt2 = n2 * t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "49.99999999999999" + ], + "split": "train" + }, + { + "Input": "in a company of 180 employees , 110 are females . a total of 90 employees have advanced degrees and the rest have a college degree only . if 35 employees are males with a college degree only , how many employees are females with advanced degrees ?", + "Output Program": [ + "n0 = 180.0\nn1 = 110.0\nn2 = 90.0\nn3 = 35.0\nt0 = n0 - n1\nt1 = t0 - n3\nanswer = n2 - t1\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "train" + }, + { + "Input": "if the sides of a square are multiplied by 10 , the area of the original square is how many times as large as the area of the resultant square ?", + "Output Program": [ + "n0 = 10.0\nt0 = n0 * n0\nanswer = t0 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 10 inches tall . carmen places her sculpture on a base that is 8 inches tall . how tall are the sculpture andbase together ?", + "Output Program": [ + "n0 = 2.0\nn1 = 10.0\nn2 = 8.0\nt0 = n0 + n1\nt1 = n0 * t0\nt2 = t1 + n1\nt3 = n2 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "3.5" + ], + "split": "train" + }, + { + "Input": "a hall is 15 m long and 12 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of 4 walls , the volume of the hall is :", + "Output Program": [ + "n0 = 15.0\nn1 = 12.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nt2 = n0 * n1 # area of rectangle\nt3 = t0 + t1\nt4 = t2 * 2.0\nt5 = t4 / t3\nanswer = n0 * n1 * t5\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "train" + }, + { + "Input": "if the sides of a triangle are 30 cm , 28 cm and 12 cm , what is its area ?", + "Output Program": [ + "n0 = 30.0\nn1 = 28.0\nn2 = 12.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "168" + ], + "split": "train" + }, + { + "Input": "the width of a rectangular hall is \u00bd of its length . if the area of the hall is 128 sq . m , what is the difference between its length and breadth ?", + "Output Program": [ + "import math\nn0 = 128.0\nt0 = 1.0 / 2.0\nt1 = n0 / t0\nt2 = math.sqrt(max(0, t1))\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is double its width . if the length is diminished by 5 cm and the width is increased by 5 cm then its area is increased by 75 cm square . what is the length of the rectangle ?", + "Output Program": [ + "n0 = 5.0\nn1 = 5.0\nn2 = 75.0\nt0 = n0 * n0\nt1 = n2 + t0\nt2 = t1 / n0\nanswer = t2 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "train" + }, + { + "Input": "the perimeters of 2 squares are 40 cm and 32 cm . find the perimeter of a third square whose area is equal to the difference of the areas of the two squares ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 40.0\nn2 = 32.0\nt0 = n1 / 4.0\nt1 = n2 / 4.0\nt2 = t0**2\nt3 = t1**2\nt4 = t2 - t3\nt5 = math.sqrt(max(0, t4))\nanswer = 4 * t5\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is increased by 20 % and its breadth is decreased by 20 % . what is the effect on its area ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "9600" + ], + "split": "train" + }, + { + "Input": "a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 100,000 and at the same time n is a perfect square and a perfect cube ?", + "Output Program": [ + "n0 = 100000.0\nt0 = 2.0 + 4.0\nanswer = t0 / 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "the perimeter of an equilateral triangle is 60 . if one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 65 , then how long is the base of isosceles triangle ?", + "Output Program": [ + "n0 = 60.0\nn1 = 65.0\nt0 = n0 / 3.0\nt1 = n1 - t0\nanswer = t1 - t0\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "if the area of a square with sides of length 12 centimeters is equal to the area of a rectangle with a width of 6 centimeters , what is the length of the rectangle , in centimeters ?", + "Output Program": [ + "n0 = 12.0\nn1 = 6.0\nt0 = n0**min(2.0, 5)\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "a circle and a rectangle have the same perimeter . the sides of the rectangle are 18 cm and 26 cm . what is the area of the circle ?", + "Output Program": [ + "import math\nn0 = 18.0\nn1 = 26.0\nt0 = n0 + n1\nt1 = t0 / 3.141592653589793\nanswer = math.pi * t1**2\nprint(answer)" + ], + "Output Answer": [ + "616.2479396518188" + ], + "split": "train" + }, + { + "Input": "the product of the squares of two positive integers is 400 . how many pairs of positive integers satisfy this condition ?", + "Output Program": [ + "n0 = 400.0\nt0 = 2.0 + 3.0\nanswer = t0 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a cubical block of metal weighs 7 pounds . how much will another cube of the same metal weigh if its sides are twice as long ?", + "Output Program": [ + "n0 = 7.0\nt0 = 2.0 * 4.0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "train" + }, + { + "Input": "the roof of an apartment building is rectangular and its length is 4 times longer than its width . if the area of the roof is 676 feet squared , what is the difference between the length and the width of the roof ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 676.0\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * n0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "39" + ], + "split": "train" + }, + { + "Input": "the area of a rectangular plot is 360 square metres . if the length is 25 % less than the breadth , what is the breadth of the plot ?", + "Output Program": [ + "import math\nn0 = 360.0\nn1 = 25.0\nt0 = n1 / 100.0\nt1 = 1.0 - t0\nt2 = n0 / t1\nanswer = math.sqrt(max(0, t2))\nprint(answer)" + ], + "Output Answer": [ + "21.908902300206645" + ], + "split": "train" + }, + { + "Input": "a semicircle has a radius of 14 . what is the approximate perimeter of the semicircle ?", + "Output Program": [ + "import math\nn0 = 14.0\nt0 = 2 * math.pi * n0\nt1 = n0 * 2.0\nt2 = t0 / 2.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "71.9822971502571" + ], + "split": "train" + }, + { + "Input": "in measuring the sides of a rectangle , one side is taken 6 % in excess , and the other 5 % in deficit . find the error percent in the area calculated from these measurements .", + "Output Program": [ + "n0 = 6.0\nn1 = 5.0\nt0 = n0 * n1\nt1 = n0 - n1\nt2 = t0 / 100.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.7" + ], + "split": "train" + }, + { + "Input": "if the diameter of circle r is 50 % of the diameter of circle s , the area of circle r is what percent of the area of circle s ?", + "Output Program": [ + "import math\nn0 = 50.0\nt0 = math.pi * n0**2\nt1 = math.pi * 100.0**2\nt2 = t0 * 100.0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular garden is three times its width . if the area of the rectangular garden is 432 square meters , then what is the width of the rectangular garden ?", + "Output Program": [ + "import math\nn0 = 432.0\nt0 = n0 / 3.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the perimeter of one face of a cube is 24 cm . its volume will be :", + "Output Program": [ + "n0 = 24.0\nt0 = n0 / 4. # square edge given perimeter\nanswer = t0**3\nprint(answer)" + ], + "Output Answer": [ + "216" + ], + "split": "train" + }, + { + "Input": "a photograph is copied onto a sheet of paper 8.5 inches by 10 inches . a 1.5 inch margin is left all around . what area in square inches does the picture cover ?", + "Output Program": [ + "n0 = 8.5\nn1 = 10.0\nn2 = 1.5\nt0 = n1 - 3.0\nt1 = n0 - 3.0\nanswer = t0 * t1 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "38.5" + ], + "split": "train" + }, + { + "Input": "square of 99 = ?", + "Output Program": [ + "n0 = 99.0\n\nanswer = n0 * n0\nprint(answer)" + ], + "Output Answer": [ + "9801" + ], + "split": "train" + }, + { + "Input": "how much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 11 inches than that of a rectangular sheet of paper measuring 5.5 inches by 11 inches ?", + "Output Program": [ + "n0 = 11.0\nn1 = 11.0\nn2 = 5.5\nn3 = 11.0\nt0 = n0 * n1 # area of rectangle\nt1 = n0 * n2 # area of rectangle\nt2 = t0 * 2.0\nt3 = t1 * 2.0\nt4 = t2 - t3\nt5 = t4 / t0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "the circumferences of two circles are 396 meters and 704 meters . find the difference between the areas of the larger and the smaller circles ?", + "Output Program": [ + "import math\nn0 = 396.0\nn1 = 704.0\nt0 = 2.0 * 3.141592653589793\nt1 = n1 / t0\nt2 = n0 / t0\nt3 = math.pi * t1**2\nt4 = math.pi * t2**2\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "26960.847359767075" + ], + "split": "train" + }, + { + "Input": "a rectangular tank needs to be coated with insulation . the tank has dimensions of 4 feet , 5 feet , and 3 feet . each square foot of insulation costs $ 20 . how much will it cost to cover the surface of the tank with insulation ?", + "Output Program": [ + "n0 = 4.0\nn1 = 5.0\nn2 = 3.0\nn3 = 20.0\nt0 = 2 * (n0 * n1 + n0 * n2 + n1 * n2) # surface of a rectangular prism\nanswer = n3 * t0\nprint(answer)" + ], + "Output Answer": [ + "1880" + ], + "split": "train" + }, + { + "Input": "there is a square of side 6 cm . a circle is inscribed inside the square . find the ratio of the area of circle to square .", + "Output Program": [ + "import math\nn0 = 6.0\nt0 = n0 / 2.0\nt1 = n0**2\nt2 = math.pi * t0**2\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.7853981633974483" + ], + "split": "train" + }, + { + "Input": "one side of a rectangular field is 4 m and its length along diagonal is 5 m . what is the area of the field ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 5.0\nt0 = n1**min(2.0, 5)\nt1 = n0**min(2.0, 5)\nt2 = t0 - t1\nt3 = math.sqrt(max(0, t2))\nanswer = n0 * t3 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "the surface of a cube is 24 sq cm . find its volume ?", + "Output Program": [ + "import math\nn0 = 24.0\nt0 = 2.0 + 4.0\nt1 = n0 / t0\nt2 = math.sqrt(max(0, t1))\nanswer = t2**3\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "6 points lie on the circumference of a ellipse . what is the positive difference between the number of triangles and the number of quadrilaterals that can be created by connecting these points ?", + "Output Program": [ + "import math\nn0 = 6.0\nt0 = math.factorial(min(15, int(n0)))\nt1 = math.factorial(min(15, int(3.0)))\nt2 = math.factorial(min(15, int(4.0)))\nt3 = math.factorial(min(15, int(2.0)))\nt4 = t1 * t1\nt5 = t2 * t3\nt6 = t0 / t4\nt7 = t0 / t5\nanswer = t6 - t7\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "if the areas of the three adjacent faces of a cuboidal box are 120 cm \u00b2 , 72 cm \u00b2 and 60 cm \u00b2 respectively , then find the volume of the box .", + "Output Program": [ + "import math\nn0 = 120.0\nn1 = 72.0\nn2 = 60.0\nt0 = n0 * n2\nt1 = t0 / n1\nt2 = math.sqrt(max(0, t1))\nt3 = n0 / t2\nt4 = n2 / t2\nanswer = t3 * t4 * t2\nprint(answer)" + ], + "Output Answer": [ + "720" + ], + "split": "train" + }, + { + "Input": "the diagonal of a rhombus are 62 m and 80 m . its area is :", + "Output Program": [ + "n0 = 62.0\nn1 = 80.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "2480" + ], + "split": "train" + }, + { + "Input": "carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 5 inches by 24 inches and jordan ' s rectangle is 2 inches long , how wide is jordan ' s rectangle , in inches ?", + "Output Program": [ + "n0 = 5.0\nn1 = 24.0\nn2 = 2.0\nt0 = n0 * n1 # area of rectangle\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "30 square stone slabs of equal size were needed to cover a floor area of 58.8 sq . m . find the length of each stone slab ?", + "Output Program": [ + "import math\nn0 = 30.0\nn1 = 58.8\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nanswer = t1 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "train" + }, + { + "Input": "what is the area of square field whose side of length 17 m ?", + "Output Program": [ + "n0 = 17.0\n\nanswer = n0**2\nprint(answer)" + ], + "Output Answer": [ + "289" + ], + "split": "train" + }, + { + "Input": "a larger cube has 125 cubic inch as a volume and in the cube there are 125 smaller cubes such that their volume is 1 cubic inch . what is the difference between the surface areas \u2019 sum of the 125 smaller cubes and the surface area of the larger cube , in square inch ?", + "Output Program": [ + "n0 = 125.0\nn1 = 125.0\nn2 = 1.0\nn3 = 125.0\nt0 = n2**(1 / 3)\nt1 = n0**(1 / 3)\nt2 = 6 * t0**2 # surface of a cube\nt3 = 6 * t1**2 # surface of a cube\nt4 = n0 * t2\nanswer = t4 - t3\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "train" + }, + { + "Input": "in measuring the sides of a rectangle , one side is taken 8 % in excess and other 5 % in deficit . find the error percentage in the area calculated from these measurements .", + "Output Program": [ + "n0 = 8.0\nn1 = 5.0\nt0 = n0 * n1\nt1 = n0 - n1\nt2 = t0 / 100.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "2.6" + ], + "split": "train" + }, + { + "Input": "a person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes . if field has a length that is twice its width , find the area of the field in square meters .", + "Output Program": [ + "n0 = 10.0\nn1 = 12.0\nn2 = 30.0\nt0 = n1 / 2.0\nt1 = t0 / n0\nt2 = t1 * 1000.0\nt3 = t2 / 2.0\nt4 = t3 / 3.0\nt5 = t4 * 2.0\nanswer = t4 * t5 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "20000" + ], + "split": "train" + }, + { + "Input": "all the faces of cubes are painted with red colour . it is then cut into 64 equal small cubes . find how many small cubes have no faces coloured ?", + "Output Program": [ + "n0 = 64.0\nt0 = n0 / 4.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "for a right angle triangle the hypotenuse is 5 and base is 3 . what is the area of the triangle ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 3.0\nt0 = 1.0 / 2.0\nt1 = n0**min(2.0, 5)\nt2 = n1**min(2.0, 5)\nt3 = t0 * 3.0\nt4 = t1 - t2\nt5 = math.sqrt(max(0, t4))\nanswer = t3 * t5\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "10 business executives and 3 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?", + "Output Program": [ + "n0 = 10.0\nn1 = 3.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nt2 = n0 * t1\nt3 = t2 / 2.0\nanswer = t3 + t0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "if a rectangular billboard has an area of 117 square feet and a perimeter of 44 feet , what is the length of each of the shorter sides ?", + "Output Program": [ + "import math\nn0 = 117.0\nn1 = 44.0\nt0 = n1 / 2.0\nt1 = n0 * 4.0\nt2 = t0**min(2.0, 5)\nt3 = t2 - t1\nt4 = math.sqrt(max(0, t3))\nt5 = t0 - t4\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "the length of the rectangular field is double its width . inside the field there is square shaped pond 7 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?", + "Output Program": [ + "import math\nn0 = 7.0\nn1 = 1.0\nn2 = 8.0\nt0 = 1 / 2.0\nt1 = n0**2\nt2 = n2 * t1\nt3 = t2 / t0\nanswer = math.sqrt(max(0, t3))\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "train" + }, + { + "Input": "in a company of 200 employees , 120 are females . a total of 100 employees have advanced degrees and the rest have a college degree only . if 40 employees are males with a college degree only , how many employees are females with advanced degrees ?", + "Output Program": [ + "n0 = 200.0\nn1 = 120.0\nn2 = 100.0\nn3 = 40.0\nt0 = n0 - n1\nt1 = t0 - n3\nanswer = n2 - t1\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "the percentage increase in the area of a rectangle , if each of its sides is increased by 20 % is", + "Output Program": [ + "n0 = 20.0\nt0 = n0 + 100.0\nt1 = t0 / 100.0\nt2 = t1 * t1\nt3 = t2 - 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "43.99999999999999" + ], + "split": "train" + }, + { + "Input": "find the area of the quadrilateral of one of its diagonals is 28 cm and its off sets 8 cm and 2 cm ?", + "Output Program": [ + "n0 = 28.0\nn1 = 8.0\nn2 = 2.0\nt0 = n1 + n2\nt1 = 1.0 / 2.0\nt2 = t0 * t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "train" + }, + { + "Input": "what positive number , when squared , is equal to the cube of the positive square root of 16 ?", + "Output Program": [ + "import math\nn0 = 16.0\nt0 = 1.0 / 2.0\nt1 = n0**min(t0, 5)\nt2 = t1**min(3.0, 5)\nanswer = math.sqrt(max(0, t2))\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a volume of 10976 l water is in a container of sphere . how many hemisphere of volume 4 l each will be required to transfer all the water into the small hemispheres ?", + "Output Program": [ + "n0 = 10976.0\nn1 = 4.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "2744" + ], + "split": "train" + }, + { + "Input": "frank the fencemaker needs to fence in a rectangular yard . he fences in the entire yard , except for one full side of the yard , which equals 40 feet . the yard has an area of 200 square feet . how many feet offence does frank use ?", + "Output Program": [ + "n0 = 40.0\nn1 = 200.0\nt0 = n1 / n0\nt1 = t0 + t0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many p cubes are painted on only 2 faces ?", + "Output Program": [ + "n0 = 27.0\nn1 = 2.0\nt0 = 1.0 / 3.0\nt1 = n0**min(t0, 5)\nanswer = t1 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "a rectangular grass field is 65 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?", + "Output Program": [ + "n0 = 65.0\nn1 = 55.0\nn2 = 2.5\nn3 = 2.0\nt0 = n2 * n3\nt1 = n0 * n1 # area of rectangle\nt2 = n0 + t0\nt3 = n1 + t0\nt4 = t2 * t3 # area of rectangle\nt5 = t4 - t1\nanswer = n3 * t5\nprint(answer)" + ], + "Output Answer": [ + "1250" + ], + "split": "train" + }, + { + "Input": "the roof of an apartment building is rectangular and its length is 3 times longer than its width . if the area of the roof is 768 feet squared , what is the difference between the length and the width of the roof ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 768.0\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * n0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "the length of rectangle is thrice its breadth and its perimeter is 64 m , find the area of the rectangle ?", + "Output Program": [ + "n0 = 64.0\nt0 = 2.0 * 3.0\nt1 = 1.0 * 2.0\nt2 = t0 + t1\nt3 = n0 / t2\nt4 = t3 * 3.0\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "192" + ], + "split": "train" + }, + { + "Input": "the surface of a cube is 384 sq cm . find its volume ?", + "Output Program": [ + "import math\nn0 = 384.0\nt0 = 2.0 + 4.0\nt1 = n0 / t0\nt2 = math.sqrt(max(0, t1))\nanswer = t2**3\nprint(answer)" + ], + "Output Answer": [ + "512" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 4 cm , the area of the rectangle is increased by 75 sq . cm . find the length of the rectangle .", + "Output Program": [ + "n0 = 5.0\nn1 = 4.0\nn2 = 75.0\n\nanswer = 100.0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "33.333333333333336" + ], + "split": "train" + }, + { + "Input": "abcd is a square aegf is a rectangle . . such that the rectangle shares 25 % of the area of the suare also ae lies on the line ab and ag lies on segment of ad . if the square shares half the area of the rectangle what is the ratio ae : ag ?", + "Output Program": [ + "n0 = 25.0\nt0 = n0 / 100.0\nt1 = 1.0 / 2.0\nt2 = 1.0 / t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 60 sq . feet , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 20.0\nn1 = 60.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "26" + ], + "split": "train" + }, + { + "Input": "the minimum number of tiles of size 16 by 24 required to form a square by placing them adjacent to one another is", + "Output Program": [ + "n0 = 16.0\nn1 = 24.0\n\nanswer = n1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "find the perimeter and area of a square of side 12 cm .", + "Output Program": [ + "n0 = 12.0\n\nanswer = n0**2\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "train" + }, + { + "Input": "the cost of the paint is rs . 20 per kg . if 1 kg of paint covers 15 sq . ft , how much will it cost to paint outside of a cube having 5 feet each side", + "Output Program": [ + "n0 = 20.0\nn1 = 1.0\nn2 = 15.0\nn3 = 5.0\nt0 = 6 * n3**2 # surface of a cube\nt1 = t0 / n2\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "train" + }, + { + "Input": "if the sides of a triangle are 26 cm , 18 cm and 10 cm , what is its area ?", + "Output Program": [ + "n0 = 26.0\nn1 = 18.0\nn2 = 10.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "if the area of a square with sides of length 3 centimeters is equal to the area of a rectangle with a width of 3 centimeters , what is the length of the rectangle , in centimeters ?", + "Output Program": [ + "n0 = 3.0\nn1 = 3.0\nt0 = n0**min(2.0, 5)\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a crate measures 5 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still fit in the crate ?", + "Output Program": [ + "n0 = 5.0\nn1 = 8.0\nn2 = 12.0\nt0 = n1 * n2\nt1 = n0 * t0\nt2 = t1 / n2\nanswer = t2 / n1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "three rugs have a combined area of 204 square meters . by overlapping the rugs to cover floor area of 140 square meters , the area that is covered by exactly two layers of rug is 24 square meters . what is the area that is covered with three layers of rug ?", + "Output Program": [ + "n0 = 204.0\nn1 = 140.0\nn2 = 24.0\nt0 = n0 - n1\nt1 = t0 - n2\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "train" + }, + { + "Input": "a rectangular grass field is 75 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 7 per sq m ?", + "Output Program": [ + "n0 = 75.0\nn1 = 55.0\nn2 = 2.5\nn3 = 7.0\nt0 = n2 * 2.0\nt1 = n0 * n1 # area of rectangle\nt2 = n0 + t0\nt3 = n1 + t0\nt4 = t2 * t3 # area of rectangle\nt5 = t4 - t1\nanswer = n3 * t5\nprint(answer)" + ], + "Output Answer": [ + "4725" + ], + "split": "train" + }, + { + "Input": "what no should be subtracted from 92555 to make it a perfect square ?", + "Output Program": [ + "import math\nn0 = 92555.0\nt0 = math.sqrt(max(0, n0))\nt1 = math.floor(t0)\nt2 = t1 * t1\nanswer = n0 - t2\nprint(answer)" + ], + "Output Answer": [ + "139" + ], + "split": "train" + }, + { + "Input": "a hall is 6 meters long and 6 meters wide . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , what is the volume of the hall ( in cubic meters ) ?", + "Output Program": [ + "n0 = 6.0\nn1 = 6.0\nt0 = n0 * n1 # area of rectangle\nt1 = 2 * (n0 + n1) # perimetere of rectangle\nt2 = t0 * 2.0\nt3 = t2 / t1\nanswer = n0 * n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "108" + ], + "split": "train" + }, + { + "Input": "the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 72 of the area of the field . what is the length of the field ?", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 1.0\nn2 = 72.0\nt0 = 1 / 2.0\nt1 = n0**2\nt2 = n2 * t1\nt3 = t2 / t0\nanswer = math.sqrt(max(0, t3))\nprint(answer)" + ], + "Output Answer": [ + "96" + ], + "split": "train" + }, + { + "Input": "a horse is tethered to one corner of a rectangular grassy field 46 m by 20 m with a rope 17 m long . over how much area of the field can it graze ?", + "Output Program": [ + "n0 = 46.0\nn1 = 20.0\nn2 = 17.0\nt0 = n2**min(2.0, 5)\nt1 = t0 * 3.141592653589793\nanswer = t1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "226.98006922186255" + ], + "split": "train" + }, + { + "Input": "find the area of a parallelogram with base 32 cm and height 22 cm ?", + "Output Program": [ + "n0 = 32.0\nn1 = 22.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "704" + ], + "split": "train" + }, + { + "Input": "a rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 2 per sq m ?", + "Output Program": [ + "n0 = 80.0\nn1 = 60.0\nn2 = 10.0\nn3 = 2.0\nt0 = n0 + n1\nt1 = t0 - n2\nt2 = n2 * t1\nanswer = n3 * t2\nprint(answer)" + ], + "Output Answer": [ + "2600" + ], + "split": "train" + }, + { + "Input": "in the rectangular coordinate system , points ( 2 , 0 ) and ( \u2013 2 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 0.0\nn2 = 2.0\nn3 = 0.0\nt0 = n0**min(2.0, 5)\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 12 inches by 15 inches and jordan ' s rectangle is 6 inches long , how wide is jordan ' s rectangle , in inches ?", + "Output Program": [ + "n0 = 12.0\nn1 = 15.0\nn2 = 6.0\nt0 = n0 * n1 # area of rectangle\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "train" + }, + { + "Input": "a larger cube has 8 cubic inch as a volume and in the cube there are 8 smaller cubes such that their volume is 1 cubic inch . what is the difference between the surface areas \u2019 sum of the 8 smaller cubes and the surface area of the larger cube , in square inch ?", + "Output Program": [ + "n0 = 8.0\nn1 = 8.0\nn2 = 1.0\nn3 = 8.0\nt0 = n2**(1 / 3)\nt1 = n0**(1 / 3)\nt2 = 6 * t0**2 # surface of a cube\nt3 = 6 * t1**2 # surface of a cube\nt4 = n0 * t2\nanswer = t4 - t3\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "train" + }, + { + "Input": "a rectangular carpet has an area of 60 sq . m . if its diagonal and longer side together equal 5 times the shorter side , the length of the carpet is :", + "Output Program": [ + "import math\nn0 = 60.0\nn1 = 5.0\nt0 = n0 * 10.0\nt1 = n1**min(2.0, 5)\nt2 = t1 - 1.0\nt3 = t0 / t2\nt4 = math.sqrt(max(0, t3))\nanswer = n0 / t4\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "in a rectangular metallic piece of paper that covers exactly the area of a cube . the length of the piece of paper is 48 inches and the width is 72 inches . what is the volume of the cube in cubic feet is 1 feet is 12 inches ?", + "Output Program": [ + "import math\nn0 = 48.0\nn1 = 72.0\nn2 = 1.0\nn3 = 12.0\nt0 = n0 / n3\nt1 = n1 / n3\nt2 = t0 * t1 # area of rectangle\nt3 = t2 / t1\nt4 = math.sqrt(t3) # square edge given area\nanswer = t4**3\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "danny is sitting on a rectangular box . the area of the front face of the box is half the area of the top face , and the area of the top face is 1.5 times the area of the side face . if the volume of the box is 5184 , what is the area of the side face of the box ?", + "Output Program": [ + "n0 = 1.5\nn1 = 5184.0\nt0 = 1.0 / 3.0\nt1 = n1**min(2.0, 5)\nt2 = t1 * 3.0\nt3 = t2**min(t0, 5)\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "287.9999999999999" + ], + "split": "train" + }, + { + "Input": "a snooker tournament charges $ 45.00 for vip seats and $ 20.00 for general admission ( \u201c regular \u201d seats ) . on a certain night , a total of 320 tickets were sold , for a total cost of $ 7,500 . how many fewer tickets were sold that night for vip seats than for general admission seats ?", + "Output Program": [ + "n0 = 45.0\nn1 = 20.0\nn2 = 320.0\nn3 = 7500.0\nt0 = 3.0 + 4.0\nt1 = 2.0 + 3.0\nt2 = n1 * n2\nt3 = t0 * 1000.0\nt4 = t1 * 100.0\nt5 = t1 * t1\nt6 = t3 + t4\nt7 = t6 - t2\nt8 = t7 / t5\nanswer = n2 - t8\nprint(answer)" + ], + "Output Answer": [ + "276" + ], + "split": "train" + }, + { + "Input": "a rectangular floor that measures 6 meters by 10 meters is to be covered with carpet squares that each measure 2 meters by 2 meters . if the carpet squares cost $ 15 apiece , what is the total cost for the number of carpet squares needed to cover the floor ?", + "Output Program": [ + "n0 = 6.0\nn1 = 10.0\nn2 = 2.0\nn3 = 2.0\nn4 = 15.0\n\nanswer = n4 * n4\nprint(answer)" + ], + "Output Answer": [ + "225" + ], + "split": "train" + }, + { + "Input": "how much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 9 inches than that of a rectangular sheet of paper measuring 4.5 inches by 11 inches ?", + "Output Program": [ + "n0 = 11.0\nn1 = 9.0\nn2 = 4.5\nn3 = 11.0\nt0 = n0 * n1 # area of rectangle\nt1 = n0 * n2 # area of rectangle\nt2 = t0 * 2.0\nt3 = t1 * 2.0\nt4 = t2 - t3\nt5 = t4 / t0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular field is 7 / 5 its width . if the perimeter of the field is 432 meters , what is the width of the field ?", + "Output Program": [ + "n0 = 7.0\nn1 = 5.0\nn2 = 432.0\nt0 = n0 / n1\nt1 = t0 + t0\nt2 = t1 + 2.0\nanswer = n2 / t2\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "train" + }, + { + "Input": "difference between the length and breadth of a rectangle is 23 m . ifits perimeter is 206 m , then its area is ? ?", + "Output Program": [ + "n0 = 23.0\nn1 = 206.0\nt0 = n1 / 2.0\nt1 = t0 - n0\nt2 = t1 / 2.0\nt3 = n0 + t2\nanswer = t3 * t2 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "2520" + ], + "split": "train" + }, + { + "Input": "a volume of 11248 l water is in a container of sphere . how many hemisphere of volume 4 l each will be required to transfer all the water into the small hemispheres ?", + "Output Program": [ + "n0 = 11248.0\nn1 = 4.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "2812" + ], + "split": "train" + }, + { + "Input": "if the difference of two numbers is 3 and the difference of their square is 39 , then the larger number is :", + "Output Program": [ + "n0 = 3.0\nn1 = 39.0\nt0 = n1 / n0\nt1 = t0 - n0\nt2 = t1 / 2.0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm ?", + "Output Program": [ + "n0 = 20.0\nn1 = 9.0\nn2 = 6.0\nt0 = n1 + n2\nt1 = 1.0 / 2.0\nt2 = t0 * t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "train" + }, + { + "Input": "a circular plate with a diameter of 10 inches is kept on another plate of 12 inches diameter . what fraction of the big plate ' s surface is not covered by the small plate ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 12.0\nt0 = n1 / 2.0\nt1 = n0 / 2.0\nt2 = math.pi * t0**2\nt3 = math.pi * t1**2\nt4 = t2 - t3\nanswer = t4 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.3055555555555555" + ], + "split": "train" + }, + { + "Input": "what is the probability of getting equilateral triangles from the vertices of regular hexagon ?", + "Output Program": [ + "import scipy\nt0 = 3.0 + 3.0\nt1 = scipy.special.comb(t0, 3.0)\nanswer = 2.0 / t1\nprint(answer)" + ], + "Output Answer": [ + "0.1" + ], + "split": "train" + }, + { + "Input": "the roof of an apartment building is rectangular and its length is 4 times longer than its width . if the area of the roof is 576 feet squared , what is the difference between the length and the width of the roof ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 576.0\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * n0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "train" + }, + { + "Input": "a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 197 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ?", + "Output Program": [ + "n0 = 1.0\nn1 = 197.0\nt0 = 0.25 + 0.25\nt1 = n1 / 2.0\nt2 = t0 + t1\nanswer = t2**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "9801" + ], + "split": "train" + }, + { + "Input": "the area of a rectangular field is equal to 50 square meters . its perimeter is equal to 30 meters . find the width of this rectangle .", + "Output Program": [ + "import math\nn0 = 50.0\nn1 = 30.0\nt0 = n1 / 2.0\nt1 = n0 * 4.0\nt2 = t0 * t0\nt3 = t2 - t1\nt4 = math.sqrt(max(0, t3))\nt5 = t0 - t4\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 2025 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?", + "Output Program": [ + "import math\nn0 = 2025.0\nn1 = 10.0\nt0 = n1 / 2.0\nt1 = math.sqrt(max(0, n0))\nt2 = t1 / t0\nt3 = t2 * 2.0\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "train" + }, + { + "Input": "if each edge of a cube is increased by 50 % , find the percentage increase in its surface area", + "Output Program": [ + "n0 = 50.0\nt0 = 3.0 / 2.0\nt1 = 2.0 * 3.0\nt2 = t0**min(2.0, 5)\nt3 = t1 * t2\nt4 = t3 - t1\nt5 = t4 / t1\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "train" + }, + { + "Input": "the diagonal of a square is 4 ? 2 cm . what will be the diameter of another square if their area is double that of the first square ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 2.0\nt0 = n0 * n1\nt1 = t0**2\nanswer = math.sqrt(max(0, t1))\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "train" + }, + { + "Input": "a volume of 10936 l water is in a container of sphere . how many hemisphere of volume 4 l each will be required to transfer all the water into the small hemispheres ?", + "Output Program": [ + "n0 = 10936.0\nn1 = 4.0\n\nanswer = n0 / n1\nprint(answer)" + ], + "Output Answer": [ + "2734" + ], + "split": "train" + }, + { + "Input": "if a rectangle have length 16 cm and diagonal 20 cm . calculate its area .", + "Output Program": [ + "import math\nn0 = 16.0\nn1 = 20.0\nt0 = n1**min(2.0, 5)\nt1 = n0**min(2.0, 5)\nt2 = t0 - t1\nt3 = math.sqrt(max(0, t2))\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "192" + ], + "split": "train" + }, + { + "Input": "a circle graph shows how the budget of a certain company was spent : 20 percent for transportation , 9 percent for research and development , 5 percent for utilities , 4 percent for equipment , 2 percent for supplies , and the remainder for salaries . if the area of each sector of the graph is proportional to the percent of the budget it represents , how many degrees of the circle are used to represent salaries ?", + "Output Program": [ + "n0 = 20.0\nn1 = 9.0\nn2 = 5.0\nn3 = 4.0\nn4 = 2.0\nt0 = n0 + n1\nt1 = n2 + t0\nt2 = n3 + t1\nt3 = n4 + t2\nt4 = t3 * 360.0\nt5 = t4 / 100.0\nanswer = 360.0 - t5\nprint(answer)" + ], + "Output Answer": [ + "216" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is halved , while its breadth is tripled . what is the % change in area ?", + "Output Program": [ + "t0 = 1.0 / 2.0\nt1 = t0 * 3.0\nt2 = t1 - 1.0\nt3 = t2 / 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "train" + }, + { + "Input": "the volume of a cube is 729 cc . find its surface .", + "Output Program": [ + "n0 = 729.0\nt0 = n0**(1 / 3)\nanswer = 6 * t0**2 # surface of a cube\nprint(answer)" + ], + "Output Answer": [ + "485.99999999999983" + ], + "split": "train" + }, + { + "Input": "a cheese factory sells its cheese in rectangular blocks . a normal block has a volume of 4 cubic feet . if a large block has twice the width , twice the depth , and twice the length of a normal block , what is the volume of cheese in a large block in cubic feet ?", + "Output Program": [ + "n0 = 4.0\nt0 = 2.0 * 2.0\nt1 = t0 * 2.0\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "the monthly rent of a shop of dimension 20 feet \u00d7 18 feet is rs . 1440 . what is the annual rent per square foot of the shop ?", + "Output Program": [ + "n0 = 20.0\nn1 = 18.0\nn2 = 1440.0\nt0 = 10.0 + 2.0\nt1 = n0 * n1 # area of rectangle\nt2 = n2 / t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is increased by 25 % and its breadth is decreased by 20 % . what is the effect on its area ?", + "Output Program": [ + "n0 = 25.0\nn1 = 20.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "10000" + ], + "split": "train" + }, + { + "Input": "12 * 18 * 6 is the volume of some material . how many cubes of edge 3 can be insert into it ?", + "Output Program": [ + "n0 = 12.0\nn1 = 18.0\nn2 = 6.0\nn3 = 3.0\nt0 = n3**3\nt1 = n0 * n1 * n2\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "a hall is 15 m long and 12 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of areas of the four walls , the volume of hall is ?", + "Output Program": [ + "n0 = 15.0\nn1 = 12.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nt2 = n0 * n1 # area of rectangle\nt3 = t0 + t1\nt4 = t2 * 2.0\nt5 = t4 / t3\nanswer = n0 * n1 * t5\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "train" + }, + { + "Input": "the floor of a rectangular room is 21 m long and 12 m wide . the room is surrounded by a veranda of width 2 m on all its sides . the area of the veranda is :", + "Output Program": [ + "n0 = 21.0\nn1 = 12.0\nn2 = 2.0\nt0 = n2 * n2\nt1 = n0 * n1 # area of rectangle\nt2 = n0 + t0\nt3 = n1 + t0\nt4 = t2 * t3 # area of rectangle\nanswer = t4 - t1\nprint(answer)" + ], + "Output Answer": [ + "148" + ], + "split": "train" + }, + { + "Input": "the length of a rectangular landscape is 8 times its breadth . there is a playground in it whose area is 1200 square mtr & which is 1 / 6 rd of the total landscape . what is the length of the landscape ?", + "Output Program": [ + "n0 = 8.0\nn1 = 1200.0\nn2 = 1.0\nn3 = 6.0\nt0 = 4.0 * n3\nanswer = t0 * 10.0\nprint(answer)" + ], + "Output Answer": [ + "240" + ], + "split": "train" + }, + { + "Input": "the area of a side of a box is 120 sq cm . the area of the other side of the box is 72 sq cm . if the area of the upper surface of the box is 60 sq cm then find the volume of the box .", + "Output Program": [ + "import math\nn0 = 120.0\nn1 = 72.0\nn2 = 60.0\nt0 = n0 / n2\nt1 = n1 * n2\nt2 = t1 / n0\nt3 = math.sqrt(max(0, t2))\nt4 = n2 / t3\nt5 = t0 * t3\nanswer = t4 * t5 * t3\nprint(answer)" + ], + "Output Answer": [ + "720" + ], + "split": "train" + }, + { + "Input": "what is the percentage increase in the area of a rectangle , if each of its sides is increased by 20 % ?", + "Output Program": [ + "n0 = 20.0\nt0 = n0 + 100.0\nt1 = 100.0 * 100.0\nt2 = t0 * t0\nt3 = t2 - t1\nanswer = t3 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "44" + ], + "split": "train" + }, + { + "Input": "in a rectangular coordinate system , what is the area of a triangle whose vertices have the coordinates ( 3 , 0 ) , ( 6 , 3 ) , and ( 6 , - 3 ) ?", + "Output Program": [ + "n0 = 3.0\nn1 = 0.0\nn2 = 6.0\nn3 = 3.0\nn4 = 6.0\nn5 = 3.0\n\nanswer = n0 * n2 / 2\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "triangle a \u2019 s base is 10 % greater than the base of triangle b , and a \u2019 s height is 10 % less than the height of triangle b . the area of triangle a is what percent less or more than the area of triangle b ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 10.0\nt0 = math.floor(100.0)\nt1 = n0 * t0\nt2 = t1 / 100.0\nt3 = t2 + t0\nt4 = t0 - t2\nt5 = t3 * t4 / 2\nanswer = t5 / t5\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "train" + }, + { + "Input": "what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 55 ?", + "Output Program": [ + "import math\nn0 = 289.0\nn1 = 55.0\nt0 = math.sqrt(max(0, n0))\nt1 = 4 * t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "3740" + ], + "split": "train" + }, + { + "Input": "you have 59 cubic blocks . what is the minimum number that needs to be taken away in order to construct a solid cube with none left over ?", + "Output Program": [ + "n0 = 59.0\nt0 = 3.0 * 3.0\nt1 = t0 * 3.0\nanswer = n0 - t1\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "if the diameter of circle r is 20 % of the diameter of circle s , the area of circle r is what percent of the area of circle s ?", + "Output Program": [ + "import math\nn0 = 20.0\nt0 = math.pi * n0**2\nt1 = math.pi * 100.0**2\nt2 = t0 * 100.0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "train" + }, + { + "Input": "a rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn . the area of the lawn is 2109 sq . m . what is the width of the road ?", + "Output Program": [ + "import math\nn0 = 60.0\nn1 = 40.0\nn2 = 2109.0\nt0 = n0 + n1\nt1 = 1.0 * 4.0\nt2 = n0 * n1\nt3 = 1.0 * 2.0\nt4 = 100.0**min(2.0, 5)\nt5 = -t0\nt6 = t2 - n2\nt7 = t1 * t6\nt8 = -t5\nt9 = t4 - t7\nt10 = math.sqrt(max(0, t9))\nt11 = t8 - t10\nanswer = t11 / t3\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "a powder tin has a square base with side 8 cm and height 14 cm . another tin has a circular base with diameter 8 cm and height 14 cm . the difference in their capacities is :", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 14.0\nn2 = 8.0\nn3 = 14.0\nt0 = n0 / 2.0\nt1 = n0 * n0 * n1\nt2 = math.pi * t0**2 * n1\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "192.28324559588634" + ], + "split": "train" + }, + { + "Input": "what is the area of a square field whose diagonal of length 26 m ?", + "Output Program": [ + "n0 = 26.0\nt0 = n0**2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "338" + ], + "split": "train" + }, + { + "Input": "a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many j cubes are painted on only 2 faces ?", + "Output Program": [ + "n0 = 27.0\nn1 = 2.0\nt0 = 1.0 / 3.0\nt1 = n0**min(t0, 5)\nanswer = t1 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "train" + }, + { + "Input": "when a certain perfect square is increased by 148 , the result is another perfect square . what is the value of the original perfect square ?", + "Output Program": [ + "n0 = 148.0\nt0 = 3.0 * 3.0\nt1 = t0 * 4.0\nanswer = t1 * t1\nprint(answer)" + ], + "Output Answer": [ + "1296" + ], + "split": "train" + }, + { + "Input": "huey ' s hip pizza sells two sizes of square pizzas : a small pizza that measures 14 inches on a side and costs $ 10 , and a large pizza that measures 21 inches on a side and costs $ 20 . if two friends go to huey ' s with $ 30 apiece , how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone ?", + "Output Program": [ + "n0 = 14.0\nn1 = 10.0\nn2 = 21.0\nn3 = 20.0\nn4 = 30.0\nt0 = n2**min(2.0, 5)\nt1 = n0**min(2.0, 5)\nt2 = t1 + t0\nt3 = t0 * 3.0\nt4 = t2 + t2\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "49" + ], + "split": "train" + }, + { + "Input": "find the curved surface area , if the radius of a cone is 7 m and slant height is 14 m ?", + "Output Program": [ + "n0 = 7.0\nn1 = 14.0\nt0 = n0 * n1\nanswer = t0 * 3.141592653589793\nprint(answer)" + ], + "Output Answer": [ + "307.8760800517997" + ], + "split": "train" + }, + { + "Input": "twenty - one dots are evenly spaced on the circumference of a circle . how many combinations of three dots can we make from these 21 dots that do not form an equilateral triangle ?", + "Output Program": [ + "n0 = 21.0\nt0 = 3.0 + 4.0\nt1 = n0 - 1.0\nt2 = n0 * t1\nt3 = t1 - 1.0\nt4 = t2 * t3\nt5 = t4 / 3.0\nt6 = t5 / 2.0\nanswer = t6 - t0\nprint(answer)" + ], + "Output Answer": [ + "1323" + ], + "split": "train" + }, + { + "Input": "if the area of circle is 616 sq cm then its circumference ?", + "Output Program": [ + "import math\nn0 = 616.0\nt0 = n0 / 3.141592653589793\nt1 = math.sqrt(max(0, t0))\nanswer = 2 * math.pi * t1\nprint(answer)" + ], + "Output Answer": [ + "87.98229536926875" + ], + "split": "train" + }, + { + "Input": "the slant height of a cone is 15 cm and radius of the base is 3 cm , find the curved surface of the cone ?", + "Output Program": [ + "n0 = 15.0\nn1 = 3.0\nt0 = n1 * 3.141592653589793\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "141.3716694115407" + ], + "split": "train" + }, + { + "Input": "a larger cube has 64 cubic inch as a volume and in the cube there are 64 smaller cubes such that their volume is 1 cubic inch . what is the difference between the surface areas \u2019 sum of the 64 smaller cubes and the surface area of the larger cube , in square inch ?", + "Output Program": [ + "n0 = 64.0\nn1 = 64.0\nn2 = 1.0\nn3 = 64.0\nt0 = n2**(1 / 3)\nt1 = n0**(1 / 3)\nt2 = 6 * t0**2 # surface of a cube\nt3 = 6 * t1**2 # surface of a cube\nt4 = n0 * t2\nanswer = t4 - t3\nprint(answer)" + ], + "Output Answer": [ + "288" + ], + "split": "train" + }, + { + "Input": "the perimeter of a triangle is 60 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle", + "Output Program": [ + "n0 = 60.0\nn1 = 2.5\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "train" + }, + { + "Input": "what is the area of square field whose side of length 20 m ?", + "Output Program": [ + "n0 = 20.0\n\nanswer = n0**2\nprint(answer)" + ], + "Output Answer": [ + "400" + ], + "split": "train" + }, + { + "Input": "the percentage increase in the area of a rectangle , if each of its sides is increased by 20 % is :", + "Output Program": [ + "n0 = 20.0\nt0 = n0 + 100.0\nt1 = t0 / 100.0\nt2 = t1 * t1\nt3 = t2 - 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "43.99999999999999" + ], + "split": "train" + }, + { + "Input": "a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 50,000 and at the same time n is a perfect square and a perfect cube ?", + "Output Program": [ + "n0 = 50000.0\nt0 = 2.0 + 4.0\nanswer = t0 / 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "train" + }, + { + "Input": "find the base k of the number system , if ( 524 ) 8 = ( 664 ) k ?", + "Output Program": [ + "import math\nn0 = 524.0\nn1 = 8.0\nn2 = 664.0\nt0 = 10.0 / 2.0\nt1 = n1 * 2.0\nt2 = n1**min(2.0, 5)\nt3 = t0 * t2\nt4 = t1 + t3\nt5 = t4 + 4.0\nt6 = 4.0 - t5\nt7 = t6 / 3.0\nt8 = t7 / 2.0\nt9 = t8 * 4.0\nt10 = 1.0 - t9\nt11 = math.sqrt(max(0, t10))\nt12 = t11 - 1.0\nanswer = t12 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "train" + }, + { + "Input": "an area of a circularplace is 17 hectares . find the cost of fencing it at the rate of rs . 3 permeter approximately .", + "Output Program": [ + "import math\nn0 = 17.56\nn1 = 3.0\nt0 = 10.0 * 1000.0\nt1 = n0 * t0\nt2 = t1 / 3.141592653589793\nt3 = math.sqrt(max(0, t2))\nt4 = 2 * math.pi * t3\nanswer = t4 * 3.0\nprint(answer)" + ], + "Output Answer": [ + "4456.443887106987" + ], + "split": "train" + }, + { + "Input": "the area of a circle is increased by 300 % . by what percent has the diameter of the circle increased ?", + "Output Program": [ + "n0 = 300.0\nt0 = 2.0 / 2.0\nanswer = t0 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "the area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm . what is the perimeter of the square ?", + "Output Program": [ + "import math\nn0 = 125.0\nn1 = 64.0\nt0 = 10.0 / 2.0\nt1 = n0 * n1 # area of rectangle\nt2 = t0 * t1\nt3 = math.sqrt(max(0, t2))\nanswer = t3 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "train" + }, + { + "Input": "find the curved surface area , if the radius of a cone is 21 m and slant height is 15 m ?", + "Output Program": [ + "n0 = 21.0\nn1 = 15.0\nt0 = n0 * n1\nanswer = t0 * 3.141592653589793\nprint(answer)" + ], + "Output Answer": [ + "989.6016858807849" + ], + "split": "train" + }, + { + "Input": "the length of a rectangle is reduced by 10 % . by what % would the width have to be increased to maintain the original area ?", + "Output Program": [ + "n0 = 10.0\nt0 = 100.0 - n0\nt1 = t0 / 100.0\nt2 = 1.0 - t1\nt3 = t2 / t1\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "11.111111111111107" + ], + "split": "train" + }, + { + "Input": "the area of a square is 144 m \u00b2 . find its perimeter .", + "Output Program": [ + "import math\nn0 = 144.0\nt0 = math.sqrt(max(0, n0))\nanswer = 4 * t0\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "if the area of a square with sides of length 6 centimeters is equal to the area of a rectangle with a width of 4 centimeters , what is the length of the rectangle , in centimeters ?", + "Output Program": [ + "n0 = 6.0\nn1 = 4.0\nt0 = n0**min(2.0, 5)\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "train" + }, + { + "Input": "a certain cube floating in a bucket of water has between 75 and 85 percent of its volume below the surface of the water . if between 9 and 16 cubic centimeters of the cube ' s volume is above the surface of the water , then the length of a side of the cube is approximately", + "Output Program": [ + "n0 = 75.0\nn1 = 85.0\nn2 = 9.0\nn3 = 16.0\nt0 = n3 * 100.0\nt1 = 100.0 - n0\nt2 = t0 / t1\nanswer = t2**(1 / 3)\nprint(answer)" + ], + "Output Answer": [ + "3.9999999999999996" + ], + "split": "train" + }, + { + "Input": "four horses are tethered at 4 corners of a square field of side 70 metres so that they just can not reach one another . the area left ungrazed by the horses is :", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 70.0\nt0 = n1 / 2.0\nt1 = n1**2\nt2 = math.pi * t0**2\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "1051.5489993525034" + ], + "split": "train" + }, + { + "Input": "the cost of the paint is rs . 36.50 per kg . if 1 kg of paint covers 16 square feet , how much will it cost to paint outside of a cube having 8 feet each side .", + "Output Program": [ + "n0 = 36.5\nn1 = 1.0\nn2 = 16.0\nn3 = 8.0\nt0 = 6 * n3**2 # surface of a cube\nt1 = t0 / n2\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "876" + ], + "split": "train" + }, + { + "Input": "a cylindrical container with 6 meters diameter and a height of 8 meters is filled to capacity with water . if the water is then used to fill several smaller cylinders ( 2 meters radius and 5 meters height ) , how many smaller cylinders can be filled to capacity before the larger cylinder becomes empty ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 8.0\nn2 = 2.0\nn3 = 5.0\nt0 = 2.0 + 4.0\nt1 = n0 / 2.0\nt2 = math.pi * n2**2 * n3\nt3 = t0 / 10.0\nt4 = math.pi * t1**2 * n1\nt5 = t4 / t2\nanswer = t5 - t3\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "train" + }, + { + "Input": "four circular cardboard pieces , each of radius 7 cm are placed in such a way that each piece touches two other pieces . the area of the space encosed by the four pieces is. four circular cardboard pieces , each of radius 7 cm are placed in such a way that each piece touches two other pieces . the area of the space encosed by the four pieces is", + "Output Program": [ + "n0 = 7.0\nn1 = 7.0\nt0 = n0 * 2.0\nt1 = n0**min(2.0, 5)\nt2 = t1 * 3.141592653589793\nt3 = t0**min(2.0, 5)\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "42.06195997410015" + ], + "split": "train" + }, + { + "Input": "the roof of an apartment building is rectangular and its length is 5 times longer than its width . if the area of the roof is 720 feet squared , what is the difference between the length and the width of the roof ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 720.0\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * n0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "train" + }, + { + "Input": "a rectangular plot 15 m \u00d7 10 m , has a path of grass outside it . if the area of grassy pathway is 54 m 2 , find the width of the path .", + "Output Program": [ + "import math\nn0 = 15.0\nn1 = 10.0\nn2 = 54.0\nn3 = 2.0\nt0 = 2 * (n0 + n1) # perimetere of rectangle\nt1 = t0 / 4.0\nt2 = t1**min(2.0, 5)\nt3 = n2 + t2\nt4 = math.sqrt(max(0, t3))\nanswer = t4 - t1\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "train" + }, + { + "Input": "how much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 13 inches than that of a rectangular sheet of paper measuring 6.5 inches by 11 inches ?", + "Output Program": [ + "n0 = 11.0\nn1 = 13.0\nn2 = 6.5\nn3 = 11.0\nt0 = n0 * n1 # area of rectangle\nt1 = n0 * n2 # area of rectangle\nt2 = t0 * 2.0\nt3 = t1 * 2.0\nt4 = t2 - t3\nt5 = t4 / t0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "train" + }, + { + "Input": "what is the measure of the angle w made by the diagonals of the any adjacent sides of a cube .", + "Output Program": [ + "\nanswer = 180.0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "train" + }, + { + "Input": "find the area of a parallelogram with base 25 cm and height 15 cm ?", + "Output Program": [ + "n0 = 25.0\nn1 = 15.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "375" + ], + "split": "train" + }, + { + "Input": "a circular well with a diameter of 2 metres , is dug to a depth of 10 metres . what is the volume of the earth dug out ?", + "Output Program": [ + "import math\nn0 = 2.0\nn1 = 10.0\nt0 = n0 / n0\nanswer = math.pi * t0**2 * n1\nprint(answer)" + ], + "Output Answer": [ + "31.41592653589793" + ], + "split": "train" + }, + { + "Input": "the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 \u03c0 \u00b7 r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams r ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 0.15\nn3 = 8.0\nn4 = 0.3\n\nanswer = n0 * n3\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "train" + }, + { + "Input": "in a certain parallelogram the degree measure of one angle exceeds that of the other by 70 what is the degree measure of the smaller angle ?", + "Output Program": [ + "n0 = 70.0\nt0 = 3600.0 / 10.0\nt1 = n0 * 2.0\nt2 = t0 - t1\nanswer = t2 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "train" + }, + { + "Input": "rectangular floors x and y have equal area . if floor x is 10 feet by 18 feet and floor y is 9 feet wide , what is the length of floor y , in feet ?", + "Output Program": [ + "n0 = 10.0\nn1 = 18.0\nn2 = 9.0\nt0 = n0 * n1 # area of rectangle\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 10 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?", + "Output Program": [ + "n0 = 25.0\nn1 = 15.0\nn2 = 12.0\nn3 = 10.0\nn4 = 6.0\nn5 = 3.0\nn6 = 4.0\nn7 = 3.0\nt0 = n0 + n1\nt1 = n2 * 2.0\nt2 = n4 * n5\nt3 = n5 * n6\nt4 = t0 * t1\nt5 = n5 * t3\nt6 = t4 - t2\nt7 = t6 - t5\nanswer = n3 * t7\nprint(answer)" + ], + "Output Answer": [ + "9060" + ], + "split": "dev" + }, + { + "Input": "the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 7 per metre approximately", + "Output Program": [ + "import math\nn0 = 17.56\nn1 = 7.0\nt0 = n0 / 3.141592653589793\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * 100.0\nt3 = 2 * math.pi * t2\nanswer = t3 * n1\nprint(answer)" + ], + "Output Answer": [ + "10398.369069916303" + ], + "split": "dev" + }, + { + "Input": "one side of a rectangular field is 14 m and one of its diagonal is 17 m . find the area of the field .", + "Output Program": [ + "import math\nn0 = 14.0\nn1 = 17.0\nt0 = n1**min(2.0, 5)\nt1 = n0**min(2.0, 5)\nt2 = t0 - t1\nt3 = math.sqrt(max(0, t2))\nanswer = n0 * t3 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "135.01111065390137" + ], + "split": "dev" + }, + { + "Input": "the area of an isosceles trapezoid with sides of length 5 and bases of length 9 and 15 is ?", + "Output Program": [ + "n0 = 5.0\nn1 = 9.0\nn2 = 15.0\n\nanswer = 4.0 * (n2 + n1) / 2 # quadrilateral area\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "dev" + }, + { + "Input": "if a 1 mm thick paper is folded so that the area is halved at every fold , then what would be the thickness of the pile after 50 folds ?", + "Output Program": [ + "import math\nn0 = 1.0\nn1 = 50.0\nt0 = n0 * 2.0\nanswer = math.log(max(1e-5, t0), 2)\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "dev" + }, + { + "Input": "the area of a square field is 625 km 2 . how long will it take for a horse to run around at the speed of 25 km / h ?", + "Output Program": [ + "import math\nn0 = 625.0\nn1 = 2.0\nn2 = 25.0\nt0 = math.sqrt(max(0, n0))\nt1 = t0 * 4.0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "dev" + }, + { + "Input": "a hall is 15 meters long and 10 meters wide . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , what is the volume of the hall ( in cubic meters ) ?", + "Output Program": [ + "n0 = 15.0\nn1 = 10.0\nt0 = n0 * n1 # area of rectangle\nt1 = 2 * (n0 + n1) # perimetere of rectangle\nt2 = t0 * 2.0\nt3 = t2 / t1\nanswer = n0 * n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "900" + ], + "split": "dev" + }, + { + "Input": "a square mirror has exactly half the area of the rectangular wall on which it is hung . if each side of the mirror is 54 inches and the width of the wall is 68 inches , what is the length of the wall , in inches ?", + "Output Program": [ + "n0 = 54.0\nn1 = 68.0\nt0 = n0**2\nt1 = t0 * 2.0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "85.76470588235294" + ], + "split": "dev" + }, + { + "Input": "a solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm . the height of the cone is :", + "Output Program": [ + "n0 = 6.0\nn1 = 12.0\nt0 = 3.0 * 4.0\nt1 = n0 * n0\nt2 = t0 * 3.0\nt3 = t2 * 3.0\nanswer = t3 / t1\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "the area of a square garden is q square feet and the perimeter is p feet . if q = p + 21 , what is the perimeter of the garden in feet ?", + "Output Program": [ + "n0 = 21.0\nt0 = 4.0 - 1.0\nt1 = n0 / t0\nanswer = t1 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "dev" + }, + { + "Input": "the length and breadth of a rectangle is increased by 10 % and 30 % respectively . what is the increase in the area ?", + "Output Program": [ + "n0 = 10.0\nn1 = 30.0\nt0 = n0 + 100.0\nt1 = n1 + 100.0\nt2 = 100.0 * 100.0 # area of rectangle\nt3 = t0 * t1 # area of rectangle\nt4 = t3 - t2\nt5 = t4 * 100.0\nanswer = t5 / t2\nprint(answer)" + ], + "Output Answer": [ + "43" + ], + "split": "dev" + }, + { + "Input": "the radius of a sphere is increased by 50 % . the increase in surface area of the sphere is :", + "Output Program": [ + "import math\nn0 = 50.0\nt0 = n0 / 100.0\nt1 = 4 * math.pi * 1.0**2\nt2 = t0 + 1.0\nt3 = 4 * math.pi * t2**2\nt4 = t3 - t1\nt5 = t4 / t1\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "125" + ], + "split": "dev" + }, + { + "Input": "sand is poured into a box so that the box is being filled at the rate of 4 cubic feet per hour . if the empty rectangular box is 7 feet long , 6 feet wide , and 2 feet deep , approximately how many hours does it take to fill the box ?", + "Output Program": [ + "n0 = 4.0\nn1 = 7.0\nn2 = 6.0\nn3 = 2.0\nt0 = n1 * n2\nt1 = n3 * t0\nanswer = t1 / n0\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "dev" + }, + { + "Input": "calculate the area of a triangle , if the sides of are 65 cm , 60 cm and 25 cm , what is its area ?", + "Output Program": [ + "n0 = 65.0\nn1 = 60.0\nn2 = 25.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "750" + ], + "split": "dev" + }, + { + "Input": "the admission charge in a water park is $ 1 by adult and $ 0.75 by child accompanying an adult . how much was there of child with an adult who paid in quite $ 3.25 to have access to the water park ?", + "Output Program": [ + "n0 = 1.0\nn1 = 0.75\nn2 = 3.25\nt0 = n0 * n2\nt1 = t0 * 2.0\nt2 = t1 - 0.25\nt3 = t2 - 0.25\nt4 = n0 + t3\nanswer = t4 - 4.0\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "a rectangle the length of which is 8 inches and the width of which is 6 inches is made up 48 1 inch by 1 inch squares . through how many of the squares does a diagonal of the rectangle pass ?", + "Output Program": [ + "n0 = 8.0\nn1 = 6.0\nn2 = 48.0\nn3 = 1.0\nn4 = 1.0\nt0 = n0 + n1\nanswer = t0 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "a diagonal of a polygon is an segment between two non - adjacent vertices of the polygon . how many diagonals does a regular 20 - sided polygon have ?", + "Output Program": [ + "n0 = 20.0\nt0 = n0 - 3.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "170" + ], + "split": "dev" + }, + { + "Input": "a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many h cubes are painted on only 2 faces ?", + "Output Program": [ + "n0 = 27.0\nn1 = 2.0\nt0 = 1.0 / 3.0\nt1 = n0**min(t0, 5)\nanswer = t1 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "the length of a rectangle is increased by 15 % and its breadth is decreased by 20 % . what is the effect on its area ?", + "Output Program": [ + "n0 = 15.0\nn1 = 20.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "9200" + ], + "split": "dev" + }, + { + "Input": "find the area of the quadrilateral of one of its diagonals is 28 cm and its off sets 9 cm and 6 cm ?", + "Output Program": [ + "n0 = 28.0\nn1 = 9.0\nn2 = 6.0\nt0 = n1 + n2\nt1 = 1.0 / 2.0\nt2 = t0 * t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "210" + ], + "split": "dev" + }, + { + "Input": "the length of a rectangle is 3 times its width . if the width of the rectangle is 6 inches , what is the rectangle ' s area , in square inches ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nt0 = n0 * n1\nanswer = n1 * t0 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "108" + ], + "split": "dev" + }, + { + "Input": "the length of a rectangle is 3 times its width . if the width of the rectangle is 4 inches , what is the rectangle ' s area , in square inches ?", + "Output Program": [ + "n0 = 3.0\nn1 = 4.0\nt0 = n0 * n1\nanswer = n1 * t0 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "48" + ], + "split": "dev" + }, + { + "Input": "the base and height of a parallelogram are 12 m and 6 m respectively . then its area is = = = = = = ?", + "Output Program": [ + "n0 = 12.0\nn1 = 6.0\n\nanswer = n0 * n1 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "dev" + }, + { + "Input": "you buy a piece of land with an area of \u00e2 \u02c6 \u0161 1600 , how long is one side of the land plot ?", + "Output Program": [ + "import math\nn0 = 1600.0\n\nanswer = math.sqrt(max(0, n0))\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "dev" + }, + { + "Input": "a small , rectangular park has a perimeter of 560 feet and a diagonal measurement of 600 feet . what is its area , in square feet ?", + "Output Program": [ + "n0 = 560.0\nn1 = 600.0\nt0 = 2.0 + 3.0\nt1 = n1 / t0\nt2 = t1 * 3.0\nt3 = t1 * 4.0\nanswer = t2 * t3\nprint(answer)" + ], + "Output Answer": [ + "172800" + ], + "split": "dev" + }, + { + "Input": "find the smallest number that should be multiplied with 54000 to make it a perfect cube .", + "Output Program": [ + "n0 = 54000.0\nt0 = n0 / 1000.0\nt1 = t0 / 3.0\nt2 = t1 / 3.0\nt3 = t2 / 3.0\nanswer = t3 * t3\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "dev" + }, + { + "Input": "right triangle xyzs the base of the prism in the figure above . if xy = xz = \u00e2 \u02c6 \u0161 9 and the height of the prism is 6 , what is the volume of the prism ?", + "Output Program": [ + "import math\nn0 = 9.0\nn1 = 6.0\nt0 = math.sqrt(max(0, n0))\nt1 = t0 * t0 / 2\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "dev" + }, + { + "Input": "if the diameter of circle r is 40 % of the diameter of circle s , the area of circle r is what percent of the area of circle s ?", + "Output Program": [ + "import math\nn0 = 40.0\nt0 = math.pi * n0**2\nt1 = math.pi * 100.0**2\nt2 = t0 * 100.0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "dev" + }, + { + "Input": "what is the perimeter of an isosceles right angled triangle . the area of the isosceles right angled triangle is 50 .", + "Output Program": [ + "import math\nn0 = 50.0\nt0 = n0 * 2.0\nt1 = math.sqrt(max(0, 2.0))\nt2 = math.sqrt(max(0, t0))\nt3 = t2 * t1\nanswer = t3 + t2 + t2 # perimeter of a triangle\nprint(answer)" + ], + "Output Answer": [ + "34.14213562373095" + ], + "split": "dev" + }, + { + "Input": "a semicircle has a radius of 10 . what is the approximate perimeter of the semicircle ?", + "Output Program": [ + "import math\nn0 = 10.0\nt0 = 2 * math.pi * n0\nt1 = n0 * 2.0\nt2 = t0 / 2.0\nanswer = t2 + t1\nprint(answer)" + ], + "Output Answer": [ + "51.41592653589793" + ], + "split": "dev" + }, + { + "Input": "the area of a triangle is with base 10 m and height 5 m ?", + "Output Program": [ + "n0 = 10.0\nn1 = 5.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "dev" + }, + { + "Input": "how many diagonals does a polygon with 13 sides have , if one of its vertices does not connect to any diagonal ?", + "Output Program": [ + "n0 = 13.0\nt0 = n0 - 1.0\nt1 = t0 - 3.0\nt2 = t0 * t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "dev" + }, + { + "Input": "the length of a rectangular garden is 2 feet longer than 3 times its width . if the perimeter of the garden is 100 feet , find the length of the garden .", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 100.0\nt0 = n0 * 4.0\nt1 = n2 - 4.0\nt2 = t1 / t0\nt3 = n1 * t2\nanswer = n0 + t3\nprint(answer)" + ], + "Output Answer": [ + "38" + ], + "split": "dev" + }, + { + "Input": "what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 40 % ?", + "Output Program": [ + "n0 = 40.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = t1**min(2.0, 5)\nt3 = t2 - 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "95.99999999999997" + ], + "split": "dev" + }, + { + "Input": "the length of the rectangular field is double its width . inside the field there is square shaped pond 9 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?", + "Output Program": [ + "import math\nn0 = 9.0\nn1 = 1.0\nn2 = 8.0\nt0 = 1 / 2.0\nt1 = n0**2\nt2 = n2 * t1\nt3 = t2 / t0\nanswer = math.sqrt(max(0, t3))\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "dev" + }, + { + "Input": "carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 10 inches tall . carmen places her sculpture on a base that is 10 inches tall . how tall are the sculpture andbase together ?", + "Output Program": [ + "n0 = 2.0\nn1 = 10.0\nn2 = 10.0\nt0 = n0 + n1\nt1 = n0 * t0\nt2 = t1 + n1\nt3 = n2 + t2\nanswer = t3 / t0\nprint(answer)" + ], + "Output Answer": [ + "3.6666666666666665" + ], + "split": "dev" + }, + { + "Input": "points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction w of the area of triangle abc is the area of triangle xyz ?", + "Output Program": [ + "n0 = 2.0\nn1 = 0.0\nn2 = 8.0\nn3 = 12.0\nn4 = 14.0\nn5 = 0.0\nn6 = 6.0\nn7 = 0.0\nn8 = 8.0\nn9 = 4.0\nn10 = 10.0\nn11 = 0.0\nt0 = 10.0 + 2.0\nt1 = 4.0**min(2.0, 5)\nt2 = t1 / 2.0\nt3 = t0**min(2.0, 5)\nt4 = t3 / 2.0\nanswer = t2 / t4\nprint(answer)" + ], + "Output Answer": [ + "0.1111111111111111" + ], + "split": "dev" + }, + { + "Input": "a square mirror has exactly half the area of the rectangular wall on which it is hung . if each side of the mirror is 21 inches and the width of the wall is 28 inches , what is the length of the wall , in inches ?", + "Output Program": [ + "n0 = 21.0\nn1 = 28.0\nt0 = n0**2\nt1 = t0 * 2.0\nanswer = t1 / n1\nprint(answer)" + ], + "Output Answer": [ + "31.5" + ], + "split": "dev" + }, + { + "Input": "a square with sides of 15 units each . what would be the area of the square . consider a square as a combination of two right angled triangles .", + "Output Program": [ + "n0 = 15.0\nt0 = n0 * n0 / 2\nanswer = t0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "225" + ], + "split": "dev" + }, + { + "Input": "an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 40 cm , find the sum of the perimeters of all the triangles .", + "Output Program": [ + "n0 = 2.0\nn1 = 1.0\nn2 = 3.0\nn3 = 2.0\nn4 = 1.0\nn5 = 40.0\nt0 = n5 + n5 + n5 # perimeter of a triangle\nanswer = t0 + t0\nprint(answer)" + ], + "Output Answer": [ + "240" + ], + "split": "dev" + }, + { + "Input": "surface area of a sphere is 2464 cm 2 . if its radius is doubled , then the surface area of the new sphere will be", + "Output Program": [ + "import math\nn0 = 2464.0\nn1 = 2.0\nt0 = 4.0 * 3.141592653589793\nt1 = n0 / t0\nt2 = math.sqrt(max(0, t1))\nt3 = t2 * 2.0\nanswer = 4 * math.pi * t3**2\nprint(answer)" + ], + "Output Answer": [ + "9856" + ], + "split": "dev" + }, + { + "Input": "the length of the rectangular field is double its width . inside the field there is square shaped pond 6 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 1.0\nn2 = 8.0\nt0 = 1 / 2.0\nt1 = n0**2\nt2 = n2 * t1\nt3 = t2 / t0\nanswer = math.sqrt(max(0, t3))\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "dev" + }, + { + "Input": "the area of a triangle is with base 2 m and height 3 m ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "dev" + }, + { + "Input": "the length of a rectangle is reduced by 20 % . by what % would the width have to be increased to maintainthe original area ?", + "Output Program": [ + "n0 = 20.0\nt0 = 100.0 - n0\nt1 = t0 / 100.0\nt2 = 1.0 - t1\nt3 = t2 / t1\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "24.999999999999993" + ], + "split": "dev" + }, + { + "Input": "find the area of a parallelogram with base 10 cm and height 20 cm .", + "Output Program": [ + "n0 = 10.0\nn1 = 20.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "dev" + }, + { + "Input": "the area of a rectangular plot is 15 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?", + "Output Program": [ + "n0 = 15.0\nn1 = 10.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "dev" + }, + { + "Input": "the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 7 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?", + "Output Program": [ + "n0 = 25.0\nn1 = 15.0\nn2 = 12.0\nn3 = 7.0\nn4 = 6.0\nn5 = 3.0\nn6 = 4.0\nn7 = 3.0\nt0 = n0 + n1\nt1 = n2 * 2.0\nt2 = n4 * n5\nt3 = n5 * n6\nt4 = t0 * t1\nt5 = n5 * t3\nt6 = t4 - t2\nt7 = t6 - t5\nanswer = n3 * t7\nprint(answer)" + ], + "Output Answer": [ + "6342" + ], + "split": "dev" + }, + { + "Input": "a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 181 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ?", + "Output Program": [ + "n0 = 1.0\nn1 = 181.0\nt0 = 0.25 + 0.25\nt1 = n1 / 2.0\nt2 = t0 + t1\nanswer = t2**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "8281" + ], + "split": "dev" + }, + { + "Input": "if the dimensions of a certain rectangular box are 5 inches by 2 inches by 3 inches , then the face of greatest area is of what area ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 3.0\n\nanswer = n0 * n2 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "15" + ], + "split": "dev" + }, + { + "Input": "the area of a triangle is with base 12 m and height 5 m ?", + "Output Program": [ + "n0 = 12.0\nn1 = 5.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "dev" + }, + { + "Input": "if the sides of a rectangle are increased by 35 % , what is the percentage increase in the area ?", + "Output Program": [ + "n0 = 35.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = t1**min(2.0, 5)\nt3 = t2 - 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "82.25000000000003" + ], + "split": "dev" + }, + { + "Input": "the percentage increase in the area of a rectangle , if each of its sides is increased by 20 % is ?", + "Output Program": [ + "n0 = 20.0\nt0 = n0 + 100.0\nt1 = t0 / 100.0\nt2 = t1 * t1\nt3 = t2 - 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "43.99999999999999" + ], + "split": "dev" + }, + { + "Input": "what is the maximum number e of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?", + "Output Program": [ + "import math\nn0 = 27.0\nn1 = 8.0\nn2 = 9.0\nn3 = 12.0\nt0 = 1 / 3.0\nt1 = n0**min(t0, 5)\nt2 = n1 / t1\nt3 = n3 / t1\nt4 = n2 / t1\nt5 = math.floor(t2)\nt6 = t3 * t4\nanswer = t5 * t6\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "dev" + }, + { + "Input": "the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 14 cm each . the radius of the sphere is", + "Output Program": [ + "import math\nn0 = 14.0\nt0 = n0 / 2.0\nt1 = 4.0 * 3.141592653589793\nt2 = n0 * t0\nt3 = t2 * 3.141592653589793\nt4 = t3 * 2.0\nt5 = t4 / t1\nanswer = math.sqrt(max(0, t5))\nprint(answer)" + ], + "Output Answer": [ + "7" + ], + "split": "dev" + }, + { + "Input": "the length and breadth of a rectangle is increased by 5 % and 15 % respectively . what is the increase in the area ?", + "Output Program": [ + "n0 = 5.0\nn1 = 15.0\nt0 = n0 + 100.0\nt1 = n1 + 100.0\nt2 = 100.0 * 100.0 # area of rectangle\nt3 = t0 * t1 # area of rectangle\nt4 = t3 - t2\nt5 = t4 * 100.0\nanswer = t5 / t2\nprint(answer)" + ], + "Output Answer": [ + "20.75" + ], + "split": "dev" + }, + { + "Input": "if the volume of two cubes are in the ratio 8 : 1 , the ratio of their edges is :", + "Output Program": [ + "n0 = 8.0\nn1 = 1.0\n\nanswer = n0**(1 / 3)\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "dev" + }, + { + "Input": "the area of a rectangular plot is 18 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?", + "Output Program": [ + "n0 = 18.0\nn1 = 10.0\n\nanswer = n0 - n1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "dev" + }, + { + "Input": "the perimeter of an isosceles right triangle is 14 + 14 sq rt 2 . what is the length of the hypotenuse of the triangle ?", + "Output Program": [ + "import math\nn0 = 14.0\nn1 = 14.0\nn2 = 2.0\nt0 = math.sqrt(max(0, n2))\nt1 = n0 * t0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "9.899494936611665" + ], + "split": "dev" + }, + { + "Input": "an error 2 % in excess is made while measuring the sideofa square . the % of error in the calculated area of the square is ?", + "Output Program": [ + "n0 = 2.0\nt0 = n0 + 100.0\nt1 = 100.0**2\nt2 = t0**2\nt3 = t2 - t1\nt4 = t3 * 100.0\nanswer = t4 / t1\nprint(answer)" + ], + "Output Answer": [ + "4.04" + ], + "split": "dev" + }, + { + "Input": "a circular ground whose diameter is 70 metres , has a 2.8 metre - broad garden around it . what is the area of the garden in square metres ?", + "Output Program": [ + "import math\nn0 = 70.0\nn1 = 2.8\nt0 = n0 / 2.0\nt1 = n1 + t0\nt2 = math.pi * t0**2\nt3 = math.pi * t1**2\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "640.3822465077428" + ], + "split": "dev" + }, + { + "Input": "find the area of a parallelogram with base 26 cm and height 16 cm ?", + "Output Program": [ + "n0 = 26.0\nn1 = 16.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "416" + ], + "split": "dev" + }, + { + "Input": "what will be the cost of building a fence around a square plot with area equal to 289 square feet , if the price per foot of building the fence is rs . 58 ?", + "Output Program": [ + "import math\nn0 = 289.0\nn1 = 58.0\nt0 = math.sqrt(max(0, n0))\nt1 = 4 * t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "3944" + ], + "split": "dev" + }, + { + "Input": "points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction d of the area of triangle abc is the area of triangle xyz ?", + "Output Program": [ + "n0 = 2.0\nn1 = 0.0\nn2 = 8.0\nn3 = 12.0\nn4 = 14.0\nn5 = 0.0\nn6 = 6.0\nn7 = 0.0\nn8 = 8.0\nn9 = 4.0\nn10 = 10.0\nn11 = 0.0\nt0 = 10.0 + 2.0\nt1 = 4.0**min(2.0, 5)\nt2 = t1 / 2.0\nt3 = t0**min(2.0, 5)\nt4 = t3 / 2.0\nanswer = t2 / t4\nprint(answer)" + ], + "Output Answer": [ + "0.1111111111111111" + ], + "split": "dev" + }, + { + "Input": "points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction c of the area of triangle abc is the area of triangle xyz ?", + "Output Program": [ + "n0 = 2.0\nn1 = 0.0\nn2 = 8.0\nn3 = 12.0\nn4 = 14.0\nn5 = 0.0\nn6 = 6.0\nn7 = 0.0\nn8 = 8.0\nn9 = 4.0\nn10 = 10.0\nn11 = 0.0\nt0 = 10.0 + 2.0\nt1 = 4.0**min(2.0, 5)\nt2 = t1 / 2.0\nt3 = t0**min(2.0, 5)\nt4 = t3 / 2.0\nanswer = t2 / t4\nprint(answer)" + ], + "Output Answer": [ + "0.1111111111111111" + ], + "split": "dev" + }, + { + "Input": "the cost of the paint is rs . 40.00 per kg . if 1 kg of paint covers 20 sq . ft , how much will it cost to paint outside of a cube having 10 feet each side", + "Output Program": [ + "n0 = 40.0\nn1 = 1.0\nn2 = 20.0\nn3 = 10.0\nt0 = 6 * n3**2 # surface of a cube\nt1 = t0 / n2\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "dev" + }, + { + "Input": "the ratio between the length and the breadth of a rectangular plot is 7 : 5 . if the perimeter of the plot is 288 metres , what is its area ?", + "Output Program": [ + "n0 = 7.0\nn1 = 5.0\nn2 = 288.0\nt0 = n0 / n1\nt1 = t0 + 1.0\nt2 = t1 * 2.0\nt3 = n2 / t2\nt4 = n0 * t3\nt5 = t4 / n1\nanswer = t5 * t3 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "5040" + ], + "split": "dev" + }, + { + "Input": "a metallic sheet is of rectangular shape with dimensions 46 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is :", + "Output Program": [ + "n0 = 46.0\nn1 = 36.0\nn2 = 8.0\nn3 = 3.0\nt0 = n2 * 2.0\nt1 = n0 - t0\nt2 = n1 - t0\nanswer = n2 * t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "4800" + ], + "split": "dev" + }, + { + "Input": "a box measuring 36 inches long by 45 inches wide by 18 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?", + "Output Program": [ + "n0 = 36.0\nn1 = 45.0\nn2 = 18.0\nt0 = n2 / 2.0\nt1 = n0 * n1\nt2 = n2 * t1\nt3 = t0**3\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "dev" + }, + { + "Input": "the cost of paint is 60 per kilograme . a kilogram paint covers 20 square feet . how much will it cost to paint the outside of a cube having each side 10 feet ?", + "Output Program": [ + "n0 = 60.0\nn1 = 20.0\nn2 = 10.0\nt0 = 2.0 * 3.0\nt1 = n2**min(2.0, 5)\nt2 = t0 * t1\nt3 = t2 / n1\nanswer = n0 * t3\nprint(answer)" + ], + "Output Answer": [ + "1800" + ], + "split": "dev" + }, + { + "Input": "if the radius of a circle that centers at the origin is 5 , how many points q on the circle have integer coordinates ?", + "Output Program": [ + "n0 = 5.0\nt0 = n0 + 4.0\nt1 = n0 * n0\nt2 = 2.0**min(2.0, 5)\nt3 = t1 - t0\nanswer = t3 - t2\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "the area of a triangle is 615 m 2 . if one of its sides is 123 metre , find the length of the perpendicular dropped on that side from opposite vertex .", + "Output Program": [ + "n0 = 615.0\nn1 = 2.0\nn2 = 123.0\nt0 = n0 * 2.0\nanswer = t0 / n2\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "find the sum of divisors of 544 which are perfect squares .", + "Output Program": [ + "import math\nn0 = 544.0\nt0 = n0 / 2.0\nt1 = t0 / 2.0\nt2 = t1 / 2.0\nt3 = t2 / 2.0\nt4 = t3 / 2.0\nt5 = n0 / t4\nt6 = t5 / 2.0\nt7 = math.sqrt(max(0, t6))\nt8 = t7 + 1.0\nanswer = t8 + t6\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "dev" + }, + { + "Input": "the diagonals of a rhombus are 10 cm and 12 cm . find its area ?", + "Output Program": [ + "n0 = 10.0\nn1 = 12.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "dev" + }, + { + "Input": "find the curved surface area , if the radius of a cone is 35 m and slant height is 30 m ?", + "Output Program": [ + "n0 = 35.0\nn1 = 30.0\nt0 = n0 * n1\nanswer = t0 * 3.141592653589793\nprint(answer)" + ], + "Output Answer": [ + "3298.6722862692827" + ], + "split": "dev" + }, + { + "Input": "the perimeter of an isosceles right triangle is 12 + 12 sq rt 2 . what is the length of the hypotenuse of the triangle ?", + "Output Program": [ + "import math\nn0 = 12.0\nn1 = 12.0\nn2 = 2.0\nt0 = math.sqrt(max(0, n2))\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "8.485281374238571" + ], + "split": "dev" + }, + { + "Input": "the cost of the paint is rs . 50 per kg . if 1 kg of paint covers 20 sq . ft , how much will it cost to paint outside of a cube having 20 feet each side", + "Output Program": [ + "n0 = 50.0\nn1 = 1.0\nn2 = 20.0\nn3 = 20.0\nt0 = 6 * n3**2 # surface of a cube\nt1 = t0 / n2\nanswer = n0 * t1\nprint(answer)" + ], + "Output Answer": [ + "6000" + ], + "split": "dev" + }, + { + "Input": "abcd is a parallelogram . bd = 2 . the angles of triangle bcd are all equal . what is the perimeter of the parallelogram ?", + "Output Program": [ + "n0 = 2.0\nt0 = n0 + n0\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "dev" + }, + { + "Input": "if circles x and y have the same area and circle x has a circumference of 18 \u03c0 , half of the radius of circle y is :", + "Output Program": [ + "n0 = 18.0\nt0 = n0 / 2.0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "4.5" + ], + "split": "dev" + }, + { + "Input": "the length of a rectangle is reduced by 22 % . by what % would the width have to be increased to maintain the original area ?", + "Output Program": [ + "n0 = 22.0\nt0 = 100.0 - n0\nt1 = t0 / 100.0\nt2 = 1.0 - t1\nt3 = t2 / t1\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "28.2051282051282" + ], + "split": "dev" + }, + { + "Input": "in a new housing development , trees are to be planted along the sidewalk of a certain street . each tree takes up one square foot of sidewalk space , and there are to be 12 feet between each tree . how many trees can be planted if the road is 157 feet long ?", + "Output Program": [ + "n0 = 12.0\nn1 = 157.0\nt0 = n0 + 1.0\nt1 = n1 - 1.0\nt2 = t1 / t0\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "dev" + }, + { + "Input": "the perimeter of a triangle is 42 cm and the inradius of the triangle is 5.0 cm . what is the area of the triangle ?", + "Output Program": [ + "n0 = 42.0\nn1 = 5.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "105" + ], + "split": "dev" + }, + { + "Input": "the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 867 sq m , then what is the breadth of the rectangular plot ?", + "Output Program": [ + "import math\nn0 = 867.0\nt0 = n0 / 3.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "17" + ], + "split": "dev" + }, + { + "Input": "the area of a square land is a square feet and the perimeter is p feet . if 5 a = 10 p + 45 , what is the perimeter of the land , in feet ?", + "Output Program": [ + "import math\nn0 = 5.0\nn1 = 10.0\nn2 = 45.0\nt0 = n2 / n0\nt1 = n1 * 4.0\nt2 = t1 / n0\nt3 = t0 * 4.0\nt4 = t2**min(2.0, 5)\nt5 = t3 + t4\nt6 = math.sqrt(max(0, t5))\nt7 = t2 + t6\nt8 = t7 / 2.0\nanswer = t8 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "dev" + }, + { + "Input": "a cube of edge 16 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 15 cm , find the rise in water level ?", + "Output Program": [ + "n0 = 16.0\nn1 = 20.0\nn2 = 15.0\nt0 = n1 * n2\nt1 = n0**3\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "13.653333333333334" + ], + "split": "dev" + }, + { + "Input": "the floor of a rectangular room is 18 m long and 12 m wide . the room is surrounded by a veranda of width 2 m on all its sides . the area of the veranda is :", + "Output Program": [ + "n0 = 18.0\nn1 = 12.0\nn2 = 2.0\nt0 = n2 * n2\nt1 = n0 * n1 # area of rectangle\nt2 = n0 + t0\nt3 = n1 + t0\nt4 = t2 * t3 # area of rectangle\nanswer = t4 - t1\nprint(answer)" + ], + "Output Answer": [ + "136" + ], + "split": "dev" + }, + { + "Input": "the radius of the two circular fields is in the ratio 4 : 10 the area of the second field is what percent greater than the area of the first ?", + "Output Program": [ + "n0 = 4.0\nn1 = 10.0\nt0 = n1**min(2.0, 5)\nt1 = n0**min(2.0, 5)\nanswer = t0 - t1\nprint(answer)" + ], + "Output Answer": [ + "84" + ], + "split": "dev" + }, + { + "Input": "the measure of the side of a square is quadrupled . if x represents the perimeter of the original square , what is the value of the new perimeter ?", + "Output Program": [ + "\nanswer = 1.0 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "dev" + }, + { + "Input": "the roof of an apartment building is rectangular and its length is 3 times longer than its width . if the area of the roof is 588 feet squared , what is the difference between the length and the width of the roof ?", + "Output Program": [ + "import math\nn0 = 3.0\nn1 = 588.0\nt0 = n1 / n0\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * n0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "28" + ], + "split": "dev" + }, + { + "Input": "a triangle and a parallelogram are constructed on the same base such that their areas are equal . if the altitude of the parallelogram is 100 m , then the altitude of the triangle is .", + "Output Program": [ + "n0 = 100.0\n\nanswer = n0 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "dev" + }, + { + "Input": "right triangle abc is to be drawn in the xy - plane so that the right angle is at a and ab is parallel to the y - axis . if the x - and y - coordinates of a , b , and c are to be integers that are consistent with the inequalities - 8 \u2264 x \u2264 2 and 4 \u2264 y \u2264 9 , then how many different triangles can be drawn that will meet these conditions ?", + "Output Program": [ + "n0 = 8.0\nn1 = 2.0\nn2 = 4.0\nn3 = 9.0\nt0 = n0 * n3\nt1 = n0 - 1.0\nt2 = n0 * t1\nanswer = t2 * t0\nprint(answer)" + ], + "Output Answer": [ + "4032" + ], + "split": "dev" + }, + { + "Input": "the value of \u201c a \u201d varies in inverse proportion as the square of \u201c b \u201d . if the value of \u201c a \u201d is equal to 40 when \u201c b \u201d is equal to 12 . what would be the value of \u201c a \u201d when \u201c b \u201d is equal to 24 ?", + "Output Program": [ + "n0 = 40.0\nn1 = 12.0\nn2 = 24.0\nt0 = n1**min(2.0, 5)\nt1 = n2**min(2.0, 5)\nt2 = n0 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 4 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?", + "Output Program": [ + "n0 = 25.0\nn1 = 15.0\nn2 = 12.0\nn3 = 4.0\nn4 = 6.0\nn5 = 3.0\nn6 = 4.0\nn7 = 3.0\nt0 = n0 + n1\nt1 = n2 * 2.0\nt2 = n4 * n5\nt3 = n5 * n6\nt4 = t0 * t1\nt5 = n5 * t3\nt6 = t4 - t2\nt7 = t6 - t5\nanswer = n3 * t7\nprint(answer)" + ], + "Output Answer": [ + "3624" + ], + "split": "dev" + }, + { + "Input": "the length of a rectangle is one fourth of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 784 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 5 units ?", + "Output Program": [ + "import math\nn0 = 784.0\nn1 = 5.0\nt0 = math.sqrt(max(0, n0))\nt1 = t0 / 4.0\nanswer = n1 * t1 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "dev" + }, + { + "Input": "if the height of a cone is increased by 140 % then its volume is increased by ?", + "Output Program": [ + "n0 = 140.0\n\nanswer = n0 * 1.0 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "dev" + }, + { + "Input": "in triangle pqr , the angle q = 90 degree , pq = 4 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz", + "Output Program": [ + "n0 = 90.0\nn1 = 4.0\nn2 = 8.0\nt0 = n1 * n2\nanswer = t0 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "3.2" + ], + "split": "dev" + }, + { + "Input": "a wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule , whose length and breadth are in the ratio of 6 : 5 . what is the area of the rectangle ?", + "Output Program": [ + "import math\nn0 = 3.5\nn1 = 6.0\nn2 = 5.0\nt0 = n1 + n2\nt1 = 2 * math.pi * n0\nt2 = t0 * 2.0\nt3 = t1 / t2\nt4 = n1 * t3\nt5 = n2 * t3\nanswer = t4 * t5 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "29.975864606614373" + ], + "split": "dev" + }, + { + "Input": "what is the measure of the angle q made by the diagonals of the any adjacent sides of a cube .", + "Output Program": [ + "\nanswer = 180.0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "dev" + }, + { + "Input": "a circular swimming pool is surrounded by a concrete wall 4 feet wide . if the area of the wall is 11 / 25 of the area of the pool , then the radius of the pool in feet is ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 11.0\nn2 = 25.0\nt0 = n1 / n2\nt1 = n0 * 2.0\nt2 = n0**min(2.0, 5)\nt3 = t0 * 4.0\nt4 = t1**min(2.0, 5)\nt5 = t3 * t2\nt6 = t5 + t4\nt7 = math.sqrt(max(0, t6))\nt8 = t1 + t7\nt9 = t8 / t0\nanswer = t9 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "dev" + }, + { + "Input": "find the area of a parallelogram with base 22 cm and height 14 cm ?", + "Output Program": [ + "n0 = 22.0\nn1 = 14.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "308" + ], + "split": "dev" + }, + { + "Input": "in a new housing development , trees are to be planted along the sidewalk of a certain street . each tree takes up one square foot of sidewalk space , and there are to be 9 feet between each tree . how many trees can be planted if the road is 151 feet long ?", + "Output Program": [ + "n0 = 9.0\nn1 = 151.0\nt0 = n0 + 1.0\nt1 = n1 - 1.0\nt2 = t1 / t0\nanswer = t2 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "dev" + }, + { + "Input": "the slant height of a cone is 35 cm and radius of the base is 14 cm , find the curved surface of the cone .", + "Output Program": [ + "n0 = 35.0\nn1 = 14.0\nt0 = n1 * 3.141592653589793\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "1539.3804002589986" + ], + "split": "dev" + }, + { + "Input": "if the length of the sides of two cubes are in the ratio 6 : 1 , what is the ratio of their total surface area ?", + "Output Program": [ + "n0 = 6.0\nn1 = 1.0\n\nanswer = n0 * n0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "dev" + }, + { + "Input": "if the volume of the cube is 729 cm 3 , then the surface area of the cube will be", + "Output Program": [ + "n0 = 729.0\nn1 = 3.0\nt0 = n0**(1 / 3)\nanswer = 6 * t0**2 # surface of a cube\nprint(answer)" + ], + "Output Answer": [ + "485.99999999999983" + ], + "split": "dev" + }, + { + "Input": "the diagonal of a rhombus are 70 m and 160 m . its area is :", + "Output Program": [ + "n0 = 70.0\nn1 = 160.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "5600" + ], + "split": "dev" + }, + { + "Input": "in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 4.5 ) , ( 8 , 0 ) , ( 0 , - 4.5 ) , ( - 8 , 0 ) ?", + "Output Program": [ + "n0 = 0.0\nn1 = 4.5\nn2 = 8.0\nn3 = 0.0\nn4 = 0.0\nn5 = 4.5\nn6 = 8.0\nn7 = 0.0\nt0 = n2 * 2.0\nt1 = n1 * 2.0\nanswer = t0 * t1 / 2\nprint(answer)" + ], + "Output Answer": [ + "72" + ], + "split": "dev" + }, + { + "Input": "a horse is tethered to one corner of a rectangular grassy field 42 m by 26 m with a rope 16 m long . over how much area of the field can it graze ?", + "Output Program": [ + "n0 = 42.0\nn1 = 26.0\nn2 = 16.0\nt0 = n2**min(2.0, 5)\nt1 = t0 * 3.141592653589793\nanswer = t1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "201.06192982974676" + ], + "split": "dev" + }, + { + "Input": "a farmer grows broccoli in his farm that is in the shape of a square . each broccoli takes 1 square foot of area in his garden . this year , he has increased his output by 101 broccoli when compared to last year . the shape of the area used for growing the broccoli has remained a square in both these years . how many broccoli did he produce this year ?", + "Output Program": [ + "n0 = 1.0\nn1 = 101.0\nt0 = n0 + n1\nt1 = t0 / 2.0\nanswer = t1**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "2601" + ], + "split": "dev" + }, + { + "Input": "a wall photo 2 inches wide is placed around a rectangular paper with dimensions 8 inches by 12 inches . what is the area of the wall photo , in square inches ?", + "Output Program": [ + "n0 = 2.0\nn1 = 8.0\nn2 = 12.0\nt0 = n0 * n1\nt1 = n1 * n2 # area of rectangle\nt2 = n2 * t0\nanswer = t2 - t1\nprint(answer)" + ], + "Output Answer": [ + "96" + ], + "split": "dev" + }, + { + "Input": "the perimeter of a triangle is 36 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle", + "Output Program": [ + "n0 = 36.0\nn1 = 2.5\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "dev" + }, + { + "Input": "if d is the smallest positive integer such that 3,150 multiplied by d is the square of an integer , then d must be", + "Output Program": [ + "n0 = 3150.0\nt0 = 2.0 + 3.0\nt1 = 100.0 / 2.0\nt2 = 1000.0 * 3.0\nt3 = t1 + t2\nt4 = t0**min(2.0, 5)\nt5 = t3 + 100.0\nt6 = t5 / 2.0\nt7 = t6 / t4\nt8 = t7 / 3.0\nt9 = t8 / 3.0\nanswer = t9 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "dev" + }, + { + "Input": "the diagonals of a rhombus are 15 cm and 20 cm . find its area ?", + "Output Program": [ + "n0 = 15.0\nn1 = 20.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "dev" + }, + { + "Input": "the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 4 per metre approximately", + "Output Program": [ + "import math\nn0 = 17.56\nn1 = 4.0\nt0 = n0 / 3.141592653589793\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * 100.0\nt3 = 2 * math.pi * t2\nanswer = t3 * n1\nprint(answer)" + ], + "Output Answer": [ + "5941.9251828093165" + ], + "split": "dev" + }, + { + "Input": "what will be the cost of building to paint which area equal to 196 sq ft , if the price per foot of building is rs . 15 ?", + "Output Program": [ + "import math\nn0 = 196.0\nn1 = 15.0\nt0 = math.sqrt(max(0, n0))\nt1 = 4 * t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "840" + ], + "split": "dev" + }, + { + "Input": "if the sides of a triangle are 26 cm , 24 cm and 15 cm , what is its area ?", + "Output Program": [ + "n0 = 26.0\nn1 = 24.0\nn2 = 15.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "180" + ], + "split": "dev" + }, + { + "Input": "what is the area a of the square with the following coordinates : ( x , y ) , ( 20 , 20 ) , ( 20 , 5 ) , ( x , 5 ) ?", + "Output Program": [ + "n0 = 20.0\nn1 = 20.0\nn2 = 20.0\nn3 = 5.0\nn4 = 5.0\nt0 = n0 - n3\nanswer = t0**2\nprint(answer)" + ], + "Output Answer": [ + "225" + ], + "split": "dev" + }, + { + "Input": "the perimeter of a triangle is 40 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ?", + "Output Program": [ + "n0 = 40.0\nn1 = 2.5\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "dev" + }, + { + "Input": "calculate the effect changes in dimension of a rectangle will have on its area , if length is increased by 40 % and its breadth is decreased by 25 % ?", + "Output Program": [ + "n0 = 40.0\nn1 = 25.0\nt0 = n0 + 100.0\nt1 = 100.0 * 100.0\nt2 = 100.0 - n1\nt3 = t0 * t2\nt4 = t3 - t1\nt5 = t4 / t1\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "dev" + }, + { + "Input": "the area of a square field is 7201 sq m . how long will a lady take to cross the field diagonally at the rate of 2.4 km / hr ?", + "Output Program": [ + "n0 = 7201.0\nn1 = 2.4\nt0 = n1 * 1000.0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "3.0004166666666667" + ], + "split": "dev" + }, + { + "Input": "the area of a circular field is 13.86 hectares . find the cost of fencing it at the rate of rs . 4.80 per metre .", + "Output Program": [ + "import math\nn0 = 13.86\nn1 = 4.8\nt0 = n0 / 3.141592653589793\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * 100.0\nt3 = 2 * math.pi * t2\nanswer = t3 * n1\nprint(answer)" + ], + "Output Answer": [ + "6334.72526658735" + ], + "split": "dev" + }, + { + "Input": "a football field is 8400 square yards . if 1200 pounds of fertilizer are spread evenly across the entire field , how many pounds of fertilizer were spread over an area of the field totaling 3500 square yards ?", + "Output Program": [ + "n0 = 8400.0\nn1 = 1200.0\nn2 = 3500.0\nt0 = n1 / n0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "dev" + }, + { + "Input": "a lady grows broccoli in her garden that is in the shape of a square . each broccoli takes 1 square foot of area in her garden . this year , she has increased her output by 79 broccoli when compared to last year . the shape of the area used for growing the broccoli has remained a square in both these years . how many broccoli did she produce this year ?", + "Output Program": [ + "n0 = 1.0\nn1 = 79.0\nt0 = n0 + n1\nt1 = t0 / 2.0\nanswer = t1**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "1600" + ], + "split": "dev" + }, + { + "Input": "the length of a rectangle is increased by 40 % while its width is halved . what is the % change in area ?", + "Output Program": [ + "n0 = 40.0\nt0 = n0 / 100.0\nt1 = 1.0 / 2.0\nt2 = t0 + 1.0\nt3 = t2 * t1\nt4 = 1.0 - t3\nanswer = t4 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "30.000000000000004" + ], + "split": "dev" + }, + { + "Input": "how many cones of radius 4 m , height 2 m can be formed from a cylinder of 12 m radius , 10 m height :", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 2.0\nn2 = 12.0\nn3 = 10.0\nt0 = math.pi * n0**2 * n1 / 3\nt1 = math.pi * n2**2 * n3\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "135" + ], + "split": "dev" + }, + { + "Input": "the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each . the radius of the sphere is", + "Output Program": [ + "import math\nn0 = 12.0\nt0 = n0 / 2.0\nt1 = 4.0 * 3.141592653589793\nt2 = n0 * t0\nt3 = t2 * 3.141592653589793\nt4 = t3 * 2.0\nt5 = t4 / t1\nanswer = math.sqrt(max(0, t5))\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "dev" + }, + { + "Input": "the area of a parallelogram is 72 sq m and its base is 12 m . then the length of the height is ?", + "Output Program": [ + "import math\nn0 = 72.0\nn1 = 12.0\nt0 = n0 / 2.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "dev" + }, + { + "Input": "if the length and breadth of a rectangular room are each increased by 1 m , then the area of floor is increased by 21 sq . m . if the length is creased by 1 m and breadth is decreased by 1 m , then the area is decreased by 5 sq . m . the perimeter of the floor is :", + "Output Program": [ + "n0 = 1.0\nn1 = 21.0\nn2 = 1.0\nn3 = 1.0\nn4 = 5.0\nt0 = n1 - n4\nt1 = n1 - n0\nt2 = t0 / 2.0\nt3 = t1 - t2\nanswer = 2 * (t2 + t3) # perimetere of rectangle\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "dev" + }, + { + "Input": "the ratio of male to female in a class is 2 : 3 . the career preference of the students in the class are to be represented in a circle graph . if the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one fourth of the males and 3 / 4 th of the females in the class ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 3.0\nn3 = 4.0\nt0 = n0 + n1\nt1 = 360.0 / t0\nt2 = n1 * t1\nt3 = n0 * t1\nt4 = t3 / 4.0\nt5 = n1 * t2\nt6 = t5 / n3\nanswer = t6 + t4\nprint(answer)" + ], + "Output Answer": [ + "198" + ], + "split": "dev" + }, + { + "Input": "a certain rectangular crate measures 6 feet by 8 feet by 10 feet . a cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces . what should the radius of the tank be if it is to be of the largest possible volume ?", + "Output Program": [ + "import math\nn0 = 6.0\nn1 = 8.0\nn2 = 10.0\nt0 = n1 / 2.0\nt1 = n0 * 3.141592653589793\nt2 = math.pi * t0**2 * n0\nt3 = t2 / t1\nanswer = math.sqrt(max(0, t3))\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "dev" + }, + { + "Input": "the volume of the sphere qq is ( dfrac { 37 } { 64 } % ) less than the volume of sphere pp and the volume of sphere rr is ( dfrac { 19 } { 27 } % ) less than that of sphere qq . by what is the surface areaof sphere rr less than the surfacearea of sphere pp ?", + "Output Program": [ + "n0 = 37.0\nn1 = 64.0\nn2 = 19.0\nn3 = 27.0\nt0 = 1.0 / 3.0\nt1 = n1**min(t0, 5)\nt2 = n3**min(t0, 5)\nt3 = t1 * t2\nt4 = t3 + t1\nt5 = t4 - t1\nt6 = t1 + t5\nt7 = t6 - t1\nt8 = t7 / t6\nanswer = t8 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "dev" + }, + { + "Input": "what will be the cost of gardening 1 meter boundary around a rectangular plot having perimeter of 340 meters at the rate of rs . 10 per square meter ?", + "Output Program": [ + "n0 = 1.0\nn1 = 340.0\nn2 = 10.0\nt0 = n1 + 4.0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "3440" + ], + "split": "dev" + }, + { + "Input": "a snooker tournament charges $ 45.00 for vip seats and $ 20.00 for general admission ( \u201c regular \u201d seats ) . on a certain night , a total of 320 tickets were sold , for a total cost of $ 7500 . how many fewer tickets were sold that night for vip seats than for general admission seats ?", + "Output Program": [ + "n0 = 45.0\nn1 = 20.0\nn2 = 320.0\nn3 = 7500.0\nt0 = n3 / n1\nt1 = n0 / n1\nt2 = t0 - n2\nt3 = t1 - 1.0\nt4 = t2 / t3\nanswer = n2 - t4\nprint(answer)" + ], + "Output Answer": [ + "276" + ], + "split": "dev" + }, + { + "Input": "a rectangular garden is to be twice as long as it is wide . if 150 yards of fencing , including the gate , will completely enclose the garden , what will be the length of the garden , in yards ?", + "Output Program": [ + "n0 = 150.0\nt0 = 1.0 + 2.0\nt1 = t0 * 2.0\nt2 = n0 / t1\nanswer = t2 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "dev" + }, + { + "Input": "what is the measure of the angle y made by the diagonals of the any adjacent sides of a cube .", + "Output Program": [ + "\nanswer = 180.0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "dev" + }, + { + "Input": "the length and breadth of a rectangle is increased by 3 % and 6 % respectively . what is the increase in the area ?", + "Output Program": [ + "n0 = 3.0\nn1 = 6.0\nt0 = n0 + 100.0\nt1 = n1 + 100.0\nt2 = 100.0 * 100.0 # area of rectangle\nt3 = t0 * t1 # area of rectangle\nt4 = t3 - t2\nt5 = t4 * 100.0\nanswer = t5 / t2\nprint(answer)" + ], + "Output Answer": [ + "9.18" + ], + "split": "dev" + }, + { + "Input": "the area of a triangle is with base 18 m and height 6 m ?", + "Output Program": [ + "n0 = 18.0\nn1 = 6.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "dev" + }, + { + "Input": "the area of a parallelogram is 288 sq m and its altitude is twice the corresponding base . then the length of the base is ?", + "Output Program": [ + "import math\nn0 = 288.0\nt0 = n0 / 2.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction q of the area of triangle abc is the area of triangle xyz ?", + "Output Program": [ + "n0 = 2.0\nn1 = 0.0\nn2 = 8.0\nn3 = 12.0\nn4 = 14.0\nn5 = 0.0\nn6 = 6.0\nn7 = 0.0\nn8 = 8.0\nn9 = 4.0\nn10 = 10.0\nn11 = 0.0\nt0 = 10.0 + 2.0\nt1 = 4.0**min(2.0, 5)\nt2 = t1 / 2.0\nt3 = t0**min(2.0, 5)\nt4 = t3 / 2.0\nanswer = t2 / t4\nprint(answer)" + ], + "Output Answer": [ + "0.1111111111111111" + ], + "split": "dev" + }, + { + "Input": "the height of a triangle is decreased by 5 % and its base increased by 10 % . its area will", + "Output Program": [ + "n0 = 5.0\nn1 = 10.0\nt0 = n1 + 100.0\nt1 = 100.0 - n0\nt2 = t0 * t1\nt3 = t2 / 100.0\nanswer = t3 - 100.0\nprint(answer)" + ], + "Output Answer": [ + "4.5" + ], + "split": "dev" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 800 sq . ft , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 20.0\nn1 = 800.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "dev" + }, + { + "Input": "the length of a rectangle is halved , while its breadth is tripled . watis the % change in area ?", + "Output Program": [ + "t0 = 1.0 / 2.0\nt1 = t0 * 3.0\nt2 = t1 - 1.0\nt3 = t2 / 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "dev" + }, + { + "Input": "there is a rectangular prism made of 1 in cubes that has been covered in tin foil . there are exactly 128 cubes that are not touching any tin foil on any of their sides . if the width of the figure created by these 128 cubes is twice the length and twice the height , what is the measure y in inches of the width of the foil covered prism ?", + "Output Program": [ + "n0 = 1.0\nn1 = 128.0\nn2 = 128.0\nt0 = 1 / 3.0\nt1 = n0 * 2.0\nt2 = n0 * t1\nt3 = n1 / t2\nt4 = t3**min(t0, 5)\nt5 = t1 * t4\nanswer = t5 + t1\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "the length of rectangle is thrice its breadth and its perimeter is 104 m , find the area of the rectangle ?", + "Output Program": [ + "n0 = 104.0\nt0 = 2.0 * 3.0\nt1 = 1.0 * 2.0\nt2 = t0 + t1\nt3 = n0 / t2\nt4 = t3 * 3.0\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "507" + ], + "split": "dev" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 34 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 34.0\nn1 = 680.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "74" + ], + "split": "dev" + }, + { + "Input": "a circular well with a diameter of 4 metres , is dug to a depth of 24 metres . what is the volume of the earth dug out ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 24.0\nt0 = n0 / 2.0\nanswer = math.pi * t0**2 * n1\nprint(answer)" + ], + "Output Answer": [ + "301.59289474462014" + ], + "split": "dev" + }, + { + "Input": "a cube is divided into 216 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that , the cube is painted with green on one set of opposite faces , red on another set of opposite faces , and blue on the third set of opposite faces . how many cubelets are painted with exactly one colour ?", + "Output Program": [ + "n0 = 216.0\nt0 = 2.0 * 4.0\nt1 = t0 * 3.0\nt2 = n0 - t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "96" + ], + "split": "dev" + }, + { + "Input": "a rectangle measures 8 cm on length and its diagonal measures 17 cm . what is the perimeter of the rectangle ?", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 17.0\nt0 = n1**min(2.0, 5)\nt1 = n0**min(2.0, 5)\nt2 = t0 - t1\nt3 = math.sqrt(max(0, t2))\nanswer = 2 * (n0 + t3) # perimetere of rectangle\nprint(answer)" + ], + "Output Answer": [ + "46" + ], + "split": "dev" + }, + { + "Input": "one side of a rectangular field is 15 m and one of its diagonal is 18 m . find the area of the field .", + "Output Program": [ + "import math\nn0 = 15.0\nn1 = 18.0\nt0 = n1**min(2.0, 5)\nt1 = n0**min(2.0, 5)\nt2 = t0 - t1\nt3 = math.sqrt(max(0, t2))\nanswer = n0 * t3 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "149.248115565993" + ], + "split": "dev" + }, + { + "Input": "a rectangular block 15 cm by 30 cm by 75 cm is cut into an exact number of equal cubes . find the least possible number of cubes ?", + "Output Program": [ + "n0 = 15.0\nn1 = 30.0\nn2 = 75.0\nt0 = 1000.0 * 3.0\nt1 = n2 * 10.0\nt2 = 2.0 * 3.0\nt3 = 1000.0 * 360.0 # area of rectangle\nt4 = t0 + t1\nt5 = t3 / 10.0\nt6 = t2 * 1000.0\nt7 = t5 - t6\nt8 = t4 + t7\nt9 = t8 / 10.0\nanswer = t8 / t9\nprint(answer)" + ], + "Output Answer": [ + "10" + ], + "split": "dev" + }, + { + "Input": "the area of a triangle is with base 4 m and height 6 m ?", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "john builds a square with a side of 12 cm from some wire . if from the same wire , he builds a rectangle with a width of 6 cm , what will be the length of the rectangle ?", + "Output Program": [ + "n0 = 12.0\nn1 = 6.0\nt0 = n1 * 2.0\nt1 = 4 * n0\nt2 = t1 - t0\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "dev" + }, + { + "Input": "a lady builds 8 cm length , 15 cm width , and 5 cm height box using 10 cubic cm cubes . what is the minimum number of cubes required to build the box ?", + "Output Program": [ + "n0 = 8.0\nn1 = 15.0\nn2 = 5.0\nn3 = 10.0\nt0 = n0 * n1\nt1 = n2 * t0\nanswer = t1 / n3\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "dev" + }, + { + "Input": "a cone of height 9 cm with diameter of its base 18 cm is carved out from a wooden solid sphere of radius 9 cm . the percentage of the wood wasted is :", + "Output Program": [ + "import math\nn0 = 9.0\nn1 = 18.0\nn2 = 9.0\nt0 = math.pi * n0**2 * n0 / 3\nt1 = 4 / 3 * math.pi * n0**3\nt2 = t1 - t0\nt3 = t2 / t1\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "dev" + }, + { + "Input": "a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 14 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?", + "Output Program": [ + "import math\nn0 = 14.0\nn1 = 1200.0\nn2 = 2.0\nn3 = 30.0\nt0 = n1 / n3\nt1 = n3**min(n2, 5)\nt2 = n3 + t0\nt3 = t0**min(n2, 5)\nt4 = t1 + t3\nt5 = math.sqrt(max(0, t4))\nt6 = t2 + t5\nanswer = n0 * t6\nprint(answer)" + ], + "Output Answer": [ + "1680" + ], + "split": "dev" + }, + { + "Input": "a hall is 15 meters long and 15 meters wide . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , what is the volume of the hall ( in cubic meters ) ?", + "Output Program": [ + "n0 = 15.0\nn1 = 15.0\nt0 = n0 * n1 # area of rectangle\nt1 = 2 * (n0 + n1) # perimetere of rectangle\nt2 = t0 * 2.0\nt3 = t2 / t1\nanswer = n0 * n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "1687.5" + ], + "split": "dev" + }, + { + "Input": "what is the total surface area in square meters of a rectangular solid whose length is 9 meters , width is 8 meters , and depth is 5 meters ?", + "Output Program": [ + "n0 = 9.0\nn1 = 8.0\nn2 = 5.0\n\nanswer = 2 * (n0 * n1 + n0 * n2 + n1 * n2) # surface of a rectangular prism\nprint(answer)" + ], + "Output Answer": [ + "314" + ], + "split": "dev" + }, + { + "Input": "if the length of an edge of cube p is thrice the length of an edge of cube q , what is the ratio of the volume of cube q to the volume of cube p ?", + "Output Program": [ + "t0 = 1 / 3.0\nanswer = t0**min(3.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "0.03703703703703703" + ], + "split": "dev" + }, + { + "Input": "what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 20 % ?", + "Output Program": [ + "n0 = 20.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = t1**min(2.0, 5)\nt3 = t2 - 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "43.99999999999999" + ], + "split": "dev" + }, + { + "Input": "a semicircular shaped window has diameter of 63 cm . its perimeter equals", + "Output Program": [ + "import math\nn0 = 63.0\nt0 = n0 / 2.0\nt1 = 2 * math.pi * t0\nt2 = t1 / 2.0\nanswer = n0 + t2\nprint(answer)" + ], + "Output Answer": [ + "161.9601685880785" + ], + "split": "dev" + }, + { + "Input": "find the area of a parallelogram with base 21 cm and height 11 cm ?", + "Output Program": [ + "n0 = 21.0\nn1 = 11.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "231" + ], + "split": "dev" + }, + { + "Input": "a rectangular garden is to be twice as long as it is wide . if 180 yards of fencing , including the gate , will completely enclose the garden , what will be the length of the garden , in yards ?", + "Output Program": [ + "n0 = 180.0\nt0 = 1.0 + 2.0\nt1 = t0 * 2.0\nt2 = n0 / t1\nanswer = t2 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "dev" + }, + { + "Input": "abcd is a square where ab = \u00e2 \u02c6 \u0161 4032 . let x be a point on ab and y be a point on cd such that ax = cy . compute the area of trapezoid axyd .", + "Output Program": [ + "n0 = 4032.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "2016" + ], + "split": "dev" + }, + { + "Input": "if a drawing has an outer circle of diameter 30 and an inner circle of diameter 24 , then what fraction of outer circle ' s surface is not covered by the inner circle ?", + "Output Program": [ + "n0 = 30.0\nn1 = 24.0\nt0 = n0 / 2.0\nt1 = n1 / 2.0\nt2 = t0**min(2.0, 5)\nt3 = t1**min(2.0, 5)\nt4 = t2 * 3.141592653589793\nt5 = t3 * 3.141592653589793\nt6 = t4 - t5\nanswer = t6 / t4\nprint(answer)" + ], + "Output Answer": [ + "0.36" + ], + "split": "dev" + }, + { + "Input": "what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 59 ?", + "Output Program": [ + "import math\nn0 = 289.0\nn1 = 59.0\nt0 = math.sqrt(max(0, n0))\nt1 = 4 * t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "4012" + ], + "split": "dev" + }, + { + "Input": "in the rectangular coordinate system , points ( 16 , 0 ) and ( \u2013 16 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c ?", + "Output Program": [ + "import math\nn0 = 16.0\nn1 = 0.0\nn2 = 16.0\nn3 = 0.0\nt0 = n0**min(2.0, 5)\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "dev" + }, + { + "Input": "a circular mat with diameter 18 inches is placed on a square tabletop , each of whose sides is 24 inches long . which of the following is closest to the fraction of the tabletop covered by the mat ?", + "Output Program": [ + "n0 = 18.0\nn1 = 24.0\nt0 = n0 / 2.0\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "0.375" + ], + "split": "dev" + }, + { + "Input": "three rugs have a combined area of 212 square meters . by overlapping the rugs to cover floor area of 140 square meters , the area that is covered by exactly two layers of rug is 24 square meters . what is the area that is covered with three layers of rug ?", + "Output Program": [ + "n0 = 212.0\nn1 = 140.0\nn2 = 24.0\nt0 = n0 - n1\nt1 = t0 - n2\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "dev" + }, + { + "Input": "the length of rectangle is thrice its breadth and its perimeter is 120 m , find the area of the rectangle ?", + "Output Program": [ + "n0 = 120.0\nt0 = 2.0 * 3.0\nt1 = 1.0 * 2.0\nt2 = t0 + t1\nt3 = n0 / t2\nt4 = t3 * 3.0\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "675" + ], + "split": "dev" + }, + { + "Input": "find the volume & curved surface area of a cylinder with diameter of base 14 cm and height 60 cm .", + "Output Program": [ + "import math\nn0 = 14.0\nn1 = 60.0\nt0 = n0 / 2.0\nt1 = 2 * math.pi * t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "2638.9378290154264" + ], + "split": "dev" + }, + { + "Input": "the area of a triangle is with base 10 m and height 10 m ?", + "Output Program": [ + "n0 = 10.0\nn1 = 10.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "dev" + }, + { + "Input": "18 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?", + "Output Program": [ + "n0 = 18.0\nn1 = 7.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nt2 = n0 * t1\nt3 = t2 / 2.0\nanswer = t3 + t0\nprint(answer)" + ], + "Output Answer": [ + "279" + ], + "split": "dev" + }, + { + "Input": "a cylindrical bucket of height 36 cm and radius 21 cm is filled with sand . the bucket is emptied on the ground and a conical heap of sand is formed , the height of the heap being 12 cm . the radius of the heap at the base is :", + "Output Program": [ + "import math\nn0 = 36.0\nn1 = 21.0\nn2 = 12.0\nt0 = n1 * n1\nt1 = n0 * t0\nt2 = t1 / 4.0\nanswer = math.sqrt(max(0, t2))\nprint(answer)" + ], + "Output Answer": [ + "63" + ], + "split": "dev" + }, + { + "Input": "if the sides of a triangle are 32 cm , 27 cm and 12 cm , what is its area ?", + "Output Program": [ + "n0 = 32.0\nn1 = 27.0\nn2 = 12.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "162" + ], + "split": "dev" + }, + { + "Input": "the size of a television screen is given as the length of the screen ' s diagonal . if the screens were flat , then the area of a square 19 - inch screen would be how many square inches greater than the area of a square 17 - inch screen ?", + "Output Program": [ + "n0 = 19.0\nn1 = 17.0\nt0 = n0**min(2.0, 5)\nt1 = n1**min(2.0, 5)\nt2 = t0 - t1\nanswer = t2 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "dev" + }, + { + "Input": "the volume of a certain substance is always directly proportional to its weight . if 48 cubic inches of the substance weigh 112 ounces , what is the volume , in cubic inches , of 63 ounces of this substance ?", + "Output Program": [ + "n0 = 48.0\nn1 = 112.0\nn2 = 63.0\nt0 = n0 / n1\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "27" + ], + "split": "dev" + }, + { + "Input": "if the difference between the length and breadth of a rectangle is 23 m and its perimeter is 266 m , what is its area ?", + "Output Program": [ + "n0 = 23.0\nn1 = 266.0\nt0 = n0 * 2.0\nt1 = n1 - t0\nt2 = t1 / 4.0\nt3 = n0 + t2\nanswer = t3 * t2 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "4290" + ], + "split": "dev" + }, + { + "Input": "the diagonal of a cube is 8 \u221a 3 . find its volume and surface area .", + "Output Program": [ + "import math\nn0 = 8.0\nn1 = 3.0\nt0 = math.sqrt(max(0, n1))\nt1 = n0 * t0\nt2 = t1 / t0\nanswer = 6 * t2**2 # surface of a cube\nprint(answer)" + ], + "Output Answer": [ + "384" + ], + "split": "dev" + }, + { + "Input": "the ratio of males to females in a class is 2 : 3 . the career preferences of the students in the class are represented in a circle graph . if the area of the graph allocated to each career preference is proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one - fourth of the males and one - half of the females in the class ?", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nt0 = n0 + n1\nt1 = n0 * 360.0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "144" + ], + "split": "dev" + }, + { + "Input": "a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 4 m , the volume of the box ( in m 3 ) is :", + "Output Program": [ + "n0 = 48.0\nn1 = 36.0\nn2 = 4.0\nn3 = 3.0\nt0 = n2 * 2.0\nt1 = n0 - t0\nt2 = n1 - t0\nanswer = n2 * t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "4480" + ], + "split": "dev" + }, + { + "Input": "abcd is a square where ab = \u221a 2016 . let x be a point on ab and y be a point on cd such that ax = cy . compute the area of trapezoid axyd .", + "Output Program": [ + "n0 = 2016.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "1008" + ], + "split": "dev" + }, + { + "Input": "what is the perimeter , in meters , of a rectangular garden 16 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide ?", + "Output Program": [ + "n0 = 16.0\nn1 = 16.0\nn2 = 12.0\nt0 = n1 * n2 # area of rectangle\nt1 = t0 / n0\nanswer = 2 * (n0 + t1) # perimetere of rectangle\nprint(answer)" + ], + "Output Answer": [ + "56" + ], + "split": "dev" + }, + { + "Input": "the area of a square is equal to five times the area of a rectangle of dimensions 32 cm * 10 cm . what is the perimeter of the square ?", + "Output Program": [ + "import math\nn0 = 32.0\nn1 = 10.0\nt0 = 10.0 / 2.0\nt1 = n0 * n1 # area of rectangle\nt2 = t0 * t1\nt3 = math.sqrt(max(0, t2))\nanswer = t3 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "160" + ], + "split": "dev" + }, + { + "Input": "the length of a rectangle i s two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1225 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?", + "Output Program": [ + "import math\nn0 = 1225.0\nn1 = 10.0\nt0 = 2.0 + 3.0\nt1 = math.sqrt(max(0, n0))\nt2 = 2.0 / t0\nt3 = t2 * t1\nanswer = n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "140" + ], + "split": "dev" + }, + { + "Input": "the sides of a square region , measured to the nearest centimeter , are 4 centimeters long . the least possible value of the actual area of the square region is", + "Output Program": [ + "n0 = 4.0\nt0 = n0 - 0.25\nt1 = t0 - 0.25\nanswer = t1**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "12.25" + ], + "split": "dev" + }, + { + "Input": "what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 60 ?", + "Output Program": [ + "import math\nn0 = 289.0\nn1 = 60.0\nt0 = math.sqrt(max(0, n0))\nt1 = 4 * t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "4080" + ], + "split": "dev" + }, + { + "Input": "the length of a rectangular plot is thrice its width . if the area of the rectangular plot is 432 sq meters , then what is the width ( in meters ) of the rectangular plot ?", + "Output Program": [ + "n0 = 432.0\nt0 = n0 / 3.0\nt1 = t0 / 3.0\nanswer = t1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "dev" + }, + { + "Input": "a rectangular tiled patio is composed of 96 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 96 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?", + "Output Program": [ + "import math\nn0 = 96.0\nn1 = 2.0\nn2 = 4.0\nn3 = 96.0\nt0 = n0 * n1\nt1 = -n2\nt2 = n2**min(n1, 5)\nt3 = n2 * t0\nt4 = t3 + t2\nt5 = math.sqrt(max(0, t4))\nt6 = t1 + t5\nt7 = t6 / n1\nanswer = n0 / t7\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "dev" + }, + { + "Input": "find the area of a parallelogram with base 12 cm and height 48 cm ?", + "Output Program": [ + "n0 = 12.0\nn1 = 48.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "576" + ], + "split": "dev" + }, + { + "Input": "the area of the square formed on the diagonal of a rectangle as its side is 108 1 / 3 % more than the area of the rectangle . if the perimeter of the rectangle is 28 units , find the difference between the sides of the rectangle ?", + "Output Program": [ + "n0 = 108.0\nn1 = 1.0\nn2 = 3.0\nn3 = 28.0\nt0 = n0 / n2\nt1 = t0 - n3\nanswer = t1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "2" + ], + "split": "dev" + }, + { + "Input": "a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 193 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ?", + "Output Program": [ + "n0 = 1.0\nn1 = 193.0\nt0 = 0.25 + 0.25\nt1 = n1 / 2.0\nt2 = t0 + t1\nanswer = t2**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "9409" + ], + "split": "dev" + }, + { + "Input": "if d is the smallest positive integer such that 3150 multiplied by d is the square of an integer , then d must be", + "Output Program": [ + "n0 = 3150.0\nt0 = 1.0 + 4.0\nt1 = 3.0**min(2.0, 5)\nt2 = t0**min(2.0, 5)\nt3 = t1 * t2\nanswer = n0 / t3\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "dev" + }, + { + "Input": "susan made a block with small cubes of 5 cubic cm volume to make a block 7 small cubes long , 7 small cubes wide and 6 small cubes deep . she realise that she has used more small cubes than she really needed . she realised that she could have glued a fewer number of cubes together ot look like a block with same dimensions , if it were made", + "Output Program": [ + "n0 = 5.0\nn1 = 7.0\nn2 = 7.0\nn3 = 6.0\nt0 = n1 * n1\nt1 = n1 - 2.0\nt2 = n3 - 2.0\nt3 = n3 * t0\nt4 = t1 * t1\nt5 = t4 * t2\nanswer = t3 - t5\nprint(answer)" + ], + "Output Answer": [ + "194" + ], + "split": "dev" + }, + { + "Input": "a rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 5 per sq m ?", + "Output Program": [ + "n0 = 80.0\nn1 = 60.0\nn2 = 10.0\nn3 = 5.0\nt0 = n0 + n1\nt1 = t0 - n2\nt2 = n2 * t1\nanswer = n3 * t2\nprint(answer)" + ], + "Output Answer": [ + "6500" + ], + "split": "dev" + }, + { + "Input": "the diagonal of a rectangle is \u221a 41 cm and its area is 20 sq . cm . the perimeter of the rectangle must be :", + "Output Program": [ + "import math\nn0 = 41.0\nn1 = 20.0\nt0 = n1 * 2.0\nt1 = math.sqrt(max(0, n0))\nt2 = t1**min(2.0, 5)\nt3 = t0 + t2\nt4 = math.sqrt(max(0, t3))\nanswer = t4 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "dev" + }, + { + "Input": "there is a square with sides of 12 . what is the circumference of the biggest circle that can be cut out of this square ?", + "Output Program": [ + "import math\nn0 = 12.0\nt0 = n0 / 2.0\nanswer = 2 * math.pi * t0\nprint(answer)" + ], + "Output Answer": [ + "37.69911184307752" + ], + "split": "dev" + }, + { + "Input": "huey ' s hip pizza sells two sizes of square pizzas : a small pizza that measures 12 inches on a side and costs $ 10 , and a large pizza that measures 18 inches on a side and costs $ 20 . if two friends go to huey ' s with $ 30 apiece , how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone ?", + "Output Program": [ + "n0 = 12.0\nn1 = 10.0\nn2 = 18.0\nn3 = 20.0\nn4 = 30.0\nt0 = n2**min(2.0, 5)\nt1 = n0**min(2.0, 5)\nt2 = t1 + t0\nt3 = t0 * 3.0\nt4 = t2 + t2\nanswer = t3 - t4\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "dev" + }, + { + "Input": "if the length of the longest chord of a certain circle is 10 , what is the radius of that certain circle ?", + "Output Program": [ + "n0 = 10.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "dev" + }, + { + "Input": "a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck ' s tank is completely filled . if the truck ' s tank has a radius of 6 feet and a height of 10 feet , how far ( in feet ) did the oil level drop in the stationary tank ?", + "Output Program": [ + "import math\nn0 = 100.0\nn1 = 25.0\nn2 = 6.0\nn3 = 10.0\nt0 = math.pi * n0**2\nt1 = math.pi * n2**2 * n3\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "0.036" + ], + "split": "test" + }, + { + "Input": "three walls have wallpaper covering a combined area of 300 square meters . by overlapping the wallpaper to cover a wall with an area of 180 square meters , the area that is covered by exactly two layers of wallpaper is 34 square meters . what is the area that is covered with three layers of wallpaper ?", + "Output Program": [ + "n0 = 300.0\nn1 = 180.0\nn2 = 34.0\nt0 = n0 - n1\nt1 = t0 - n2\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "43" + ], + "split": "test" + }, + { + "Input": "34 . the side surface of a cylinder is rolled with a rectangular plate . if the perimeter of the circular base is 9 feet , and the diagonal of the rectangular plate was 15 ft . what is height of the of the cylinder ?", + "Output Program": [ + "import math\nn0 = 34.0\nn1 = 9.0\nn2 = 15.0\nt0 = n2**min(2.0, 5)\nt1 = n1**min(2.0, 5)\nt2 = t0 - t1\nanswer = math.sqrt(max(0, t2))\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "test" + }, + { + "Input": "the mass of 1 cubic meter of a substance is 300 kg under certain conditions . what is the volume in cubic centimeters of 1 gram of this substance under these conditions ? ( 1 kg = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )", + "Output Program": [ + "n0 = 1.0\nn1 = 300.0\nn2 = 1.0\nn3 = 1.0\nn4 = 1000.0\nn5 = 1.0\nn6 = 1.0\nn7 = 0.0\nt0 = n4 * n4\nt1 = n1 * n4\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "3.3333333333333335" + ], + "split": "test" + }, + { + "Input": "a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 3 feet . how many feet does the squirrel travels if the post is 18 feet tall and 3 feet in circumference ?", + "Output Program": [ + "n0 = 3.0\nn1 = 18.0\nn2 = 3.0\nt0 = n1 / n0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "test" + }, + { + "Input": "in an electric circuit , two resistors with resistances 3 ohm and 5 ohm are connected in parallel . in this case , if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of two resistors . what is the value ?", + "Output Program": [ + "n0 = 3.0\nn1 = 5.0\nt0 = n0 + n1\nt1 = n0 * n1\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "1.875" + ], + "split": "test" + }, + { + "Input": "a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 40 cents . how many cents does a solution of 1 liter of spirit and 2 liters of water cost ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 40.0\nn3 = 1.0\nn4 = 2.0\nt0 = n0 + n4\nt1 = n0 / t0\nt2 = n2 * t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "40" + ], + "split": "test" + }, + { + "Input": "if the length of the longest chord of a certain circle is 18 , what is the radius of that certain circle ?", + "Output Program": [ + "n0 = 18.0\n\nanswer = n0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "test" + }, + { + "Input": "the area of a rectangular field is equal to 500 square meters . its perimeter is equal to 90 meters . find the width of this rectangle .", + "Output Program": [ + "import math\nn0 = 500.0\nn1 = 90.0\nt0 = n1 / 2.0\nt1 = n0 * 4.0\nt2 = t0 * t0\nt3 = t2 - t1\nt4 = math.sqrt(max(0, t3))\nt5 = t0 - t4\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "test" + }, + { + "Input": "a carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet . if the carpenter were to make a similar sandbox twice as long , twice as wide , and twice as high as the first sandbox , what would be the capacity , in cubic feet , of the second sandbox ?", + "Output Program": [ + "n0 = 10.0\nt0 = 2.0**min(3.0, 5)\nanswer = n0 * t0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "test" + }, + { + "Input": "what is the max number of rectangular boxes , each measuring 5 inches by 2 inches by 7 inches , that can be packed into a rectangular packing box measuring 15 inches by 20 inches by 35 inches , if all boxes are aligned in the same direction ?", + "Output Program": [ + "n0 = 5.0\nn1 = 2.0\nn2 = 7.0\nn3 = 15.0\nn4 = 20.0\nn5 = 35.0\nt0 = n3 * n4\nt1 = n0 * n1\nt2 = n5 * t0\nt3 = n2 * t1\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "test" + }, + { + "Input": "find the area of a parallelogram with base 24 cm and height 12 cm ?", + "Output Program": [ + "n0 = 24.0\nn1 = 12.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "288" + ], + "split": "test" + }, + { + "Input": "a parallelogram has a base that is four time the size of it ' s height . the total area of this parallelogram is 2,304 sq ft . what is the height of the parallelogram ?", + "Output Program": [ + "import math\nn0 = 2304.0\nt0 = 1000.0 * 2.0\nt1 = 100.0 * 3.0\nt2 = t0 + t1\nt3 = t2 + 4.0\nt4 = t3 / 4.0\nanswer = math.sqrt(max(0, t4))\nprint(answer)" + ], + "Output Answer": [ + "24" + ], + "split": "test" + }, + { + "Input": "in measuring the sides of a rectangle , one side is taken 4 % in excess , and the other 3 % in deficit . find the error percent in the area calculated from these measurements .", + "Output Program": [ + "n0 = 4.0\nn1 = 3.0\nt0 = n0 * n1\nt1 = n0 - n1\nt2 = t0 / 100.0\nanswer = t1 - t2\nprint(answer)" + ], + "Output Answer": [ + "0.88" + ], + "split": "test" + }, + { + "Input": "how much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 15 inches than that of a rectangular sheet of paper measuring 7.5 inches by 11 inches ?", + "Output Program": [ + "n0 = 11.0\nn1 = 15.0\nn2 = 7.5\nn3 = 11.0\nt0 = n0 * n1 # area of rectangle\nt1 = n0 * n2 # area of rectangle\nt2 = t0 * 2.0\nt3 = t1 * 2.0\nt4 = t2 - t3\nt5 = t4 / t0\nanswer = t5 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "100" + ], + "split": "test" + }, + { + "Input": "a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 30 cents . how many cents does a solution of 1 liter of spirit and 2 liters of water cost ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 30.0\nn3 = 1.0\nn4 = 2.0\nt0 = n0 + n4\nt1 = n0 / t0\nt2 = n2 * t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "30" + ], + "split": "test" + }, + { + "Input": "a certain barrel , which is a right circular cylinder , is filled to capacity with 60 gallons of oil . the first barrel is poured into a second barrel , also a right circular cylinder , which is empty . the second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel . if all of the oil in the first barrel is poured into the second barrel , how much empty capacity , in gallons , is left in the second barrel ?", + "Output Program": [ + "n0 = 60.0\nt0 = 2.0**min(3.0, 5)\nt1 = n0 * t0\nanswer = t1 - n0\nprint(answer)" + ], + "Output Answer": [ + "420" + ], + "split": "test" + }, + { + "Input": "a cube has a volume of 125 cubic feet . if a similar cube is twice as long , twice as wide , and twice as high , then the volume , in cubic feet of such cube is ?", + "Output Program": [ + "n0 = 125.0\nt0 = n0**(1 / 3)\nt1 = t0 * 2.0\nanswer = t1**3\nprint(answer)" + ], + "Output Answer": [ + "999.9999999999994" + ], + "split": "test" + }, + { + "Input": "a horse is tethered to one corner of a rectangular grassy field 36 m by 20 m with a rope 18 m long . over how much area of the field can it graze ?", + "Output Program": [ + "n0 = 36.0\nn1 = 20.0\nn2 = 18.0\nt0 = n2**min(2.0, 5)\nt1 = t0 * 3.141592653589793\nanswer = t1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "254.46900494077323" + ], + "split": "test" + }, + { + "Input": "the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 \u03c0 \u00b7 r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams t ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 0.15\nn3 = 8.0\nn4 = 0.3\n\nanswer = n0 * n3\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "test" + }, + { + "Input": "a closed cylindrical tank contains 36 pie cubic feet of water and its filled to half its capacity . when the tank is placed upright on its circular base on level ground , the height of water in the tank is 4 feet . when the tank is placed on its side on level ground , what is the height , in feet , of the surface of the water above the ground ?", + "Output Program": [ + "import math\nn0 = 36.0\nn1 = 4.0\nt0 = n0 * 3.141592653589793\nt1 = t0 / n1\nt2 = t1 / 3.141592653589793\nanswer = math.sqrt(max(0, t2))\nprint(answer)" + ], + "Output Answer": [ + "3" + ], + "split": "test" + }, + { + "Input": "a rectangular with dimensions 35 inches by 45 inches is to be divided into squares of equal size . which of the following could be a length of a side of the squares ?", + "Output Program": [ + "n0 = 35.0\nn1 = 45.0\nt0 = n1 - n0\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "test" + }, + { + "Input": "the sides of a square region , measured to the nearest centimeter , are 10 centimeters long . the least possible value of the actual area of the square region is", + "Output Program": [ + "n0 = 10.0\nt0 = n0 - 0.25\nt1 = t0 - 0.25\nanswer = t1**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "90.25" + ], + "split": "test" + }, + { + "Input": "if the side length of square b is sqrt ( 5 ) times that of square a , the area of square b is how many times the area of square a ?", + "Output Program": [ + "import math\nn0 = 5.0\nt0 = math.sqrt(max(0, n0))\nanswer = t0**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "5.000000000000001" + ], + "split": "test" + }, + { + "Input": "in triangle pqr , the angle q = 90 degree , pq = 5 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz", + "Output Program": [ + "n0 = 90.0\nn1 = 5.0\nn2 = 8.0\nt0 = n1 * n2\nanswer = t0 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "test" + }, + { + "Input": "if the radius of a circle is decreased 50 % , what happens to the area ?", + "Output Program": [ + "n0 = 50.0\nt0 = n0 / 100.0\nt1 = t0**min(2.0, 5)\nt2 = t1 * 100.0\nanswer = 100.0 - t2\nprint(answer)" + ], + "Output Answer": [ + "75" + ], + "split": "test" + }, + { + "Input": "find the area of the quadrilateral of one of its diagonals is 50 cm and its off sets 15 cm and 5 cm ?", + "Output Program": [ + "n0 = 50.0\nn1 = 15.0\nn2 = 5.0\nt0 = n1 + n2\nt1 = 1.0 / 2.0\nt2 = t0 * t1\nanswer = n0 * t2\nprint(answer)" + ], + "Output Answer": [ + "500" + ], + "split": "test" + }, + { + "Input": "a right circular cone is exactly fitted inside a cube in such away that the edges of the base of the cone are touching the edges of one of the faces of the cube and the vertex is on the opposite face of the cube . if the volume of the cube is 343 cc , what approximately is the volume of the cone ?", + "Output Program": [ + "import math\nn0 = 343.0\nt0 = n0**(1 / 3)\nt1 = t0 / 2.0\nanswer = math.pi * t1**2 * t0 / 3\nprint(answer)" + ], + "Output Answer": [ + "89.79719001510823" + ], + "split": "test" + }, + { + "Input": "the area of a rhombus is equal to the area of a rectangle whose length is 20 cm and the breadth is 10 cm . if one of the diagonals is 32 cm what is the length of other diagonal ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nn2 = 32.0\nt0 = n0 * n1 # area of rectangle\nt1 = t0 * 2.0\nanswer = t1 / n2\nprint(answer)" + ], + "Output Answer": [ + "12.5" + ], + "split": "test" + }, + { + "Input": "difference between the length & breadth of a rectangle is 10 m . if its perimeter is 206 m , then its area is ?", + "Output Program": [ + "n0 = 10.0\nn1 = 206.0\nt0 = n0 * 4.0\nt1 = n0 * 3.0\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "test" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 10 sq . feet , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "test" + }, + { + "Input": "what is the ratio between perimeters of two squares one having 8 times the diagonal then the other ?", + "Output Program": [ + "n0 = 8.0\nt0 = n0 / n0\nanswer = n0 / t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "test" + }, + { + "Input": "a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 191 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ?", + "Output Program": [ + "n0 = 1.0\nn1 = 191.0\nt0 = 0.25 + 0.25\nt1 = n1 / 2.0\nt2 = t0 + t1\nanswer = t2**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "9216" + ], + "split": "test" + }, + { + "Input": "a circle graph shows how the budget of a certain company was spent : 61 percent for salaries , 10 percent for research and development , 6 percent for utilities , 5 percent for equipment , 3 percent for supplies , and the remainder for transportation . if the area of each sector of the graph is proportional to the percent of the budget it represents , how many degrees of the circle are used to represent transportation ?", + "Output Program": [ + "n0 = 61.0\nn1 = 10.0\nn2 = 6.0\nn3 = 5.0\nn4 = 3.0\nt0 = n0 + n1\nt1 = n2 + t0\nt2 = n3 + t1\nt3 = n4 + t2\nt4 = 100.0 - t3\nt5 = t4 * 360.0\nanswer = t5 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "54" + ], + "split": "test" + }, + { + "Input": "a diagonal of a polygon is an segment between two non - adjacent vertices of the polygon . how many diagonals does a regular 10 - sided polygon have ?", + "Output Program": [ + "n0 = 10.0\nt0 = n0 - 3.0\nt1 = n0 * t0\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "35" + ], + "split": "test" + }, + { + "Input": "if paint costs $ 3.10 per quart , and a quart covers 20 square feet , how much will it cost to paint the outside of a cube 10 feet on each edge ?", + "Output Program": [ + "n0 = 3.1\nn1 = 20.0\nn2 = 10.0\nt0 = n0 / n1\nt1 = 6 * n2**2 # surface of a cube\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "93" + ], + "split": "test" + }, + { + "Input": "how many odd numbers between 10 and 1,000 are the squares of integers ?", + "Output Program": [ + "n0 = 10.0\nn1 = 1000.0\n\nanswer = n0 + 4.0\nprint(answer)" + ], + "Output Answer": [ + "14" + ], + "split": "test" + }, + { + "Input": "the area of a parallelogram is 72 cm ^ 2 and its altitude is twice the corresponding base . what is the length of the base ?", + "Output Program": [ + "import math\nn0 = 72.0\nn1 = 2.0\nt0 = n0 / 2.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "test" + }, + { + "Input": "the surface of a cube is 294 sq cm . find its volume ?", + "Output Program": [ + "import math\nn0 = 294.0\nt0 = 2.0 + 4.0\nt1 = n0 / t0\nt2 = math.sqrt(max(0, t1))\nanswer = t2**3\nprint(answer)" + ], + "Output Answer": [ + "343" + ], + "split": "test" + }, + { + "Input": "the total surface area of a cuboid length 12 m , breadth 10 m and height 8 m .", + "Output Program": [ + "n0 = 12.0\nn1 = 10.0\nn2 = 8.0\n\nanswer = 2 * (n0 * n1 + n0 * n2 + n1 * n2) # surface of a rectangular prism\nprint(answer)" + ], + "Output Answer": [ + "592" + ], + "split": "test" + }, + { + "Input": "in a company of 170 employees , 110 are females . a total of 80 employees have advanced degrees and the rest have a college degree only . if 25 employees are males with college degree only , how many employees are females with advanced degrees ?", + "Output Program": [ + "n0 = 170.0\nn1 = 110.0\nn2 = 80.0\nn3 = 25.0\nt0 = n0 - n1\nt1 = t0 - n3\nanswer = n2 - t1\nprint(answer)" + ], + "Output Answer": [ + "45" + ], + "split": "test" + }, + { + "Input": "the measurement of a rectangular box with lid is 25 cmx 6 cmx 18 cm . find the volume of the largest sphere that can be inscribed in the box ( in terms of \u03c0 cm 3 ) . ( hint : the lowest measure of rectangular box represents the diameter of the largest sphere )", + "Output Program": [ + "n0 = 25.0\nn1 = 6.0\nn2 = 18.0\nn3 = 3.0\nt0 = 4.0 / 3.0\nt1 = n3**min(3.0, 5)\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "test" + }, + { + "Input": "the length of a rectangle is two - seventh of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 5929 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 25 units ?", + "Output Program": [ + "import math\nn0 = 5929.0\nn1 = 25.0\nt0 = 3.0 + 4.0\nt1 = math.sqrt(max(0, n0))\nt2 = 2.0 / t0\nt3 = t2 * t1\nanswer = n1 * t3 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "550" + ], + "split": "test" + }, + { + "Input": "the length of each side of an equilateral triangle having an area of 4 \u00e2 \u02c6 \u0161 3 cm 2 is ?", + "Output Program": [ + "import math\nn0 = 4.0\nn1 = 3.0\nn2 = 2.0\nt0 = 1.0 / n2\nt1 = math.sqrt(max(0, n1))\nt2 = n0 * t1\nt3 = t0 * t0\nt4 = t3 * t1\nt5 = t2 / t4\nanswer = math.sqrt(max(0, t5))\nprint(answer)" + ], + "Output Answer": [ + "4" + ], + "split": "test" + }, + { + "Input": "if the sides of a rectangle are increased by 25 % , what is the percentage increase in the area ?", + "Output Program": [ + "n0 = 25.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = t1**min(2.0, 5)\nt3 = t2 - 1.0\nanswer = t3 * 100.0\nprint(answer)" + ], + "Output Answer": [ + "56.25" + ], + "split": "test" + }, + { + "Input": "a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 3 inches wide on each side , the total area would have been ( m + 64 ) square inches . what is the perimeter of the photograph , in inches ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 64.0\nt0 = n1 * 2.0\nt1 = n0 * 2.0\nt2 = t0**min(2.0, 5)\nt3 = t1**min(2.0, 5)\nt4 = t2 - t3\nt5 = n2 - t4\nanswer = t5 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "16" + ], + "split": "test" + }, + { + "Input": "the area of a parallelogram is 72 sq m and its altitude is twice the corresponding base . then the length of the base is ?", + "Output Program": [ + "import math\nn0 = 72.0\nt0 = n0 / 2.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "test" + }, + { + "Input": "the mass of 1 cubic meter of a substance is 400 kg under certain conditions . what is the volume in cubic centimeters of 1 gram of this substance under these conditions ? ( 1 kg = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )", + "Output Program": [ + "n0 = 1.0\nn1 = 400.0\nn2 = 1.0\nn3 = 1.0\nn4 = 1000.0\nn5 = 1.0\nn6 = 1.0\nn7 = 0.0\nt0 = n4 * n4\nt1 = n1 * n4\nanswer = t0 / t1\nprint(answer)" + ], + "Output Answer": [ + "2.5" + ], + "split": "test" + }, + { + "Input": "if the sides of a triangle are 52 cm , 48 cm and 20 cm , what is its area ?", + "Output Program": [ + "n0 = 52.0\nn1 = 48.0\nn2 = 20.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "480" + ], + "split": "test" + }, + { + "Input": "a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 50 cents . how many cents does a solution of 1 liter of spirit and 3 liters of water cost ?", + "Output Program": [ + "n0 = 1.0\nn1 = 1.0\nn2 = 50.0\nn3 = 1.0\nn4 = 3.0\nt0 = n0 + n4\nt1 = n0 / t0\nt2 = n2 * t1\nanswer = t0 * t2\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "test" + }, + { + "Input": "a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 10 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?", + "Output Program": [ + "import math\nn0 = 10.0\nn1 = 1200.0\nn2 = 2.0\nn3 = 30.0\nt0 = n1 / n3\nt1 = n3**min(n2, 5)\nt2 = n3 + t0\nt3 = t0**min(n2, 5)\nt4 = t1 + t3\nt5 = math.sqrt(max(0, t4))\nt6 = t2 + t5\nanswer = n0 * t6\nprint(answer)" + ], + "Output Answer": [ + "1200" + ], + "split": "test" + }, + { + "Input": "the length of a rectangle is 2 times its width . if the width of the rectangle is 4 inches , what is the rectangle ' s area , in square inches ?", + "Output Program": [ + "n0 = 2.0\nn1 = 4.0\nt0 = n0 * n1\nanswer = n1 * t0 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "test" + }, + { + "Input": "a room is 30 m long and 24 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , the volume of the hall is :", + "Output Program": [ + "n0 = 30.0\nn1 = 24.0\nt0 = n0 * n1 # area of rectangle\nt1 = 2 * (n0 + n1) # perimetere of rectangle\nt2 = t0 * 2.0\nt3 = t2 / t1\nanswer = n0 * n1 * t3\nprint(answer)" + ], + "Output Answer": [ + "9600" + ], + "split": "test" + }, + { + "Input": "the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 2 per metre approximately", + "Output Program": [ + "import math\nn0 = 17.56\nn1 = 2.0\nt0 = n0 / 3.141592653589793\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * 100.0\nt3 = 2 * math.pi * t2\nanswer = t3 * n1\nprint(answer)" + ], + "Output Answer": [ + "2970.9625914046583" + ], + "split": "test" + }, + { + "Input": "a metallic sheet is of rectangular shape with dimensions 48 m x 34 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is :", + "Output Program": [ + "n0 = 48.0\nn1 = 34.0\nn2 = 8.0\nn3 = 3.0\nt0 = n2 * 2.0\nt1 = n0 - t0\nt2 = n1 - t0\nanswer = n2 * t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "4608" + ], + "split": "test" + }, + { + "Input": "the surface area of a sphere is 4 \u03c0 r 2 , where r is the radius of the sphere . if the area of the base of a hemisphere is 3 , what is the surface area e of that hemisphere ?", + "Output Program": [ + "n0 = 4.0\nn1 = 2.0\nn2 = 3.0\nt0 = n2 / 3.141592653589793\nt1 = n0 * 3.141592653589793\nt2 = t0 * t1\nt3 = t0 * 3.141592653589793\nt4 = t2 / n1\nanswer = t4 + t3\nprint(answer)" + ], + "Output Answer": [ + "9" + ], + "split": "test" + }, + { + "Input": "eric throws 2 dice , and his score is the sum of the values shown . sandra throws one dice and her score is the square of the value shown . what is the probabilty that sandras score will be strictly higher than erics score ? ?", + "Output Program": [ + "n0 = 2.0\nt0 = n0 * 3.0\nt1 = t0**min(2.0, 5)\nt2 = t0 * t1\nt3 = t1 - 10.0\nt4 = t3 + 3.0\nt5 = t4 + t1\nt6 = t5 + t1\nt7 = t6 + t1\nanswer = t7 / t2\nprint(answer)" + ], + "Output Answer": [ + "0.6342592592592593" + ], + "split": "test" + }, + { + "Input": "find the volume and surface area of a cuboid 16 m long , 14 m broad and 7 m high .", + "Output Program": [ + "n0 = 16.0\nn1 = 14.0\nn2 = 7.0\nt0 = n0 * n1\nt1 = n1 * n2\nt2 = n0 * n2\nt3 = t0 + t1\nt4 = t3 + t2\nanswer = t4 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "868" + ], + "split": "test" + }, + { + "Input": "the perimeter of a triangle is 44 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ?", + "Output Program": [ + "n0 = 44.0\nn1 = 2.5\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "test" + }, + { + "Input": "what is the measure of the angle x made by the diagonals of the any adjacent sides of a cube .", + "Output Program": [ + "\nanswer = 180.0 / 3.0\nprint(answer)" + ], + "Output Answer": [ + "60" + ], + "split": "test" + }, + { + "Input": "a circle graph shows how the budget of a certain company was spent : 55 percent for salaries , 9 percent for research and development , 5 percent for utilities , 4 percent for equipment , 2 percent for supplies , and the remainder for transportation . if the area of each sector of the graph is proportional to the percent of the budget it represents , how many degrees of the circle are used to represent transportation ?", + "Output Program": [ + "n0 = 55.0\nn1 = 9.0\nn2 = 5.0\nn3 = 4.0\nn4 = 2.0\nt0 = n0 + n1\nt1 = n2 + t0\nt2 = n3 + t1\nt3 = n4 + t2\nt4 = 100.0 - t3\nt5 = t4 * 360.0\nanswer = t5 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "90" + ], + "split": "test" + }, + { + "Input": "a square is drawn inside a right - angled triangle with the two perpendicular sides as 12 cm and 8 cm . what is the side of the largest possible square that can be drawn ?", + "Output Program": [ + "n0 = 12.0\nn1 = 8.0\nt0 = n0 * n1\nt1 = t0 / 2.0\nanswer = t1 / 10.0\nprint(answer)" + ], + "Output Answer": [ + "4.8" + ], + "split": "test" + }, + { + "Input": "the squared value of the diagonal of a rectangle is ( 64 + b 2 ) sq cm , where b is less than 8 cm . what is the breadth of that rectangle ?", + "Output Program": [ + "import math\nn0 = 64.0\nn1 = 2.0\nn2 = 8.0\nt0 = math.sqrt(max(0, n0))\nanswer = t0 - 2.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "test" + }, + { + "Input": "suppose you have three identical prisms with congruent equilateral triangles as the end - polygons . suppose you attach them by the rectangular faces so they are perfectly aligned . there will be some large faces created by two or more co - planar faces of the individual prisms : count each such large face as one . given that , how many faces does the resultant solid have ?", + "Output Program": [ + "t0 = 1.0 + 4.0\nanswer = t0 + 1.0\nprint(answer)" + ], + "Output Answer": [ + "6" + ], + "split": "test" + }, + { + "Input": "a box measuring 49 inches long by 21 inches wide by 14 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?", + "Output Program": [ + "n0 = 49.0\nn1 = 21.0\nn2 = 14.0\nt0 = n2 / 2.0\nt1 = n0 * n1\nt2 = n2 * t1\nt3 = t0**3\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "42" + ], + "split": "test" + }, + { + "Input": "what will be the cost of building a fence around a square plot with area equal to 64 sq ft , if the price per foot of building the fence is rs . 58 ?", + "Output Program": [ + "import math\nn0 = 64.0\nn1 = 58.0\nt0 = math.sqrt(max(0, n0))\nt1 = 4 * t0\nanswer = n1 * t1\nprint(answer)" + ], + "Output Answer": [ + "1856" + ], + "split": "test" + }, + { + "Input": "what is the area of square field whose side of length 18 m ?", + "Output Program": [ + "n0 = 18.0\n\nanswer = n0**2\nprint(answer)" + ], + "Output Answer": [ + "324" + ], + "split": "test" + }, + { + "Input": "one side of a rectangular field is 15 m and one of its diagonals is 17 m . find the area of the field .", + "Output Program": [ + "import math\nn0 = 15.0\nn1 = 17.0\nt0 = n1**min(2.0, 5)\nt1 = n0**min(2.0, 5)\nt2 = t0 - t1\nt3 = math.sqrt(max(0, t2))\nanswer = n0 * t3 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "120" + ], + "split": "test" + }, + { + "Input": "three walls have wallpaper covering a combined area of 280 square meters . by overlapping the wallpaper to cover a wall with an area of 180 square meters , the area that is covered by exactly two layers of wallpaper is 36 square meters . what is the area that is covered with three layers of wallpaper ?", + "Output Program": [ + "n0 = 280.0\nn1 = 180.0\nn2 = 36.0\nt0 = n0 - n1\nt1 = t0 - n2\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "32" + ], + "split": "test" + }, + { + "Input": "find the area of a parallelogram with base 20 cm and height 10 cm ?", + "Output Program": [ + "n0 = 20.0\nn1 = 10.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "test" + }, + { + "Input": "danny is sitting on a rectangular box . the area of the front face of the box is half the area of the top face , and the area of the top face is 1.5 times the area of the side face . if the volume of the box is 1536 , what is the area of the side face of the box ?", + "Output Program": [ + "n0 = 1.5\nn1 = 1536.0\nt0 = 1.0 / 3.0\nt1 = n1**min(2.0, 5)\nt2 = t1 * 3.0\nt3 = t2**min(t0, 5)\nanswer = t3 / n0\nprint(answer)" + ], + "Output Answer": [ + "127.99999999999996" + ], + "split": "test" + }, + { + "Input": "a lawn is in the form of a rectangle having its sides in the ratio 2 : 3 . the area of the lawn is ( 1 / 6 ) hectares . find the length and breadth of the lawn .", + "Output Program": [ + "n0 = 2.0\nn1 = 3.0\nn2 = 1.0\nn3 = 6.0\nt0 = 10.0 * 1000.0\nt1 = t0 / n3\nt2 = n1 * t1\nanswer = t2 / 100.0\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "test" + }, + { + "Input": "in a certain parallelogram the degree measure of one angle exceeds that of the other by 20 what is the degree measure of the smaller angle ?", + "Output Program": [ + "n0 = 20.0\nt0 = 3600.0 / 10.0\nt1 = n0 * 2.0\nt2 = t0 - t1\nanswer = t2 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "80" + ], + "split": "test" + }, + { + "Input": "the length of rectangle is thrice its breadth and its perimeter is 72 m , find the area of the rectangle ?", + "Output Program": [ + "n0 = 72.0\nt0 = 2.0 * 3.0\nt1 = 1.0 * 2.0\nt2 = t0 + t1\nt3 = n0 / t2\nt4 = t3 * 3.0\nanswer = t3 * t4\nprint(answer)" + ], + "Output Answer": [ + "243" + ], + "split": "test" + }, + { + "Input": "the pressure someone experiences as he or she dives deeper and deeper in the ocean increases linearly . on the surface , the pressure is close to 15 pounds per square inch . 33 feet below the surface , the pressure is 30 pounds . if 25000 pounds per sq inch can crush your bones , what depth is extremely dangerous for humans ?", + "Output Program": [ + "n0 = 15.0\nn1 = 33.0\nn2 = 30.0\nn3 = 25000.0\nt0 = 3.0 * 4.0\nt1 = n3 - n0\nt2 = n2 - n0\nt3 = n1 * t0\nt4 = t2 / t3\nt5 = t1 / t4\nanswer = t5 / t0\nprint(answer)" + ], + "Output Answer": [ + "54967" + ], + "split": "test" + }, + { + "Input": "find the area of a parallelogram with base 26 cm and height 12 cm ?", + "Output Program": [ + "n0 = 26.0\nn1 = 12.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "312" + ], + "split": "test" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 680 sq . feet , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 20.0\nn1 = 680.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "88" + ], + "split": "test" + }, + { + "Input": "points a , b , and , c have xy - coordinates ( 20 ) , ( 812 ) , and ( 140 ) , respectively . points x , y , and z have xy - coordinates ( 60 ) , ( 84 ) , and ( 100 ) , respectively . what fraction c of the area of triangle abc is the area of triangle xyz ?", + "Output Program": [ + "n0 = 20.0\nn1 = 812.0\nn2 = 140.0\nn3 = 60.0\nn4 = 84.0\nn5 = 100.0\nt0 = 4.0 * 4.0\nt1 = 2.0 * 4.0\nt2 = t0 / 2.0\nt3 = n0 - t1\nt4 = t3 / 2.0\nt5 = t4 * t3\nanswer = t2 / t5\nprint(answer)" + ], + "Output Answer": [ + "0.1111111111111111" + ], + "split": "test" + }, + { + "Input": "in a rectangular coordinate system , what is the area of a rectangle whose vertices have the coordinates ( - 4 , 1 ) , ( 1 , 1 ) , ( 1 , - 3 ) and ( - 4 , - 3 ) ?", + "Output Program": [ + "n0 = 4.0\nn1 = 1.0\nn2 = 1.0\nn3 = 1.0\nn4 = 1.0\nn5 = 3.0\nn6 = 4.0\nn7 = 3.0\nt0 = n0 + n1\nt1 = n1 + n5\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "20" + ], + "split": "test" + }, + { + "Input": "if the radius of a cylinder is doubled and so is the height , what is the new volume of the cylinder divided by the old one ?", + "Output Program": [ + "import math\nt0 = 1.0 * 2.0\nt1 = math.pi * 1.0**2 * 1.0\nt2 = math.pi * t0**2 * t0\nanswer = t2 / t1\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "test" + }, + { + "Input": "the total surface area of a solid hemisphere of diameter 14 cm , is :", + "Output Program": [ + "n0 = 14.0\nt0 = n0 / 2.0\nt1 = 3.0 * 3.141592653589793\nt2 = t0**min(2.0, 5)\nanswer = t1 * t2\nprint(answer)" + ], + "Output Answer": [ + "461.8141200776996" + ], + "split": "test" + }, + { + "Input": "the perimeter of a triangle is 44 cm and the in radius of the triangle is 2.5 cm . what is the area of the triangle ?", + "Output Program": [ + "n0 = 44.0\nn1 = 2.5\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "55" + ], + "split": "test" + }, + { + "Input": "if the area of a square with sides of length 11 centimeters is equal to the area of a rectangle with a width of 11 centimeters , what is the length of the rectangle , in centimeters ?", + "Output Program": [ + "n0 = 11.0\nn1 = 11.0\nt0 = n0**min(2.0, 5)\nanswer = t0 / n1\nprint(answer)" + ], + "Output Answer": [ + "11" + ], + "split": "test" + }, + { + "Input": "a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many cubes are painted on only 2 faces ?", + "Output Program": [ + "n0 = 27.0\nn1 = 2.0\nt0 = 1.0 / 3.0\nt1 = n0**min(t0, 5)\nanswer = t1 * 4.0\nprint(answer)" + ], + "Output Answer": [ + "12" + ], + "split": "test" + }, + { + "Input": "calculate the area of a triangle , if the sides of are 52 cm , 48 cm and 20 cm , what is its area ?", + "Output Program": [ + "n0 = 52.0\nn1 = 48.0\nn2 = 20.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "480" + ], + "split": "test" + }, + { + "Input": "the diameter of a circle is 4 / \u03c0 . find the circumference of the circle .", + "Output Program": [ + "import math\nn0 = 4.0\nt0 = n0 / 3.141592653589793\nanswer = 2 * math.pi * t0\nprint(answer)" + ], + "Output Answer": [ + "8" + ], + "split": "test" + }, + { + "Input": "if the sides of a triangle are 31 cm , 29 cm and 15 cm , what is its area ?", + "Output Program": [ + "n0 = 31.0\nn1 = 29.0\nn2 = 15.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "217.5" + ], + "split": "test" + }, + { + "Input": "what will be the area of a semi - circle of 14 metres diameter ?", + "Output Program": [ + "import math\nn0 = 14.0\nt0 = n0 / 2.0\nt1 = math.pi * t0**2\nanswer = t1 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "76.96902001294993" + ], + "split": "test" + }, + { + "Input": "the volume of a cube is 2197 cc . find its surface .", + "Output Program": [ + "n0 = 2197.0\nt0 = n0**(1 / 3)\nanswer = 6 * t0**2 # surface of a cube\nprint(answer)" + ], + "Output Answer": [ + "1013.9999999999997" + ], + "split": "test" + }, + { + "Input": "15 business executives and 3 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?", + "Output Program": [ + "n0 = 15.0\nn1 = 3.0\nt0 = n0 * n1\nt1 = n0 - 1.0\nt2 = n0 * t1\nt3 = t2 / 2.0\nanswer = t3 + t0\nprint(answer)" + ], + "Output Answer": [ + "150" + ], + "split": "test" + }, + { + "Input": "the area of a triangle is with base 5.5 m and height 6 m ?", + "Output Program": [ + "n0 = 5.5\nn1 = 6.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "16.5" + ], + "split": "test" + }, + { + "Input": "a rectangular lawn of dimensions 120 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?", + "Output Program": [ + "n0 = 120.0\nn1 = 60.0\nn2 = 10.0\nn3 = 3.0\nt0 = n0 + n1\nt1 = t0 - n2\nt2 = n2 * t1\nanswer = n3 * t2\nprint(answer)" + ], + "Output Answer": [ + "5100" + ], + "split": "test" + }, + { + "Input": "the length of a rectangle is increased by 35 % and its breadth is decreased by 20 % . what is the effect on its area ?", + "Output Program": [ + "n0 = 35.0\nn1 = 20.0\nt0 = n0 + 100.0\nt1 = 100.0 - n1\nanswer = t0 * t1\nprint(answer)" + ], + "Output Answer": [ + "10800" + ], + "split": "test" + }, + { + "Input": "a girl walking at the rate of 9 km per hour crosses a square field diagonally in 12 seconds . the area of the field is :", + "Output Program": [ + "n0 = 9.0\nn1 = 12.0\nt0 = n0 * 1000.0\nt1 = 10.0 * 360.0\nt2 = t0 / t1\nt3 = n1 * t2\nt4 = t3 * t3\nanswer = t4 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "450" + ], + "split": "test" + }, + { + "Input": "the perimeter of a triangle is 40 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle", + "Output Program": [ + "n0 = 40.0\nn1 = 2.5\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "50" + ], + "split": "test" + }, + { + "Input": "the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 1323 sq m , then what is the breadth of the rectangular plot ?", + "Output Program": [ + "import math\nn0 = 1323.0\nt0 = n0 / 3.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "21" + ], + "split": "test" + }, + { + "Input": "if the complement of a certain angle is 7 times the measure of that certain angle , then what is the measure of that certain angle ?", + "Output Program": [ + "n0 = 7.0\nt0 = n0 + 1.0\nt1 = 100.0 - 10.0\nanswer = t1 / t0\nprint(answer)" + ], + "Output Answer": [ + "11.25" + ], + "split": "test" + }, + { + "Input": "the area of a triangle is with base 2 m and height 5 m ?", + "Output Program": [ + "n0 = 2.0\nn1 = 5.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "5" + ], + "split": "test" + }, + { + "Input": "if o is the center of the circle in the figure above and the area of the unshaded sector is 5 , what is the area of the shaded region ?", + "Output Program": [ + "n0 = 5.0\n\nanswer = n0**min(2.0, 5)\nprint(answer)" + ], + "Output Answer": [ + "25" + ], + "split": "test" + }, + { + "Input": "the diagonals of a rhombus are 18 cm and 22 cm . find its area ?", + "Output Program": [ + "n0 = 18.0\nn1 = 22.0\n\nanswer = n0 * n1 / 2\nprint(answer)" + ], + "Output Answer": [ + "198" + ], + "split": "test" + }, + { + "Input": "a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 256 sq . feet , how many feet of fencing will be required ?", + "Output Program": [ + "n0 = 20.0\nn1 = 256.0\nt0 = n1 / n0\nt1 = t0 * 2.0\nanswer = n0 + t1\nprint(answer)" + ], + "Output Answer": [ + "45.6" + ], + "split": "test" + }, + { + "Input": "what is the max number of rectangular boxes , each measuring 4 inches by 6 inches by 10 inches , that can be packed into a rectangular packing box measuring 16 inches by 18 inches by 30 inches , if all boxes are aligned in the same direction ?", + "Output Program": [ + "n0 = 4.0\nn1 = 6.0\nn2 = 10.0\nn3 = 16.0\nn4 = 18.0\nn5 = 30.0\nt0 = n3 * n4\nt1 = n0 * n1\nt2 = n5 * t0\nt3 = n2 * t1\nanswer = t2 / t3\nprint(answer)" + ], + "Output Answer": [ + "36" + ], + "split": "test" + }, + { + "Input": "a rectangular grass field is 70 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?", + "Output Program": [ + "n0 = 70.0\nn1 = 55.0\nn2 = 2.5\nn3 = 2.0\nt0 = n2 * n3\nt1 = n0 * n1 # area of rectangle\nt2 = n0 + t0\nt3 = n1 + t0\nt4 = t2 * t3 # area of rectangle\nt5 = t4 - t1\nanswer = n3 * t5\nprint(answer)" + ], + "Output Answer": [ + "1300" + ], + "split": "test" + }, + { + "Input": "calculate the area of a triangle , if the sides of are 39 cm , 36 cm and 15 cm , what is its area ?", + "Output Program": [ + "n0 = 39.0\nn1 = 36.0\nn2 = 15.0\nt0 = n1 / 2.0\nanswer = n2 * t0\nprint(answer)" + ], + "Output Answer": [ + "270" + ], + "split": "test" + }, + { + "Input": "the length of a rectangular plot is 10 mtr more than its width . the cost of fencing the plot along its perimeter at the rate of rs . 6.5 mtr is rs . 1690 . the perimeter of the plot is ?", + "Output Program": [ + "n0 = 10.0\nn1 = 6.5\nn2 = 1690.0\nt0 = n2 / n1\nt1 = t0 / 2.0\nt2 = t1 - n0\nt3 = t2 / 2.0\nt4 = t3 + n0\nt5 = t4 + t3\nanswer = t5 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "260" + ], + "split": "test" + }, + { + "Input": "a room is a square of side 50 feet . a second room is of area 100 square yards . a third room is of area 200 square feet . which of these can seat maximum people ? ( hint : 1 yard = 3 feet )", + "Output Program": [ + "n0 = 50.0\nn1 = 100.0\nn2 = 200.0\nn3 = 1.0\nn4 = 3.0\n\nanswer = n1 * 2.0\nprint(answer)" + ], + "Output Answer": [ + "200" + ], + "split": "test" + }, + { + "Input": "find the area of a parallelogram with base 15 cm and height 40 cm ?", + "Output Program": [ + "n0 = 15.0\nn1 = 40.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "600" + ], + "split": "test" + }, + { + "Input": "the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 507 sq m , then what is the breadth of the rectangular plot ?", + "Output Program": [ + "import math\nn0 = 507.0\nt0 = n0 / 3.0\nanswer = math.sqrt(max(0, t0))\nprint(answer)" + ], + "Output Answer": [ + "13" + ], + "split": "test" + }, + { + "Input": "the perimeter of a rectangular yard is completely surrounded by a fence that measures 12 meters . what is the length of the yard if the area of the yard is 9 meters squared ?", + "Output Program": [ + "n0 = 12.0\nn1 = 9.0\n\nanswer = 4.0 - 3.0\nprint(answer)" + ], + "Output Answer": [ + "1" + ], + "split": "test" + }, + { + "Input": "a rectangular wall is covered entirely with two kinds of decorative tiles : regular and jumbo . 1 / 3 of the tiles are jumbo tiles , which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles . if regular tiles cover 50 square feet of the wall , and no tiles overlap , what is the area of the entire wall ?", + "Output Program": [ + "n0 = 1.0\nn1 = 3.0\nn2 = 50.0\nt0 = n2 * n1\nt1 = t0 / 2.0\nt2 = n1 * t1\nanswer = n2 + t2\nprint(answer)" + ], + "Output Answer": [ + "275" + ], + "split": "test" + }, + { + "Input": "the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 6 per metre approximately", + "Output Program": [ + "import math\nn0 = 17.56\nn1 = 6.0\nt0 = n0 / 3.141592653589793\nt1 = math.sqrt(max(0, t0))\nt2 = t1 * 100.0\nt3 = 2 * math.pi * t2\nanswer = t3 * n1\nprint(answer)" + ], + "Output Answer": [ + "8912.887774213974" + ], + "split": "test" + }, + { + "Input": "a horse is tethered to one corner of a rectangular grassy field 36 m by 20 m with a rope 12 m long . over how much area of the field can it graze ?", + "Output Program": [ + "n0 = 36.0\nn1 = 20.0\nn2 = 12.0\nt0 = n2**min(2.0, 5)\nt1 = t0 * 3.141592653589793\nanswer = t1 / 4.0\nprint(answer)" + ], + "Output Answer": [ + "113.09733552923255" + ], + "split": "test" + }, + { + "Input": "if the difference between the length and breadth of a rectangle is 23 m and its perimeter is 206 m , what is its area ?", + "Output Program": [ + "n0 = 23.0\nn1 = 206.0\nt0 = n0 * 2.0\nt1 = n1 - t0\nt2 = t1 / 4.0\nt3 = n0 + t2\nanswer = t3 * t2 # area of rectangle\nprint(answer)" + ], + "Output Answer": [ + "2520" + ], + "split": "test" + }, + { + "Input": "if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?", + "Output Program": [ + "n0 = 20.0\nn1 = 12.0\nn2 = 16.0\nt0 = n1 * n2\nanswer = t0 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "96" + ], + "split": "test" + }, + { + "Input": "if length of a rectangle is equal to side of a square and breadth of rectangle is half of length . if area of square is 36 sq . m . calculate the area of rectangle ?", + "Output Program": [ + "import math\nn0 = 36.0\nt0 = math.sqrt(max(0, n0))\nt1 = t0 / 2.0\nanswer = t1 * t0\nprint(answer)" + ], + "Output Answer": [ + "18" + ], + "split": "test" + }, + { + "Input": "the parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places", + "Output Program": [ + "import math\nn0 = 16.0\nn1 = 14.0\nt0 = 2 * (n0 + n1) # perimetere of rectangle\nt1 = t0 / 4. # square edge given perimeter\nt2 = t1 / 2.0\nt3 = 2 * math.pi * t2\nanswer = t3 / 2.0\nprint(answer)" + ], + "Output Answer": [ + "23.561944901923447" + ], + "split": "test" + }, + { + "Input": "find the area of a parallelogram with base 20 cm and height 40 cm ?", + "Output Program": [ + "n0 = 20.0\nn1 = 40.0\n\nanswer = n0 * n1\nprint(answer)" + ], + "Output Answer": [ + "800" + ], + "split": "test" + } + ], + "Metadata": [ + { + "Answer": 5, + "Options": "a ) 5 units , b ) 10 units , c ) 15 units , d ) 20 units , e ) 25 units", + "Correct": "a", + "Explanation": "\"the base of the isosceles triangle is 45 - 20 - 20 = 5 units the answer is a .\"" + }, + { + "Answer": 16, + "Options": "['a ) 8', 'b ) 16', 'c ) 24', 'd ) 32', 'e ) 48']", + "Correct": "b", + "Explanation": "from the info that the maximum sides of the cubes is 4 , we know that the gcf of 12 ( = 2 ^ 2 * 3 ) andbis 4 ( = 2 ^ 2 ) , sob = 2 ^ x , where x > = 2 . from the second premise , we know that the lcm of 12 ( 2 ^ 2 * 3 ) andbis 80 ( 2 ^ 4 * 5 ) , sob = 2 ^ 4 or 2 ^ 4 * 5 ( 16 or 80 ) . combining 2 premises shows the answer is b ( 16 ) ." + }, + { + "Answer": 10, + "Options": "['a ) 8', 'b ) 8 \u03c0', 'c ) 9 \u221a 3', 'd ) 10', 'e ) 12']", + "Correct": "d", + "Explanation": "property of a right triangle inscribed in a circle is that when an angle is made from diameter of the circle , it is a right triangle . or if a right triangle is made inscribed in a circle , its its longest side is the diameter of the circle . hence diameter = ( 6 ^ 2 + 8 ^ 2 ) ^ 1 / 2 = 10 d is the answer" + }, + { + "Answer": 42.06195997410015, + "Options": "['a ) 24 cm 2', 'b ) 42 cm 2', 'c ) 154 cm 2', 'd ) 196 cm 2', 'e ) none of these']", + "Correct": "b", + "Explanation": "the shaded area gives the required region . area of the shaded region = area of the square \u2013 area of four quadrants of the circles = ( 14 ) 2 - 4 \u00d7 1 \u2044 4 \u03c0 ( 7 ) 2 = 196 - 22 \u2044 7 \u00d7 49 = 196 - 154 = 42 cm 2 answer b" + }, + { + "Answer": 32, + "Options": "['a ) 16', 'b ) 48', 'c ) 64', 'd ) 32', 'e ) 8']", + "Correct": "d", + "Explanation": "number of ounces per cylinder 8 number of cylinders 6 ounces needed 48 ounces used 16 answer d" + }, + { + "Answer": 169, + "Options": "a ) 169 , b ) 196 , c ) 266 , d ) 288 , e ) 261", + "Correct": "a", + "Explanation": "\"13 * 13 = 169 sq m answer : a\"" + }, + { + "Answer": 20.92844953645635, + "Options": "a ) 20 , b ) 21 , c ) 19 , d ) 17 , e ) 15", + "Correct": "b", + "Explanation": "\"sum of the squares of 3 different positive integers = 219 13 ^ 2 + 7 ^ 2 + 1 ^ 2 = 219 now , sum of these 3 different integers = 13 + 7 + 1 = 21 ans - b\"" + }, + { + "Answer": 1535.9999999999995, + "Options": "['a ) 4096 sq cm', 'b ) 1536 sq cm', 'c ) 1024 sq cm', 'd ) 2048 sq cm', 'e ) 512 sq cm']", + "Correct": "b", + "Explanation": "volume = a x a x a = a ^ 3 volume of cube = 8 x 512 = 4096 cm ^ 3 4096 = a ^ 3 a = 16 surface area of cube = 6 a ^ 2 = 6 x 16 ^ 2 = 1536 answer is b" + }, + { + "Answer": 40, + "Options": "a ) 25 cm , b ) 30 cm , c ) 40 cm , d ) 45 cm , e ) 60 cm", + "Correct": "c", + "Explanation": "let breadth = x cm then , length = 2 x cm area = x \u00d7 2 x = 2 x 2 sq . cm . new length = ( 2 x \u2212 5 ) cm new breadth = ( x + 5 ) cm new area = ( 2 x \u2212 5 ) ( x + 5 ) sq . cm . given that , new area = initial area + 75 sq . cm . \u21d2 ( 2 x \u2212 5 ) ( x + 5 ) = 2 x 2 + 75 \u21d2 2 x 2 + 10 x \u2212 5 x \u2212 25 = 2 x 2 + 75 \u21d2 5 x \u2212 25 = 75 \u21d2 5 x = 75 + 25 = 100 \u21d2 x = 1005 = 20 cm length = 2 x = 2 \u00d7 20 = 40 cm c" + }, + { + "Answer": 5.76, + "Options": "a ) 5.76 cm , b ) 8.25 cm , c ) 11.25 cm , d ) 15.12 cm , e ) 20.62 cm", + "Correct": "a", + "Explanation": "\"increase in volume = volume of the cube = 12 * 12 * 12 cm ^ 3 rise in water level = volume / area = 12 * 12 * 12 / 20 * 15 = 5.76 cm answer is a\"" + }, + { + "Answer": 576, + "Options": "['a ) $ 200', 'b ) $ 576', 'c ) $ 480', 'd ) $ 960', 'e ) $ 1,920']", + "Correct": "b", + "Explanation": "the width of the rectangular floor ( 24 m ) is a multiple of one side of the square ( 8 m ) , and the length of the floor ( 64 m ) is also a multiple of the side of the square . so the number of carpets to cover the floor is ( 24 / 8 ) * ( 64 / 8 ) = 24 . the total cost is 24 * 24 = $ 576 . the answer is , therefore , b ." + }, + { + "Answer": 3300, + "Options": "a ) 2288 , b ) 2779 , c ) 3300 , d ) 3900 , e ) 2781", + "Correct": "c", + "Explanation": "\"area = ( l + b \u00e2 \u20ac \u201c d ) d ( 80 + 40 \u00e2 \u20ac \u201c 10 ) 10 = > 1100 m 2 1100 * 3 = rs . 3300 answer : c\"" + }, + { + "Answer": 16, + "Options": "a ) $ 1 , b ) $ 2 , c ) $ 4 , d ) $ 8 , e ) $ 16", + "Correct": "e", + "Explanation": "let x be the radius of b and 2 h be the height of b . therefore , radius of c = 2 x and height = h vol of b = 3.14 * x ^ 2 * 2 h vol of a = 3.14 * 4 x ^ 2 * h cost to fill half of b = $ 4 - - > cost to fill full b = $ 8 - - > 3.14 * x ^ 2 * 2 h = 8 - - > 3.14 * x ^ 2 * h = 4 - - > 4 * ( 3.14 * x ^ 2 * h ) = $ 16 ans e" + }, + { + "Answer": 64, + "Options": "a ) 48 , b ) 32 , c ) 24 , d ) 18 , e ) 64", + "Correct": "e", + "Explanation": "\"for example our cube have a side 1 meter , so we have 1 cubical meter in this cube and this cubical meter weigth 6 pounds if we take cube with side 2 meters we will have 8 cubical meters in this cube 8 meters * 8 pounds = 64 pounds so answer is e and similar but more theoretical approach : if we have sides a and b than they have equal ration with their areas : a / b = a ^ 2 / b ^ 2 and they have equal ration with their volumes : a / b = a ^ 3 / b ^ 3 we have two sides 1 / 2 so their volume will be in ratio 1 / 8 weight of one cube * volume of another cube 8 * 8 = 64 so answer is e\"" + }, + { + "Answer": 8, + "Options": "['a ) 4', 'b ) 8', 'c ) 12', 'd ) 16', 'e ) 20']", + "Correct": "b", + "Explanation": "area of the square = 8 x 8 = 64 let ' l ' be the unknown diagonal 0.5 x 16 x ' l ' = 64 which gives ' l ' = 8 cm answer : b" + }, + { + "Answer": 8, + "Options": "['a ) 5 m', 'b ) 12 m', 'c ) 6 m', 'd ) 8 m', 'e ) 10 m']", + "Correct": "d", + "Explanation": "height of the cuboid = volume * base area = 144 / 18 = 8 metre answer is option d" + }, + { + "Answer": 32, + "Options": "a ) 48 , b ) 32 , c ) 24 , d ) 18 , e ) 12", + "Correct": "b", + "Explanation": "\"for example our cube have a side 1 meter , so we have 1 cubical meter in this cube and this cubical meter weigth 4 pounds if we take cube with side 2 meters we will have 8 cubical meters in this cube 8 meters * 4 pounds = 32 pounds so answer is b and similar but more theoretical approach : if we have sides a and b than they have equal ration with their areas : a / b = a ^ 2 / b ^ 2 and they have equal ration with their volumes : a / b = a ^ 3 / b ^ 3 we have two sides 1 / 2 so their volume will be in ratio 1 / 8 weight of one cube * volume of another cube 4 * 8 = 32 so answer is b\"" + }, + { + "Answer": 16, + "Options": "['a ) 4 : 1', 'b ) 6 : 1', 'c ) 8 : 1', 'd ) 16 : 1', 'e ) 64 : 1']", + "Correct": "d", + "Explanation": "let x be the length of the small cube ' s side . the total surface area of the small cube is 6 x ^ 2 . the total surface area of the large cube is 6 ( 4 x ) ^ 2 = 96 x ^ 2 . the ratio of surface areas is 16 : 1 . the answer is d ." + }, + { + "Answer": 1450, + "Options": "a ) 1450 , b ) 1971 , c ) 9676 , d ) 1679 , e ) 2691", + "Correct": "a", + "Explanation": "\"area = ( l + b + 2 d ) 2 d = ( 85 + 55 + 2.5 * 2 ) 2 * 2.5 = > 725 725 * 2 = rs . 1450 answer : a\"" + }, + { + "Answer": 625, + "Options": "a ) 900 , b ) 800 , c ) 700 , d ) 625 , e ) 650", + "Correct": "d", + "Explanation": "\"area of the rhombus = 1 / 2 d 1 d 2 = ( 1 / 2 \u00e3 \u2014 25 \u00e3 \u2014 50 ) cm ( power ) 2 = 25 \u00e3 \u2014 25 = 625 cm ( power ) 2 answer is d .\"" + }, + { + "Answer": 245, + "Options": "a ) 230 , b ) 141 , c ) 66 , d ) 245 , e ) 21", + "Correct": "d", + "Explanation": "\"r = 7 h = 5 \u03c0 * 7 * 7 * 5 = 45 \u03c0 cc answer : d\"" + }, + { + "Answer": 3750, + "Options": "a ) 100 , b ) 250 , c ) 750 , d ) 3750 , e ) 5625", + "Correct": "d", + "Explanation": "\"6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 40 * 25 * 1 / 2 = 500 feet ^ 3 of water must be removed , which equals to 500 * 7.5 = 3750 gallons . answer : d .\"" + }, + { + "Answer": 863.9999999999997, + "Options": "a ) 864 , b ) 556 , c ) 255 , d ) 287 , e ) 267", + "Correct": "a", + "Explanation": "\"a 3 = 1728 = > a = 12 6 a 2 = 6 * 12 * 12 = 864 answer : a\"" + }, + { + "Answer": 75, + "Options": "a ) 432 , b ) 212 , c ) 75 , d ) 992 , e ) 212", + "Correct": "c", + "Explanation": "\"2 ( 3 x + x ) = 40 l = 15 b = 5 lb = 15 * 5 = 75 answer : c\"" + }, + { + "Answer": 3.3379421944391545, + "Options": "a ) 3.34 sq m , b ) 98.8 sq m , c ) 67.8 sq m , d ) 27.9 sq m , e ) 19.9 sq m", + "Correct": "a", + "Explanation": "\"area of the path = area of the outer circle - area of the inner circle = \u220f { 4 / 2 + 25 / 100 } 2 - \u220f [ 4 / 2 ] 2 = \u220f [ 2.252 - 22 ] = \u220f ( 0.25 ) ( 4.25 ) { ( a 2 - b 2 = ( a - b ) ( a + b ) } = ( 3.14 ) ( 1 / 4 ) ( 17 / 4 ) = 53.38 / 16 = 3.34 sq m answer : a\"" + }, + { + "Answer": 20, + "Options": "a ) 22 , b ) 20 , c ) 88 , d ) 387 , e ) 19", + "Correct": "b", + "Explanation": "\"let the radius of the pool be rft radius of the pool including the wall = ( r + 4 ) ft area of the concrete wall = { \\ color { black } \\ pi \\ left [ ( r + 4 ) ^ { 2 } - r ^ { 2 } \\ right ] } = { \\ color { black } \\ pi \\ left [ ( r + 4 + r ) ( r + 4 - r ) \\ right ] = 8 \\ pi ( r + 2 ) } sq feet { \\ color { black } \\ rightarrow 8 \\ pi ( r + 2 ) = \\ frac { 11 } { 25 } \\ pi r ^ { 2 } \\ rightarrow 11 r ^ { 2 } = 200 ( r + 2 ) } radius of the pool r = 20 ft answer : b ) 20 ft\"" + }, + { + "Answer": 8, + "Options": "['a ) 4', 'b ) 5', 'c ) 6', 'd ) 8', 'e ) 10']", + "Correct": "d", + "Explanation": "for max volume of cylinder ( pi * r ^ 2 * h ) we need to max out r ^ 2 * h . we do n ' t know what the dimensions of the crate refer to . . therefore for max vol base should be 18 x 16 i . e . of radius 16 / 2 = 8 d" + }, + { + "Answer": 140, + "Options": "a ) 126 , b ) 156 , c ) 190 , d ) 140 , e ) 260", + "Correct": "d", + "Explanation": "\"sol . let width = x , length = ( 10 + x ) perimeter = 2 ( x + ( 10 + x ) ) = 2 ( 2 x = 10 ) & 2 ( 2 x + 10 ) * 6.5 = 910 x = 30 required perimeter = 2 ( 30 + 40 ) = 140 d\"" + }, + { + "Answer": 2, + "Options": "a ) 1 : 2 , b ) 2 : 1 , c ) 3 : 1 , d ) data inadequate , e ) none of these", + "Correct": "b", + "Explanation": "\"area of \u03b4 ebc = 1 \u2044 2 \u00d7 bc \u00d7 ef = 1 \u2044 2 \u00d7 bc \u00d7 ab [ since , ef = ab ] area of \u03b4 ebc = 1 \u2044 2 \u00d7 area of \u03b4 abcd \\ required ratio = 2 : 1 . answer b\"" + }, + { + "Answer": 112.5, + "Options": "['a ) 110 sq . m', 'b ) 111.5 aq . m', 'c ) 112.5 sq . m', 'd ) 114 sq . m', 'e ) none of these']", + "Correct": "c", + "Explanation": "explanation : distance covered in 9 seconds = ( 6 \u00d7 1000 / 3600 ) \u00d7 9 = 15 m diagonal of square field = 15 m side of square = a then diagonal of that square = \u221a 2 a hence area of the square = a 2 = ( 152 ) / 2 = 112.5 sq . m answer : option c" + }, + { + "Answer": 10, + "Options": "['a ) 11', 'b ) 10', 'c ) 99', 'd ) 17', 'e ) 12']", + "Correct": "b", + "Explanation": "1 / 2 * 4 * 5 = 10 m 2 answer : b" + }, + { + "Answer": 56.25, + "Options": "a ) 56.28 , b ) 56.25 , c ) 56.2 , d ) 56.24 , e ) 56.21", + "Correct": "b", + "Explanation": "\"a = 100 a 2 = 10000 a = 125 a 2 = 15625 - - - - - - - - - - - - - - - - 10000 - - - - - - - - - 5625 100 - - - - - - - ? = > 56.25 % answer : b\"" + }, + { + "Answer": 1200, + "Options": "['a ) 720', 'b ) 900', 'c ) 1200', 'd ) 1800', 'e ) 2100']", + "Correct": "c", + "Explanation": "2 ( 15 + 12 ) x h = 2 ( 15 x 12 ) h = 180 / 27 m = 20 / 3 m . volume = 15 x 12 x 20 / 3 m 3 answer : option c" + }, + { + "Answer": 16, + "Options": "['a ) 4', 'b ) 8', 'c ) 16', 'd ) 32', 'e ) 64']", + "Correct": "c", + "Explanation": "area of fed = 2 sq inches = 1 / 2 * de * fd = 1 / 2 * de ^ 2 because the sides of a square are equal , hence half of the sides will also be equal . de ^ 2 = 4 de = fd = 2 hence the side of the square = 4 area if the square = 4 * 4 = 16 correct option : c" + }, + { + "Answer": 18, + "Options": "a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 14", + "Correct": "c", + "Explanation": "\"let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 972 3 b 2 = 972 b 2 = 324 b = 18 m . answer : option c\"" + }, + { + "Answer": 25.44000000000002, + "Options": "['a ) decreases by 25.44 %', 'b ) increases by 25.44 %', 'c ) no change in area', 'd ) decreases by 12 %', 'e ) none']", + "Correct": "b", + "Explanation": "a 1 = pi ( 100 ) ^ 2 a 2 = pi ( 112 ) ^ 2 so ( a 2 - a 1 ) / a 1 * 100 = 25.44 answer : b" + }, + { + "Answer": 49, + "Options": "a ) 56 , b ) 88 , c ) 112 , d ) 49 , e ) 120", + "Correct": "d", + "Explanation": "\"area of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 7 + 7 = 14 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 14 * 7 = 49 d is the answer\"" + }, + { + "Answer": 3, + "Options": "a ) 3 cm , b ) 4 cm , c ) 6 cm , d ) 8 cm , e ) none", + "Correct": "a", + "Explanation": "\"solution 4 \u00ee r 2 = 2 \u00ee 3 x 6 \u00e2 \u2021 \u2019 r 2 = ( 3 x 6 / 2 ) \u00e2 \u2021 \u2019 9 \u00e2 \u2021 \u2019 r = 3 cm . answer a\"" + }, + { + "Answer": 16, + "Options": "a ) 88 m 2 , b ) 10 m 2 , c ) 16 m 2 , d ) 77 m 2 , e ) 31 m 2", + "Correct": "c", + "Explanation": "\"1 / 2 * 8 * 4 = 16 m 2 answer : c\"" + }, + { + "Answer": 300, + "Options": "a ) 40 , b ) 50 , c ) 60 , d ) 200 , e ) 300", + "Correct": "e", + "Explanation": "\"alternate approach backsolving ( using answer options to reach the correct answer ) can work wonders here if one is fast in calculations . given perimeter is 900 so , 2 ( l + b ) = 900 or , l + b = 450 now use the answer options ( given length ; breath will be half the length ) ( a ) 40 l = 40 ; b = 20 l + b = 60 ( b ) 50 l = 50 ; b = 25 l + b = 75 ( c ) 60 l = 60 ; b = 30 l + b = 90 ( d ) 200 l = 200 ; b = 100 l + b = 300 ( e ) 300 l = 300 ; b = 150 l + b = 450 thus you see no , need of any calculations , u can reach the correct option only by checking options ; correct answer will be ( e )\"" + }, + { + "Answer": 8, + "Options": "['a ) becomes 8 times', 'b ) becomes 9 times', 'c ) is double', 'd ) becomes 6 times', 'e ) none']", + "Correct": "a", + "Explanation": "sol . let original edge = a . then , volume = a \u00b3 new edge = 2 a . so , new volume = ( 2 a ) \u00b3 = 8 a \u00b3 \u2234 volume becomes 8 times answer a" + }, + { + "Answer": 3.1666666666666665, + "Options": "['a ) 3.17 feet', 'b ) 3.2 feet', 'c ) 3.3 feet', 'd ) 3.4 feet', 'e ) 3.5 feet']", + "Correct": "a", + "Explanation": "we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 4 = 38 38 / 12 = 3.17 feet answer : a" + }, + { + "Answer": 5, + "Options": "['a ) 5 / ( \u221a 6 )', 'b ) 5 \u00b7 \u221a ( 2 / 3 )', 'c ) 5 \u00b7 \u221a ( 3 / 2 )', 'd ) 5 \u00b7 \u221a 3', 'e ) 5 \u00b7 \u221a 6']", + "Correct": "b", + "Explanation": "n cube c , let ' s say that each side has side length x so , the diagonal = \u221a ( x \u00b2 + x \u00b2 + x \u00b2 ) = \u221a ( 3 x \u00b2 ) here , we ' re told that the diagonal has length 5 , so we can write : 5 = \u221a ( 3 x \u00b2 ) square both sides to get : 25 = 3 x \u00b2 divide both sides by 3 to get : 25 / 3 = x \u00b2 square root both sides : \u221a ( 25 / 3 ) = x or . . . . ( \u221a 25 ) / ( \u221a 3 ) = x simplify : 5 / ( \u221a 3 ) = x answer : b" + }, + { + "Answer": 190, + "Options": "a ) 100 , b ) 777 , c ) 998 , d ) 190 , e ) 2879", + "Correct": "d", + "Explanation": "\"100 % answer : d\"" + }, + { + "Answer": 23.561944901923447, + "Options": "['a ) 77.14 cm', 'b ) 47.14 cm', 'c ) 84.92 cm', 'd ) 94.94 cm', 'e ) 23.57 cm']", + "Correct": "e", + "Explanation": "let the side of the square be a cm . parameter of the rectangle = 2 ( 16 + 14 ) = 60 cm parameter of the square = 60 cm i . e . 4 a = 60 a = 15 diameter of the semicircle = 15 cm circimference of the semicircle = 1 / 2 ( \u220f ) ( 15 ) = 1 / 2 ( 22 / 7 ) ( 15 ) = 330 / 14 = 23.57 cm to two decimal places answer : e" + }, + { + "Answer": 25, + "Options": "a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 25", + "Correct": "e", + "Explanation": "\"try filling the numbers into the answer y x y = find the closest to 625 . answer e\"" + }, + { + "Answer": 3, + "Options": "['a ) 3 m', 'b ) 4 m', 'c ) 5 m', 'd ) 6 m', 'e ) 2 m']", + "Correct": "a", + "Explanation": "total area of cross roads = 60 x + 40 x \u2212 x 2 but total area of the cross roads = 291 m 2 hence , 60 x + 40 x \u2212 x 2 = 291 \u21d2 100 x \u2212 x 2 = 291 \u21d2 x 2 \u2212 100 x + 291 = 0 \u21d2 ( x \u2212 97 ) ( x \u2212 3 ) = 0 \u21d2 x = 3 answer : a" + }, + { + "Answer": 0.4, + "Options": "a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 2 / 5", + "Correct": "e", + "Explanation": "the area of the right triangle is ( 1 / 2 ) * 4 * 10 = 20 . only the points ( a , b ) below the line y = x satisfy a - b > 0 . the part of the triangle which is below the line y = x has an area of ( 1 / 2 ) ( 4 ) ( 4 ) = 8 . p ( a - b > 0 ) = 8 / 20 = 2 / 5 the answer is e ." + }, + { + "Answer": 56, + "Options": "a ) 12 , b ) 45 , c ) 87 , d ) 56 , e ) 23", + "Correct": "d", + "Explanation": "\"volume of prism = area of base * height = 1 / 2 * ( square root of 14 ) * ( square root of 14 ) * 8 = 56 answer : d\"" + }, + { + "Answer": 30, + "Options": "a ) 18 square inches , b ) 20 square inches , c ) 24 square inches , d ) 28 square inches , e ) 30 square inches", + "Correct": "e", + "Explanation": "\"total = a + b + c - ( sum of exactly 2 - group overlaps ) - 2 * ( all three ) + neither 80 % * 175 = 224 - 24 - 2 * ( all three ) + 0 2 * ( all three ) = 224 - 24 - 140 all three = 30 answer : e\"" + }, + { + "Answer": 49, + "Options": "a ) 7 , b ) 14 , c ) 28 , d ) 35 , e ) 49", + "Correct": "e", + "Explanation": "we want to know the smallest x that will make 1512 x a cube of some number . let ' s call that number y . let ' s first figure out what we ' re working with . the prime factorization of 450 can be visualized : . . . . . . . . . 1512 . . . . . . . . / . . . . . . . \\ . . . . . . 216 . . . . . . 7 . . . . . / . . \\ . . . . . . . 36 . . . . 6 . . . . . . / . \\ . . . . / . \\ . . . . 6 \u2026 . 6 \u2026 2 \u2026 3 . / . \\ . . / \\ 2 . . 3 2 \u2026 3 so , we have 2 * 2 * 2 * 3 * 3 * 3 * 7 that can be multiplied together to get 1512 . now we need to figure out what we need to make 1512 * x into a cube of y ( y ^ 3 = 1512 * x ) . we have two 5 s , two 3 s , and one 2 . to arrange these numbers in identical triples ( 2 , 3,7 ) , we need at least one more 5 , one 3 , and two 2 ' s . each of these triples will give us the value of y ( 2 * 3 * 7 = 42 ) , which , multiplied by itself three times , gives us 1512 * x . looking at the factors we need to complete the triples , we get 7 * 7 = 49 . we know this is the smallest number possible because prime factors by definition can not be broken down any further . therefore , we can go with answer choice d . if time permits , we can do a sanity check . we calculated that y should be 2 * 3 * 7 , or 42 . 42 * 42 * 42 = 74088 . also , 1512 * 49 = 74088 . answer : e" + }, + { + "Answer": 384, + "Options": "a ) 379 , b ) 384 , c ) 345 , d ) 342 , e ) 376", + "Correct": "b", + "Explanation": "\"area of a parallelogram = base * height = 24 * 16 = 384 cm 2 area of a parallelogram = base * height = 24 * 16 = 384 cm 2 answer : option b\"" + }, + { + "Answer": 18, + "Options": "['a ) 18 cm', 'b ) 28 cm', 'c ) 30 cm', 'd ) 38 cm', 'e ) 42 cm']", + "Correct": "a", + "Explanation": "l 2 + b 2 = 41 . also , lb = 20 . ( l + b ) 2 = ( l 2 + b 2 ) + 2 lb = 41 + 40 = 81 ( l + b ) = 9 . perimeter = 2 ( l + b ) = 18 cm . a )" + }, + { + "Answer": 110, + "Options": "a ) 329 , b ) 288 , c ) 150 , d ) 238 , e ) 110", + "Correct": "e", + "Explanation": "\"1 / 2 * 11 * 20 = 110 answer : e\"" + }, + { + "Answer": 4940, + "Options": "a ) 4940 , b ) 5120 , c ) 6420 , d ) 8960 , e ) 7960", + "Correct": "a", + "Explanation": "\"clearly , l = ( 48 - 10 ) m = 38 m , b = ( 36 - 10 ) m = 26 m , h = 8 m . volume of the box = ( 38 x 26 x 5 ) m 3 = 4940 m 3 . answer : option a\"" + }, + { + "Answer": 5625, + "Options": "a ) a ) 3820 , b ) b ) 930 , c ) c ) 9309 , d ) d ) 3900 , e ) e ) 5625", + "Correct": "e", + "Explanation": "\"explanation : area = ( l + b \u2013 d ) d ( 80 + 60 \u2013 15 ) 15 = > 1875 m 2 1875 * 3 = rs . 5625 answer : option e\"" + }, + { + "Answer": 64, + "Options": "a ) 225 , b ) 64 , c ) 772 , d ) 882 , e ) 21", + "Correct": "b", + "Explanation": "\"8 * 8 = 64 sq m answer : b\"" + }, + { + "Answer": 14.04, + "Options": "a ) 7 , b ) 11 , c ) 13 , d ) 14 , e ) 38", + "Correct": "d", + "Explanation": "\"maximum number of points on the surface is 72 % * 39 = 28.08 . . . or 28 since it has to be an integer now note that if two points form a diameter , they can not be part of any other diameter . so in the best case we can pair up the points we have 28 points , so at best we can form 14 pairs ( 28 ) . so , answer is ( d )\"" + }, + { + "Answer": 27.428571428571427, + "Options": "a ) 21.4 , b ) 23.4 , c ) 25.4 , d ) 26.4 , e ) 27.4", + "Correct": "e", + "Explanation": "\"since the mirror is 42 inches in all sides , it must be a square . area of a square is a = a ^ 2 ; 24 ^ 2 = 576 . area of rectangle is double of that 2 * 576 = 1152 . now a = lw and we need find w so a / l = w ; 1152 / 42 = 27.4 answer ! answer : e\"" + }, + { + "Answer": 85, + "Options": "a ) 75 , b ) 80 , c ) 85 , d ) 90 , e ) 95", + "Correct": "c", + "Explanation": "\"in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 \u00b0 ) . given : x + ( x + 10 ) = 180 - - > x = 85 . answer : c .\"" + }, + { + "Answer": 49, + "Options": "a ) 225 , b ) 662 , c ) 772 , d ) 882 , e ) 49", + "Correct": "e", + "Explanation": "\"7 * 7 = 49 sq m answer : e\"" + }, + { + "Answer": 4, + "Options": "a ) 2 \u221a 2 , b ) 4 , c ) 5 , d ) 4 \u221a 2 , e ) none of these", + "Correct": "b", + "Explanation": "\"area of sector , a = x / 360 * pi * r ^ 2 circumference of the sector = 16 = > x / 360 * 2 * pi * r + 2 r = 16 = > 2 a / r + 2 r = 16 = > a = ( r 16 - 2 r ^ 2 ) / 2 = r 8 - r ^ 2 we will now max using derivations max value of a will found at a = 0 i . e 8 - 2 r = 0 r = 4 b\"" + }, + { + "Answer": 300, + "Options": "['a ) 100 %', 'b ) 200 %', 'c ) 250 %', 'd ) 300 %', 'e ) 400 %']", + "Correct": "d", + "Explanation": "if length is l and width is b then area = l * b now new l and b is 2 l and 2 b respectively . so new area is = 4 * l * b % increase = 300 % answer : d" + }, + { + "Answer": 50, + "Options": "a ) 76 , b ) 27 , c ) 19 , d ) 50 , e ) 11", + "Correct": "d", + "Explanation": "\"let x and y be the length and breadth of the rectangle respectively . then , x - 4 = y + 3 or x - y = 7 - - - - ( i ) area of the rectangle = xy ; area of the square = ( x - 4 ) ( y + 3 ) ( x - 4 ) ( y + 3 ) = xy < = > 3 x - 4 y = 12 - - - - ( ii ) solving ( i ) and ( ii ) , we get x = 16 and y = 9 . perimeter of the rectangle = 2 ( x + y ) = [ 2 ( 16 + 9 ) ] cm = 50 cm . answer : d\"" + }, + { + "Answer": 143, + "Options": "['a ) 180 m 2', 'b ) 164 m 2', 'c ) 152 m 2', 'd ) 143 m 2', 'e ) none of these']", + "Correct": "d", + "Explanation": "side of square carpet = \u221a area = \u221a 169 = 13 m after cutting of one side , measure of one side = 13 \u2013 2 = 11 m and other side = 13 m ( remain same ) \u2234 area of rectangular room = 13 \u00d7 11 = 143 m 2 answer d" + }, + { + "Answer": 150, + "Options": "a ) 150 a 2 cm 2 , b ) 170 a 2 cm 2 , c ) 125 a 2 cm 2 , d ) 175 a 2 cm 2 , e ) 120 a 2 cm 2", + "Correct": "a", + "Explanation": "\"6 a 2 = 6 * 5 a * 5 a = 150 a 2 answer : a\"" + }, + { + "Answer": 0.2098765432098765, + "Options": "['a ) 13 / 15', 'b ) 12 / 4', 'c ) 16 / 17', 'd ) 22 / 16', 'e ) 17 / 81']", + "Correct": "e", + "Explanation": "the questions asks us to find the surface which is not covered by the ring x i . e . , area of the surface not covered . where as circumference is the length along the edge of the circle , 2 * pi * r implies the length of the curve pi * r ^ 2 implies area enclosed by that curve . . hence area of the circle is considered for this problem area of the ring x = pi * r ^ 2 , where r = 8 = > pi * 64 area of the ring y = pi * 81 surface not covered by the ring x = pi * 81 - pi * 64 = pi * 17 fraction of ring y ' s surface is not covered by a ring x = pi * 17 / total area of the ring y = > pi * 17 / pi * 81 17 / 81 answer e" + }, + { + "Answer": 13.5, + "Options": "a ) 11 m 2 , b ) 10 m 2 , c ) 13.5 m 2 , d ) 19 m 2 , e ) 12.5 m 2", + "Correct": "c", + "Explanation": "\"1 / 2 * 4.5 * 6 = 13.5 m 2 answer : c\"" + }, + { + "Answer": 101, + "Options": "a ) 64 , b ) 72 , c ) 86 , d ) 98 , e ) 101", + "Correct": "e", + "Explanation": "\"use the options . the options which after getting added to 24 shows a cube of a number could be right . here 64 + 24 = 88 72 + 24 = 96 86 + 24 = 110 98 + 24 = 122 101 + 24 = 125 - - - ( 5 * 5 * 5 ) so we have 101 as the answer ! e\"" + }, + { + "Answer": 15, + "Options": "a ) 15 , b ) 77 , c ) 25 , d ) 87 , e ) 171", + "Correct": "a", + "Explanation": "\"explanation : let the integer be x . then , x + x 2 = 240 x 2 + x - 240 = 0 ( x + 16 ) ( x \u2013 15 ) = 0 x = 15 answer : a\"" + }, + { + "Answer": 180, + "Options": "a ) 176 , b ) 190 , c ) 180 , d ) 278 , e ) 292", + "Correct": "c", + "Explanation": "\"1 / 2 * 30 * 12 = 180 answer : c\"" + }, + { + "Answer": 33, + "Options": "['a ) 21', 'b ) 88937', 'c ) 269', 'd ) 279', 'e ) 2701']", + "Correct": "a", + "Explanation": "answer : a" + }, + { + "Answer": 1800, + "Options": "['a ) rs . 2250', 'b ) rs . 3600', 'c ) rs . 2700', 'd ) rs . 1800', 'e ) none of these']", + "Correct": "d", + "Explanation": "explanation : total surface area of the cube = 6 x ( 10 ) 2 = 600 sq . m 1 kg covers 20 sq . m area , for 600 we need = 600 / 20 = 30 kg paper . expenditure = rate x quantity = rs . 60 x 30 kg = rs . 1800 answer is d" + }, + { + "Answer": 0.16, + "Options": "a ) 2 / 5 , b ) 2 / 25 , c ) 5 / 2 , d ) 5 / 4 , e ) 4 / 25", + "Correct": "e", + "Explanation": "\"the area of rectangle a is ab . c = 5 a / 2 and d = 5 b / 2 . the area of rectangle b is cd = 25 ab / 4 . the ratio of rectangle a ' s area to rectangle b ' s area is ab / ( 25 ab / 4 ) = 4 / 25 . the answer is e .\"" + }, + { + "Answer": 2638.9378290154264, + "Options": "a ) 2550 , b ) 2640 , c ) 3960 , d ) 4280 , e ) 5490", + "Correct": "b", + "Explanation": "\"cone curved surface area = \u00ef \u20ac rl 22 / 7 \u00e3 \u2014 28 \u00e3 \u2014 30 = 88 \u00e3 \u2014 30 = 2640 m ( power 2 ) answer is b .\"" + }, + { + "Answer": 28, + "Options": "a ) 18 square inches , b ) 20 square inches , c ) 24 square inches , d ) 28 square inches , e ) 30 square inches", + "Correct": "d", + "Explanation": "\"total = a + b + c - ( sum of exactly 2 - group overlaps ) - 2 * ( all three ) + neither 80 % * 175 = 220 - 24 - 2 * ( all three ) + 0 2 * ( all three ) = 220 - 24 - 140 all three = 28 answer : d\"" + }, + { + "Answer": 3.3333333333333335, + "Options": "['a ) 1.32', 'b ) 3.33', 'c ) 3.58', 'd ) 4.34', 'e ) 5.18']", + "Correct": "b", + "Explanation": "height of triangle = \u221a ( 13 ^ 2 - ( 10 / 2 ) ^ 2 ) = 12 area of triangle = r * s where , r = radius of inscribed circle & s = ( a + b + c ) / 2 area of triangle = 1 / 2 * b * h = 1 / 2 * 10 * 12 = 60 s = ( 13 + 13 + 10 ) / 2 = 18 r = area of triangle / s = 60 / 18 = 10 / 3 = 3.33 answer : b" + }, + { + "Answer": 75, + "Options": "a ) 75 , b ) 129 , c ) 150 , d ) 123 , e ) 117", + "Correct": "a", + "Explanation": "\"1 / 2 * 10 * 15 = 75 answer : a\"" + }, + { + "Answer": 24, + "Options": "a ) 30 , b ) 28 , c ) 36 , d ) 42 , e ) 24", + "Correct": "e", + "Explanation": "\"a strip of 3 meters is covering the inner rectangular rug for all 4 sides . length of inner rug = 12 - ( 2 * 3 ) breadth of inner rug = 10 - ( 2 * 3 ) area of rug = 6 * 4 = 24 sq . mt \u00e2 nswer : e\"" + }, + { + "Answer": 8, + "Options": "a ) 12 h , b ) 10 h , c ) 8 h , d ) 6 h , e ) none of these", + "Correct": "c", + "Explanation": "\"area of field = 576 km 2 . then , each side of field = \u221a 576 = 24 km distance covered by the horse = perimeter of square field = 24 \u00d7 4 = 96 km \u2234 time taken by horse = distances / peed = 96 / 12 = 8 h answer c\"" + }, + { + "Answer": 600, + "Options": "['a ) 600', 'b ) 881', 'c ) 767', 'd ) 261', 'e ) 121']", + "Correct": "a", + "Explanation": "consider the rhombus abcd . let the diagonals intersect at e . since diagonals bisect at right angles in a rhombus . be 2 + ae 2 = ab 2 252 = 152 + ae 2 ae = \u221a ( 625 - 225 ) = \u221a 400 = 20 , ac = 20 + 20 = 40 cm . area of a rhombus = 1 / 2 * d 1 d 2 = 1 / 2 * 40 * 30 = 600 sq . cm . answer : a" + }, + { + "Answer": 600, + "Options": "['a ) 600 m 2', 'b ) 540 m 2', 'c ) 680 m 2', 'd ) 574 m 2', 'e ) none of these']", + "Correct": "a", + "Explanation": "in a parallelogram . area = diagonal \u00d7 length of perpendicular on it . = 30 \u00d7 20 = 600 m 2 answer a" + }, + { + "Answer": 180, + "Options": "a ) 180 cm 2 , b ) 150 cm 2 , c ) 168 cm 2 , d ) 198 cm 2 , e ) 987 cm 2", + "Correct": "a", + "Explanation": "\"1 / 2 * 24 ( 9 + 6 ) = 180 cm 2 answer : a\"" + }, + { + "Answer": 60, + "Options": "['a ) 30', 'b ) 45', 'c ) 60', 'd ) 75', 'e ) 90']", + "Correct": "c", + "Explanation": "c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be 60 . . c" + }, + { + "Answer": 23, + "Options": "a ) 34 , b ) 36 , c ) 23 , d ) 40 , e ) 42", + "Correct": "c", + "Explanation": "\"let length and breadth of photograph be l and b respectively . perimeter is given by 2 * ( l + b ) - - - - - ( 1 ) according to the question : ( l + 4 ) ( b + 4 ) = m - - - - ( 2 ) and ( l + 8 ) ( b + 8 ) = m + 94 - - - - - - - - - > ( l + 8 ) ( b + 8 ) - 94 = m - - - - - - ( 3 ) equating ( 2 ) and ( 3 ) ( l + 4 ) ( b + 4 ) = ( l + 8 ) ( b + 8 ) - 94 lb + 4 l + 4 b + 16 = lb + 8 l + 8 b + 64 - 94 simplify 4 l + 4 b = 46 - - - - - - > 2 ( l + b ) = 23 ( check eq ( 1 ) ) answer is c\"" + }, + { + "Answer": 15, + "Options": "a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25", + "Correct": "c", + "Explanation": "\"l * w = 300 : area , l is the length and w is the width . 2 l + 2 w = 70 : perimeter l = 35 - w : solve for l ( 35 - w ) * w = 300 : substitute in the area equation w = 15 and l = 20 : solve for w and find l using l = 35 - w . correct answer c\"" + }, + { + "Answer": 56, + "Options": "a ) 112 , b ) 64 , c ) 42 , d ) 24 , e ) 56", + "Correct": "e", + "Explanation": "\"length of side 1 = 7 + 1 = 8 length of side 2 = 6 + 1 = 7 area of rectangle = 7 * 8 = 56 e is the answer\"" + }, + { + "Answer": 12544, + "Options": "['a ) 12541', 'b ) 12542', 'c ) 12544', 'd ) 12545', 'e ) can not be determined']", + "Correct": "c", + "Explanation": "explanatory answer the shape of the area used for growing cauliflower has remained a square in both the years . let the side of the square area used for growing cauliflower this year be x ft . therefore , the area of the ground used for cultivation this year = x 2 sq . ft . let the side of the square area used for growing cauliflower last year be y ft . therefore , the area of the ground used for cultivation last year = y 2 sq . ft . as the number of cauliflower grown has increased by 223 , the area would have increased by 223 sq ft because each cauliflower takes 1 sq ft space . hence , x 2 - y 2 = 223 ( x + y ) ( x - y ) = 223 . 223 is a prime number and hence it will have only two factors . i . e . , 223 and 1 . therefore , 223 can be expressed as product of 2 numbers in only way = 223 * 1 i . e . , ( x + y ) ( x - y ) = 223 * 1 so , ( x + y ) should be 223 and ( x - y ) should be 1 . solving the two equations we get x = 112 and y = 111 . therefore , number of cauliflower produced this year = x 2 = 1122 = 12544 . alternative approach : use answer choices the area in both the years are squares of two numbers . that rules out choice a , b and d . as 12541,12542 and 12545 are not the square of any number . check choice c : if this year ' s produce is 12544 , last year ' s produce would have been 12544 - 223 = 12321 12321 is the square of 111 . so , 12544 is the answer . choice c ." + }, + { + "Answer": 68.70953354520753, + "Options": "['a ) 68', 'b ) 69', 'c ) 70', 'd ) 71', 'e ) 72']", + "Correct": "b", + "Explanation": "x ^ 2 = 4321 + 400 = 4721 4761 = 69 * 69 x = 69 answer : b" + }, + { + "Answer": 74.07407407407408, + "Options": "['a ) 20', 'b ) 10', 'c ) 50', 'd ) 74', 'e ) 73']", + "Correct": "d", + "Explanation": "calculate the volume of the larger cylinder and divide it by the volume of the smaller cylinder . volume of cylinder = \u03c0 r 2 h larger cylinder volume = 3141.59 smaller cylinder volume = 42.41 therefore the number of cylinders b that can be filled to capacity = 3141.59 / 42.41 = 74.1 answer is d 74 smaller cylinders can be filled to capacity ." + }, + { + "Answer": 46.27433388230814, + "Options": "a ) 16 , b ) 25 , c ) 33 , d ) 46 , e ) 58", + "Correct": "d", + "Explanation": "\"the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 9 + 2 * 9 which is about 46 . the answer is d .\"" + }, + { + "Answer": 100, + "Options": "a ) 30 square inches , b ) 75 square inches , c ) 100 square inches , d ) 89 square inches , e ) 92 square inches", + "Correct": "c", + "Explanation": "\"if the width is 5 in and the length is 4 times the width , then the length is 4 * 5 = 20 in the area is given by 5 * 20 = 100 square inches correct answer c\"" + }, + { + "Answer": 30, + "Options": "['a ) 20', 'b ) 30', 'c ) 40', 'd ) 55', 'e ) 48']", + "Correct": "b", + "Explanation": "length of side 1 = 5 + 1 = 6 length of side 2 = 4 + 1 = 5 area of rectangle = 6 * 5 = 30 b is the answer" + }, + { + "Answer": 64, + "Options": "a ) 48 , b ) 56 , c ) 64 , d ) 76 , e ) 192", + "Correct": "c", + "Explanation": "\"say length of garden is l meters . then ( l * 8 ) = 16 * 12 [ given area is same . area = l * b ] therefore l works out to 24 meters . perimeter of garden = 2 * ( 24 + 8 ) = 64 meter . answer is c\"" + }, + { + "Answer": 450, + "Options": "['a ) 360', 'b ) 450', 'c ) 560', 'd ) 670', 'e ) 780']", + "Correct": "b", + "Explanation": "length = 5 * a breadth = 5 * ( a + 1 ) or 5 * ( a + 2 ) base area - > multiple of 25 450 = 25 * 18 answer : b" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 6 , c ) 10 , d ) 13 , e ) 28", + "Correct": "a", + "Explanation": "\"suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 30 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , number of tiles = ( r - 2 ) * ( c + 4 ) = 30 comparing both of them we get c * r = ( r - 2 ) * ( c + 4 ) = > 4 r - 2 c = 8 c = 2 r - 4 putting it in c * r = 30 ( 2 r - 4 ) * r = 30 2 r ^ 2 - 4 r - 30 = 0 r can not be negative so r = 5 and c = 6 so , answer will be a\"" + }, + { + "Answer": 35, + "Options": "['a ) 10 : 17', 'b ) 2 : 5', 'c ) 5 : 16', 'd ) 10 : 19', 'e ) 32 : 25']", + "Correct": "d", + "Explanation": "answer : d ." + }, + { + "Answer": 4.0000000000000036, + "Options": "['a ) 4 % increase', 'b ) 6 % increase', 'c ) 5 % decrease', 'd ) 4 % decrease', 'e ) none of these']", + "Correct": "d", + "Explanation": "percentage change = x - y - xy \u2044 100 = 20 \u2013 20 \u2013 20 \u00d7 20 / 100 = \u2212 4 % = 4 % decrease answer d" + }, + { + "Answer": 300, + "Options": "a ) 180 cm , b ) 220 cm , c ) 240 cm , d ) 270 cm , e ) 300 cm", + "Correct": "e", + "Explanation": "\"we have 50 for first triangle , when we join mid - points of first triangle we get the second equilateral triangle then the length of second one is 25 and continues . so we have 50,25 , 12.5 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 50 / 1 - ( 1 / 2 ) = 100 equilateral triangle perimeter is 3 a = 3 * 100 = 300 . so option e .\"" + }, + { + "Answer": 40, + "Options": "a ) 5 square meters , b ) 36 square meters , c ) 40 square meters , d ) 83.3 square meters , e ) 120 square meters", + "Correct": "c", + "Explanation": "\"300 - 180 = 120 sq m of the wallpaper overlaps ( in either two layers or three layers ) if 36 sq m has two layers , 120 - 40 = 80 sq m of the wallpaper overlaps in three layers . 80 sq m makes two extra layers hence the area over which it makes two extra layers is 40 sq m . answer ( c ) .\"" + }, + { + "Answer": 195, + "Options": "a ) 188 cm 2 , b ) 150 cm 2 , c ) 168 cm 2 , d ) 195 cm 2 , e ) 987 cm 2", + "Correct": "d", + "Explanation": "\"1 / 2 * 26 ( 9 + 6 ) = 195 cm 2 answer : d\"" + }, + { + "Answer": 80, + "Options": "a ) 40 , b ) 50 , c ) 60 , d ) 80 , e ) 100", + "Correct": "d", + "Explanation": "\"alternate approach backsolving ( using answer options to reach the correct answer ) can work wonders here if one is fast in calculations . given perimeter is 240 so , 2 ( l + b ) = 240 or , l + b = 120 now use the answer options ( given length ; breath will be half the length ) ( a ) 40 l = 40 ; b = 20 l + b = 60 ( b ) 50 l = 50 ; b = 25 l + b = 75 ( c ) 60 l = 60 ; b = 30 l + b = 90 ( d ) 80 l = 80 ; b = 40 l + b = 120 ( e ) 100 l = 100 ; b = 50 l + b = 150 thus you see no , need of any calculations , u can reach the correct option only by checking options ; correct answer will be ( d )\"" + }, + { + "Answer": 126, + "Options": "a ) 176 , b ) 190 , c ) 150 , d ) 126 , e ) 292", + "Correct": "d", + "Explanation": "\"1 / 2 * 14 * 18 = 126 answer : d\"" + }, + { + "Answer": 85, + "Options": "a ) 34 , b ) 40 , c ) 85 , d ) 88 , e ) none", + "Correct": "c", + "Explanation": "\"explanation we have : l = 20 ft and lb = 650 sq . ft . so , b = 32.5 ft . length of fencing = ( l + 2 b ) = ( 20 + 65 ) ft = 85 ft . answer c\"" + }, + { + "Answer": 55, + "Options": "a ) 35 , b ) 45 , c ) 55 , d ) 65 , e ) 75", + "Correct": "c", + "Explanation": "first x with nothing given about the firstwemake that x second 2 x the second is double the first , third x \u2212 40 the third is 40 less than the first f + s + t = 180 all three angles add to 180 ( x ) + ( 2 x ) + ( x \u2212 40 ) = 180 replace f , s , and t with the labeled values . x + 2 x + x \u2212 40 = 180 here the parenthesis are not needed . 4 x \u2212 40 = 180 combine like terms , x + 2 x + x + 40 + 40 add 40 to both sides 4 x = 220 the variable ismultiplied by 4 4 4 divide both sides by 4 x = 55 our solution for x first 55 replace xwith 55 in the original list of angles second 2 ( 55 ) = 110 our angles are 55 , 110 , and 15 third ( 55 ) \u2212 40 = 15 correct answer c" + }, + { + "Answer": 104, + "Options": "a ) 102 , b ) 104 , c ) 110 , d ) 90 , e ) 84", + "Correct": "b", + "Explanation": "\"if i calculate it using the formulae , # diagonals = n ( n - 3 ) / 2 each vertex sends of n - 3 diagonals n = 17 - 1 then 16 * ( 16 - 3 ) / 2 = 104 correct option : b\"" + }, + { + "Answer": 2463.0086404143976, + "Options": "['a ) 2644', 'b ) 2446', 'c ) 2464', 'd ) 6442', 'e ) 6424']", + "Correct": "c", + "Explanation": "sphere total surface area = 4 \u03c0 r ( power 2 ) = 4 \u00d7 22 / 7 \u00d7 14 \u00d7 14 = 2464 answer is c ." + }, + { + "Answer": 2749, + "Options": "a ) 2812 , b ) 8231 , c ) 2734 , d ) 4222 , e ) 2749", + "Correct": "e", + "Explanation": "\"a volume of 4 l can be kept in 1 hemisphere therefore , a volume of 10996 l can be kept in ( 10996 / 4 ) hemispheres ans . 2749 answer : e\"" + }, + { + "Answer": 120.00000000000001, + "Options": "['a ) 100 m', 'b ) 120 m', 'c ) 95 m', 'd ) 80 m', 'e ) 150 m']", + "Correct": "b", + "Explanation": "given that the length of the rectangular field l = 90 m and breadth = b = 80 m . then its area lb = 90 x 80 sq . m we know that the area of square = ( 1 / 2 ) x ( diagonal ) 2 from the given question , we have area of square plot = area of rectangular field that is , 90 x 80 = 1 / 2 x diagonal 2 diagonal ^ 2 = 2 x 7200 = 14400 = ( 120 ) 2 diagonal = 120 m . hence b" + }, + { + "Answer": 29.845130209103033, + "Options": "a ) 77.14 cm , b ) 47.14 cm , c ) 84.92 cm , d ) 29.85 cm , e ) 23.57 cm", + "Correct": "d", + "Explanation": "\"let the side of the square be a cm . parameter of the rectangle = 2 ( 22 + 16 ) = 76 cm parameter of the square = 76 cm i . e . 4 a = 76 a = 19 diameter of the semicircle = 19 cm circimference of the semicircle = 1 / 2 ( \u220f ) ( 19 ) = 1 / 2 ( 22 / 7 ) ( 19 ) = 418 / 14 = 29.85 cm to two decimal places answer : d\"" + }, + { + "Answer": 18, + "Options": "['a ) 22 cm', 'b ) 20 cm', 'c ) 18 cm', 'd ) 10 cm', 'e ) none of these']", + "Correct": "c", + "Explanation": "explanation : area of triangle , a 1 = 1 / 2 \u2217 base \u2217 height = 1 / 2 \u2217 15 \u2217 12 = 90 cm 2 area of second triangle = 2 \u2217 a 1 = 180 cm 2 1 / 2 \u2217 20 \u2217 height = 180 = > height = 18 cm option c" + }, + { + "Answer": 25, + "Options": "a ) 40 , b ) 15 , c ) 25 , d ) 32 , e ) 45", + "Correct": "c", + "Explanation": "\"area of tile = 20 * 30 = 600 area of floor = 100 * 150 = 15000 no of tiles = 15000 / 600 = 25 so , the no of tile = 25 answer : c\"" + }, + { + "Answer": 70, + "Options": "a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90", + "Correct": "c", + "Explanation": "\"let l be the length and w be the width . l = ( 7 / 5 ) w perimeter : 2 l + 2 w = 336 , 2 ( 7 / 5 ) w + 2 w = 336 solve the above equation to find : w = 70 m and l = 98 m . correct answer c ) 70\"" + }, + { + "Answer": 5, + "Options": "['a ) 1', 'b ) 2', 'c ) 3', 'd ) 4', 'e ) 5']", + "Correct": "e", + "Explanation": "200 kg - 1 cubic meter ; 200,000 g - 1 cubic meter ; 200,000 g - 1 , 000,000 cubic centimeters ; 1 g - 1 , 000,000 / 200,000 = 10 / 2 = 5 cubic centimeters . answer : e ." + }, + { + "Answer": 178, + "Options": "a ) 244 ft , b ) 88 ft , c ) 122 ft , d ) 178 ft , e ) 66 ft", + "Correct": "d", + "Explanation": "\"given that length and area , so we can find the breadth . length x breadth = area 8 x breadth = 680 breadth = 85 feet area to be fenced = 2 b + l = 2 ( 85 ) + 8 = 178 feet answer : d ) 178 ft\"" + }, + { + "Answer": 98, + "Options": "['a ) 98', 'b ) 104', 'c ) 100', 'd ) 61', 'e ) 51']", + "Correct": "a", + "Explanation": "cube use to make perfect 5 * 5 * 5 = 125 no need of cube to make hollow = ( 5 - 2 ) * ( 5 - 2 ) * ( 5 - 2 ) = 27 so total cube need to make hollow cube is = 125 - 27 = 98 answer : a" + }, + { + "Answer": 75, + "Options": "a ) 50 cm 2 , b ) 60 cm 2 , c ) 75 cm 2 , d ) 90 cm 2 , e ) 150 cm 2", + "Correct": "c", + "Explanation": "\"1 / 2 * 15 ( 6 + 4 ) = 75 cm 2 answer : c\"" + }, + { + "Answer": 48, + "Options": "a ) 48 , b ) 99 , c ) 266 , d ) 28 , e ) 17", + "Correct": "a", + "Explanation": "\"explanation : if you double the sides of a cube , the ratio of the surface areas of the old and new cubes will be 1 : 4 . the ratio of the volumes of the old and new cubes will be 1 : 8 . weight is proportional to volume . so , if the first weighs 6 pounds , the second weighs 6 x 8 pounds = 48 . answer : a ) 48\"" + }, + { + "Answer": 3.9999999999999996, + "Options": "a ) 3 : 1 , b ) 3 : 2 , c ) 3 : 5 , d ) 4 : 1 , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : let the edges be a and b of two cubes , then a 3 / b 3 = 64 / 1 = > ( a / b ) 3 = ( 4 / 1 ) 3 a / b = 4 / 1 = > a : b = 4 : 1 option d\"" + }, + { + "Answer": 851.7546894755278, + "Options": "['a ) 675.5 m 2', 'b ) 780.6 m 2', 'c ) 785.8 m 2', 'd ) 850.5 m 2', 'e ) 950.5 m 2']", + "Correct": "d", + "Explanation": "required area = ( 63 * 63 \u2013 4 * 1 / 4 * 22 / 7 * 63 / 2 * 63 / 2 ) = 850.5 m 2 answer : d" + }, + { + "Answer": 26, + "Options": "['a ) 15', 'b ) 22', 'c ) 26', 'd ) 33', 'e ) 44']", + "Correct": "c", + "Explanation": "c 26 only the box in the very centre of the stack will not suffer the strokes of the paint brush , whereas all the other 26 boxes will have at least one side painted ." + }, + { + "Answer": 0.36, + "Options": "['a ) 5 / 3', 'b ) 9 / 5', 'c ) 9 / 25', 'd ) 3 / 5', 'e ) 25 / 9']", + "Correct": "c", + "Explanation": "the area of rectangle a is ab . c = 5 a / 3 and d = 5 b / 3 . the area of rectangle b is cd = 25 ab / 9 . the ratio of rectangle a ' s area to rectangle b ' s area is ab / ( 25 ab / 9 ) = 9 / 25 . the answer is c ." + }, + { + "Answer": 98.00000000000001, + "Options": "['a ) 98 m', 'b ) 102 m', 'c ) 95 m', 'd ) 105 m', 'e ) 96 m']", + "Correct": "a", + "Explanation": "let the diagonal be d metres , then 1 / 2 d ( power ) 2 = 4802 d 2 = 9604 d = \u221a 9604 d = 98 m answer is a ." + }, + { + "Answer": 40, + "Options": "['a ) 45 m 3', 'b ) 40 m 3', 'c ) 60 m 3', 'd ) 600 m 3', 'e ) 300 m 3']", + "Correct": "b", + "Explanation": "lb = 20 ; lh = 10 ; fh = 8 ( lbh ) 2 = 20 * 10 * 8 = > lbh = 40 m 3 answer : b" + }, + { + "Answer": 112, + "Options": "a ) 136 cu cm , b ) 112 cu cm , c ) 164 cu cm , d ) 180 cu cm , e ) none", + "Correct": "b", + "Explanation": "\"sol . surface area = [ 2 ( 8 x 4 + 4 x 2 + 8 x 2 ) ] = ( 2 x 56 ) = 112 cu cm answer b\"" + }, + { + "Answer": 28.2051282051282, + "Options": "a ) 15 % , b ) 20 % , c ) 28 % , d ) 35 % , e ) 40 %", + "Correct": "c", + "Explanation": "\"sol . required change = ( 22 * 100 ) / ( 100 - 22 ) = 28 % c\"" + }, + { + "Answer": 3060, + "Options": "a ) 2510 , b ) 2535 , c ) 3060 , d ) 2515 , e ) 2520", + "Correct": "c", + "Explanation": "\"length = breadth + 23 . therefore , 4 \u00d7 breadth + 2 \u00d7 23 = 226 m \u21d2 breadth = 45 m length = 45 + 23 = 68 m area = 68 \u00d7 45 = 3060 m 2 answer is c .\"" + }, + { + "Answer": 56, + "Options": "a ) 14 , b ) 47 , c ) 54 , d ) 56 , e ) 240", + "Correct": "d", + "Explanation": "\"area = length x breadth 320 = 40 x breadth so , breadth = 8 units fencing required is - breadth + breadth + length 8 + 8 + 40 = > 56 feet answer must be ( d ) 56\"" + }, + { + "Answer": 124, + "Options": "['a ) 124 m 2', 'b ) 120 m 2', 'c ) 108 m 2', 'd ) 58 m 2', 'e ) none of these']", + "Correct": "a", + "Explanation": "area of the outer rectangle = 19 \u00d7 16 = 304 m 2 area of the inner rectangle = 15 \u00d7 12 = 180 m 2 required area = ( 304 \u2013 180 ) = 124 m 2 answer a" + }, + { + "Answer": 293.28484447717375, + "Options": "a ) 223.28 , b ) 293.28 , c ) 293.78 , d ) 291.28 , e ) 193.28", + "Correct": "b", + "Explanation": "\"area of the rhombus = 1 / 2 * p * \u221a 4 ( a ) 2 - ( p ) 2 a = 20 ; p = 16 a = 1 / 2 * 16 * \u221a 4 ( 20 ) 2 - ( 16 ) 2 = 1 / 2 * 16 * \u221a 1600 - 256 = 1 / 2 * 16 * \u221a 1344 a = 293.28 answer : b\"" + }, + { + "Answer": 50, + "Options": "a ) 30 % , b ) 40 % , c ) 50 percent , d ) 60 % , e ) 70 %", + "Correct": "c", + "Explanation": "\"let original length = x and original breadth new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c\"" + }, + { + "Answer": 5440, + "Options": "a ) 5440 , b ) 5120 , c ) 6420 , d ) 7500 , e ) 8960", + "Correct": "a", + "Explanation": "\"l = ( 50 - 16 ) m = 34 m , b = ( 36 - 16 ) m = 20 m , h = 8 m . volume of the box = ( 34 x 20 x 8 ) m 3 = 5440 m 3 . answer : option a\"" + }, + { + "Answer": 76, + "Options": "a ) 2 , b ) 4 , c ) 16 , d ) 38 , e ) 76", + "Correct": "e", + "Explanation": "\"pythogoras will help here ! let the sides be x and diagonal be d then d ^ 2 = 2 x ^ 2 and area = x ^ 2 now plug in the given diagonal values to find x values and then subtract the areas ans will be 21 ^ 2 / 2 - 17 ^ 2 / 2 = 152 / 2 = 76 ans e .\"" + }, + { + "Answer": 130, + "Options": "a ) 130 feet , b ) 22 feet , c ) 20 feet , d ) 15 feet , e ) 10 feet", + "Correct": "a", + "Explanation": "\"explanation : we are given with length and area , so we can find the breadth . as length * breadth = area = > 10 * breadth = 600 = > breadth = 60 feet area to be fenced = 2 b + l = 2 * 60 + 10 = 130 feet answer : option a\"" + }, + { + "Answer": 125, + "Options": "['a ) 296', 'b ) 289', 'c ) 270', 'd ) 125', 'e ) 278']", + "Correct": "d", + "Explanation": "1 * 1 * 1 = 2 / 10 * 2 / 10 * 2 / 10 * x x = 125 answer : d" + }, + { + "Answer": 148, + "Options": "['a ) 190', 'b ) 180', 'c ) 170', 'd ) 160', 'e ) 148']", + "Correct": "e", + "Explanation": "let no of sits in vip enclosure is x then x * 40 + 10 ( 320 - x ) = 7500 or 25 x = 7500 - 3200 , x = 4300 / 25 = 172 vip = 172 general = 320 - 172 = 148 e" + }, + { + "Answer": 49.02857142857143, + "Options": "a ) 40 m 2 , b ) 45 m 2 , c ) 49 m 2 , d ) 51 m 2 , e ) 55 m 2", + "Correct": "c", + "Explanation": "\"39 / 360 * 22 / 7 * 12 * 12 = 49 m 2 answer : c\"" + }, + { + "Answer": 150, + "Options": "a ) 150 cm , b ) 767 cm , c ) 88 cm , d ) 666 cm , e ) 776 cm", + "Correct": "a", + "Explanation": "\"area of each slab = 67.5 / 30 m 2 = 2.25 m 2 length of each slab \u221a 2.25 = 1.5 m = 150 cm\"" + }, + { + "Answer": 1.1199999999999999, + "Options": "['a ) 1.04', 'b ) 1.12', 'c ) 1.24', 'd ) 1.4', 'e ) 1.5']", + "Correct": "b", + "Explanation": "a 1 = l * b a 2 = ( l * 140 / 100 ) * ( b * 80 / 100 ) = 1.12 * lb so , area of garden is by 1.12 times of old area . answer : b" + }, + { + "Answer": 77, + "Options": "a ) 56 , b ) 77 , c ) 112 , d ) 116 , e ) 120", + "Correct": "b", + "Explanation": "\"area of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 11 + 11 = 22 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 22 * 7 = 77 b is the answer\"" + }, + { + "Answer": 24.36, + "Options": "a ) 11.36 m 2 , b ) 10.36 m 2 , c ) 18.36 m 2 , d ) 19.36 m 2 , e ) 24.36 m 2", + "Correct": "e", + "Explanation": "\"1 / 2 * 8.4 * 5.8 = 24.36 m 2 answer : e\"" + }, + { + "Answer": 16, + "Options": "a ) 13 , b ) 16 , c ) 34 , d ) 43 , e ) 42", + "Correct": "b", + "Explanation": "\"explanation : a / 2 = 8 * 8 = > a = 8 * 8 * 2 x * 2 x = 8 * 8 * 2 x = 8 = > 2 x = 16 answer : option b\"" + }, + { + "Answer": 1392, + "Options": "a ) 3944 , b ) 2882 , c ) 2999 , d ) 2667 , e ) 1392", + "Correct": "e", + "Explanation": "\"let the side of the square plot be a ft . a 2 = 36 = > a = 6 length of the fence = perimeter of the plot = 4 a = 24 ft . cost of building the fence = 24 * 58 = rs . 1392 . answer : e\"" + }, + { + "Answer": 38.48451000647496, + "Options": "['a ) 32', 'b ) 36.5', 'c ) 38.5', 'd ) 39', 'e ) 39.5']", + "Correct": "c", + "Explanation": "area covered by goat = pi * r ^ 2 / 4 ( here we divide by 4 because rope is tied at the corner of the plot and only 1 / 4 part , the goat can graze ) where r = 7 m = length of rope so area = ( 22 / 7 ) * 7 * 7 / 4 = 38.5 sq m answer : c" + }, + { + "Answer": 0.07, + "Options": "a ) 0.7 , b ) 0.07 , c ) 0.007 , d ) 7 , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : ( . 000343 ) 1 / 3 = ( 343 / 106 ) 1 / 3 = ( 7 * 7 * 7 / 102 * 102 * 102 ) 1 / 3 = 7 / 102 = 7 / 100 = 0.07 answer b\"" + }, + { + "Answer": 11, + "Options": "['a ) 10', 'b ) 11', 'c ) 12', 'd ) 13', 'e ) 14']", + "Correct": "b", + "Explanation": "1 cut makes two pieces a second cut can make 4 pieces by cutting through 2 of the pieces a third cut can make 7 pieces by cutting through 3 of the pieces a fourth cut can make 11 pieces by cutting through 4 of the pieces b" + }, + { + "Answer": 4, + "Options": "a ) 7 , b ) 2 , c ) 3 , d ) 4 , e ) 6", + "Correct": "d", + "Explanation": "\"let the width = w total area of the pool and deck = ( 2 w + 10 ) ( 2 w + 12 ) we can test the answer choices along with unit digit method a ) 2 feet . . . . . . . . . . . 14 * 16 has unit digit 4 . . . . . . . . . . eliminate b ) 2.5 feet . . . . . . . . . 15 * 17 has unit digit 5 . . . . . . . . . . eliminate c ) 3 feet . . . . . . . . . . . . 16 * 18 has unit digit 8 . . . . . . . . . . . eliminate d ) 4 feet . . . . . . . . . . . . 18 * 20 has unit digit 0 . . . . . . . . . . . hold e ) 5 feet . . . . . . . . . . . . 20 * 22 has unit digit 0 . . . . . . . . . . . eliminate ( bigger size ) answer : d w = 4\"" + }, + { + "Answer": 4530, + "Options": "a ) 2277 , b ) 2977 , c ) 2677 , d ) 4530 , e ) 1971", + "Correct": "d", + "Explanation": "\"area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 5 = rs . 4530 answer : d\"" + }, + { + "Answer": 360, + "Options": "['a ) 360 cc', 'b ) 60 cc', 'c ) 300 cc', 'd ) 36 cc', 'e ) 39 cc']", + "Correct": "a", + "Explanation": "r 1 = x r 2 = 3 x \u03c0 * x 2 * h = 40 \u03c0 9 x 2 h = 40 * 9 = 360 answer : a" + }, + { + "Answer": 1349.9999999999995, + "Options": "a ) 1350 , b ) 1150 , c ) 1456 , d ) 1254 , e ) 1489", + "Correct": "a", + "Explanation": "a 3 = 3375 = > a = 15 6 a 2 = 6 * 15 * 15 = 1350 answer : a" + }, + { + "Answer": 1560, + "Options": "a ) 1276 , b ) 1560 , c ) 2832 , d ) 1299 , e ) 1236", + "Correct": "b", + "Explanation": "\"explanation : l * 30 = 1200 \u00e8 l = 40 40 + 30 + 50 = 120 120 * 13 = 1560 answer : option b\"" + }, + { + "Answer": 25, + "Options": "a ) 34 , b ) 40 , c ) 25 , d ) 88 , e ) 78", + "Correct": "c", + "Explanation": "\"we have : l = 20 ft and lb = 50 sq . ft . so , b = 2.5 ft . length of fencing = ( l + 2 b ) = ( 20 + 5 ) ft = 25 ft . answer : c\"" + }, + { + "Answer": 1950, + "Options": "a ) 1940 , b ) 1950 , c ) 1960 , d ) 1990 , e ) 1980", + "Correct": "b", + "Explanation": "\"area of the rhombus = 1 / 2 d 1 d 2 = ( 1 / 2 \u00d7 65 \u00d7 60 ) cm ( power ) 2 = 65 \u00d7 30 = 1950 cm ( power ) 2 answer is b .\"" + }, + { + "Answer": 55, + "Options": "a ) 30 cm , b ) 40 cm , c ) 50 cm , d ) 55 cm , e ) 60 cm", + "Correct": "d", + "Explanation": "\"perimeter of triangle = a + b + c perimeter = 5 cm + 20 cm + 30 cm = 55 cm answer : d .\"" + }, + { + "Answer": 130, + "Options": "a ) 100 , b ) 777 , c ) 998 , d ) 729 , e ) 130", + "Correct": "e", + "Explanation": "\"100 % answer : e\"" + }, + { + "Answer": 16.376666666666665, + "Options": "a ) 6 cm , b ) 8.25 cm , c ) 11.25 cm , d ) 16.37 cm , e ) 20.62 cm", + "Correct": "d", + "Explanation": "\"increase in volume = volume of the cube = 17 * 17 * 17 cm ^ 3 rise in water level = volume / area = 17 * 17 * 17 / 20 * 15 = 16.37 cm answer is d\"" + }, + { + "Answer": 84, + "Options": "a ) 78 , b ) 82 , c ) 84 , d ) 86 , e ) 88", + "Correct": "c", + "Explanation": "\"least number of cubes will be required when the cubes that could fit in are biggest . 7 is the biggest number that could divide all three , 49 , 42 and 14 . thus side of cube must be 7 , and total number of cubes = 49 / 7 * 42 / 7 * 14 / 7 = 84 ans c .\"" + }, + { + "Answer": 1099.5574287564277, + "Options": "['a ) 4400', 'b ) 2200', 'c ) 5500', 'd ) 1100', 'e ) 3300']", + "Correct": "d", + "Explanation": "h = 14 cm and r = 5 cm cylinder volume = \u03c0 r ( power 2 ) h = ( 22 / 7 \u00d7 5 \u00d7 5 \u00d7 14 ) cm ( power 3 ) = 1100 cm ( power 3 ) answer is d ." + }, + { + "Answer": 293.9999999999999, + "Options": "a ) 864 , b ) 556 , c ) 294 , d ) 287 , e ) 267", + "Correct": "c", + "Explanation": "\"a 3 = 343 = > a = 7 6 a 2 = 6 * 7 * 7 = 294 answer : c\"" + }, + { + "Answer": 32, + "Options": "a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 32", + "Correct": "e", + "Explanation": "\"try filling the numbers into the answer y x y = find the closest to 1024 . answer e\"" + }, + { + "Answer": 340, + "Options": "a ) 126 , b ) 156 , c ) 340 , d ) 321 , e ) 260", + "Correct": "c", + "Explanation": "\"sol . let width = x , length = ( 10 + x ) perimeter = 2 ( x + ( 10 + x ) ) = 2 ( 2 x = 10 ) & 2 ( 2 x + 10 ) * 6.5 = 2210 x = 80 required perimeter = 2 ( 80 + 90 ) = 340 c\"" + }, + { + "Answer": 8, + "Options": "['a ) 4', 'b ) 7', 'c ) 8', 'd ) 13', 'e ) 26']", + "Correct": "c", + "Explanation": "assume the sides to be x and y . perimeter = 2 x + 2 y = 42 hence x + y = 21 - ( i ) area = xy = 104 - ( ii ) since these are the sides of a billboard , we are dealing with positive numbers only and the options tell us that they are integers . 104 can be written as a product of two numbers as 104 * 1 or 52 * 2 or 26 * 4 or 13 * 8 of these , only 13 * 8 satisfies the equation ( i ) hence the lengths are 13 and 8 length of shorter side = 8 answer : c" + }, + { + "Answer": 2870, + "Options": "['a ) 2870', 'b ) 2000', 'c ) 5650', 'd ) 6650', 'e ) 7650']", + "Correct": "a", + "Explanation": "n ( n + 1 ) ( 2 n + 1 ) / 6 20 ( 21 ) ( 21 ) / 6 = 2870 answer : a" + }, + { + "Answer": 4.04, + "Options": "a ) 4.00 % , b ) 4.04 % , c ) 4.26 % , d ) 4.56 % , e ) 4.67 %", + "Correct": "b", + "Explanation": "\"100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 102 x 102 ) cm 2 . ( a 2 - a 1 ) = [ ( 102 ) 2 - ( 100 ) 2 ] = ( 102 + 100 ) x ( 102 - 100 ) = 404 cm 2 . percentage error = 404 x 100 % = 4.04 % 100 x 100 b\"" + }, + { + "Answer": 16, + "Options": "a ) 11 , b ) 10 , c ) 787 , d ) 16 , e ) 12", + "Correct": "d", + "Explanation": "\"1 / 2 * 4 * 8 = 16 m 2 answer : d\"" + }, + { + "Answer": 15393.804002589986, + "Options": "['a ) 12300', 'b ) 14500', 'c ) 15400', 'd ) 16700', 'e ) 18200']", + "Correct": "c", + "Explanation": "area covered by goat = pi * r ^ 2 / 4 ( here we divide by 4 because the trainer is standing in a corner of the ground and only in 1 / 4 part , the voice can be heard ) where r = 14 m = length reaching the voice so area = ( 22 / 7 ) * 140 * 140 / 4 = 15400 sq m answer : c" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 24 , c ) 20 , d ) 30 , e ) 36", + "Correct": "a", + "Explanation": "\"length of side 1 = 3 + 1 = 4 length of side 2 = 2 + 1 = 3 area of rectangle = 4 * 3 = 12 a is the answer\"" + }, + { + "Answer": 512, + "Options": "a ) 125 cm 3 , b ) 400 cm 3 , c ) 512 cm 3 , d ) 625 cm 3 , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : edge of cude = 32 / 4 = 8 cm volume = a * a * a = 8 * 8 * 8 = 512 cm cube option c\"" + }, + { + "Answer": 192, + "Options": "a ) $ 1.60 , b ) $ 16.00 , c ) $ 96.00 , d ) $ 108.00 , e ) $ 192.00", + "Correct": "e", + "Explanation": "\"total surface area = 6 a ^ 2 = 6 * 10 * 10 = 600 each quart covers 20 sqr ft thus total number of quarts = 600 / 10 = 60 cost will be 60 * 3.2 = $ 192 ans : e\"" + }, + { + "Answer": 32, + "Options": "['a ) 29', 'b ) 30', 'c ) 31', 'd ) 32', 'e ) 33']", + "Correct": "d", + "Explanation": "the triangle is symmetric about the x - axis . the part above the x - axis forms a triangle with a base of 8 and a height of 4 . the area of this part is ( 1 / 2 ) ( 8 ) ( 4 ) . we can double this to find the area of the whole triangle . the total area is ( 2 ) ( 1 / 2 ) ( 8 ) ( 4 ) = 32 . the answer is d ." + }, + { + "Answer": 16, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 16", + "Correct": "e", + "Explanation": "\"let t be the number of trees . then the length required for trees on the sidewalk will be 1 * t = t to maximize the number of trees , the number of 10 feet spaces between trees should be 1 less than total number of trees . for example , if there are 3 trees , then there should be 2 spaces between them . so the number of 10 feet spaces will be t - 1 . then , the length of sidewalk required for 10 feet spaces will be 10 * ( t - 1 ) it is given that total lenght of sidewalk is 166 feet . or 10 ( t - 1 ) + t = 166 or 10 t - 10 + t = 166 or t = 16 answer : - e\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 8 , c ) 6 , d ) 10 , e ) 16", + "Correct": "a", + "Explanation": "\"1 ) draw a simple cube 2 ) draw 9 squares on each face of the cube ( so that it looks like a rubik ' s cube ) - this is what the cube will look like when it ' s cut into 27 equal smaller cubes . 3 ) remember that the outside of the cube is the part that ' s painted . . . . the mini - cubes with 2 painted sides are all on the edge of the cube , in themiddleof the edge . there are 4 in front , 4 in back and 4 more on thestripthat runs around the left / top / right / bottom of the cube . l = 4 + 4 + 4 = 12 . answer a\"" + }, + { + "Answer": 1080, + "Options": "a ) 120 cm 2 , b ) 765 cm 2 , c ) 1080 cm 2 , d ) 197 cm 2 , e ) 275 cm 2", + "Correct": "c", + "Explanation": "\"the triangle with sides 78 cm , 72 cm and 30 cm is right angled , where the hypotenuse is 78 cm . area of the triangle = 1 / 2 * 72 * 30 = 1080 cm 2 answer : c\"" + }, + { + "Answer": 483.80526865282815, + "Options": "a ) 426 , b ) 284 , c ) 483 , d ) 256 , e ) 428", + "Correct": "c", + "Explanation": "\"\u03c0 * 22 * 7 = 483 answer : c\"" + }, + { + "Answer": 180, + "Options": "a ) 126 , b ) 156 , c ) 180 , d ) 321 , e ) 260", + "Correct": "c", + "Explanation": "\"sol . let width = x , length = ( 10 + x ) perimeter = 2 ( x + ( 10 + x ) ) = 2 ( 2 x = 10 ) & 2 ( 2 x + 10 ) * 6.5 = 1170 x = 40 required perimeter = 2 ( 40 + 50 ) = 180 c\"" + }, + { + "Answer": 8, + "Options": "a ) 165 \u220f cm , b ) 65 \u220f cm , c ) 12 \u220f cm , d ) 14 \u220f cm , e ) 16 \u220f cm", + "Correct": "c", + "Explanation": "let the radii of the larger and the smaller circles be l cm and s cm respectively . let the side of the square be a cm . a 2 = 784 = ( 4 ) ( 196 ) = ( 22 ) . ( 142 ) a = ( 2 ) ( 14 ) = 28 a = 2 l , l = a / 2 = 14 l = ( 7 / 3 ) s therefore s = ( 3 / 7 ) ( l ) = 6 circumference of the smaller circle = 2 \u220f s = 12 \u220f cm . answer : c" + }, + { + "Answer": 64, + "Options": "a ) 74 % , b ) 64 % , c ) 84 % , d ) 94 % , e ) 34 %", + "Correct": "b", + "Explanation": "\"let diameter of circle r , dr = 80 and diameter of circle s , ds = 100 radius of circle r , rr = 40 radius of circle s , rs = 50 area of circle r / area of circle s = ( pi * rr ^ 2 ) / ( pi * rs ^ 2 ) = ( 40 / 50 ) ^ 2 = ( 8 / 10 ) ^ 2 = 64 % answer : b\"" + }, + { + "Answer": 81, + "Options": "a ) 36 , b ) 49 , c ) 64 , d ) 81 , e ) 100", + "Correct": "d", + "Explanation": "\"we know that the perimeter of square = 4 \u00e3 \u2014 side side = 9 cm therefore , perimeter = 4 \u00e3 \u2014 9 cm = 36 cm now , area of the square = ( side \u00e3 \u2014 side ) sq . units = 9 \u00e3 \u2014 9 cm \u00e2 \u00b2 = 81 cm \u00e2 \u00b2 answer : d\"" + }, + { + "Answer": 20, + "Options": "['a ) 10', 'b ) 15', 'c ) 20', 'd ) 25', 'e ) 30']", + "Correct": "c", + "Explanation": "( n / 2 ) - x = 6 n - x = 16 solving these two = > n = number of students = 20 answer : c" + }, + { + "Answer": 220, + "Options": "a ) 140 , b ) 150 , c ) 160 , d ) 170 , e ) 220", + "Correct": "e", + "Explanation": "\"given that the area of the square = 3025 sq . units = > side of square = \u221a 3025 = 55 units the radius of the circle = side of the square = 55 units length of the rectangle = 2 / 5 * 55 = 22 units given that breadth = 10 units area of the rectangle = lb = 22 * 10 = 220 sq . units answer : option e\"" + }, + { + "Answer": 384, + "Options": "['a ) 0', 'b ) 36', 'c ) 180', 'd ) 216', 'e ) 384']", + "Correct": "e", + "Explanation": "no of cubes that can be accommodated in box = ( 10 * 12 * 16 ) / ( 4 * 4 * 4 ) 12 * 16 in numerator can be perfectly divided by 4 * 4 in denominator . side with length 10 ca n ' t be perfectly divided by 4 and hence is the limiting factor . closet multiple of 4 less that 10 is 8 . so vacant area in cube = = 12 * 16 * ( 10 - 8 ) = 12 * 16 * 2 = 384 answer : e" + }, + { + "Answer": 160, + "Options": "a ) 140 , b ) 99 , c ) 88 , d ) 160 , e ) 12", + "Correct": "d", + "Explanation": "\"given that the area of the square = 1600 sq . units = > side of square = \u221a 1600 = 40 units the radius of the circle = side of the square = 40 units length of the rectangle = 2 / 5 * 40 = 16 units given that breadth = 10 units area of the rectangle = lb = 16 * 10 = 160 sq . units answer : d\"" + }, + { + "Answer": 112, + "Options": "a ) 73 , b ) 32 , c ) 34 , d ) 43 , e ) 112", + "Correct": "e", + "Explanation": "\"explanation : a / 98 = 8 * 8 = > a = 8 * 8 * 98 x * 2 x = 8 * 8 * 98 x = 56 = > 2 x = 112 answer : option e\"" + }, + { + "Answer": 21, + "Options": "['a ) 14 cms', 'b ) 21 cms', 'c ) 42 cms', 'd ) none of these', 'e ) 56 cms']", + "Correct": "b", + "Explanation": "explanation : 3.78 meters = 378 cm = 2 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 7 5.25 meters = 525 cm = 5 \u00d7 5 \u00d7 3 \u00d7 7 hence common factors are 3 and 7 hence lcm = 3 \u00d7 7 = 21 hence largest size of square tiles that can be paved exactly with square tiles is 21 cm . answer : b" + }, + { + "Answer": 130, + "Options": "a ) 107 , b ) 108 , c ) 130 , d ) 150 , e ) 145", + "Correct": "c", + "Explanation": "\"number of cubes required = volume of box / volume of cube = 10 * 13 * 5 / 5 = 130 cubes answer : c\"" + }, + { + "Answer": 16, + "Options": "a ) 4 , b ) 8 , c ) 12 , d ) 16 , e ) 18", + "Correct": "d", + "Explanation": "\"let length of rectangle = l 8 ^ 2 = l * 4 = > l = 64 / 4 = 16 answer d\"" + }, + { + "Answer": 270, + "Options": "a ) 180 o , b ) 270 o , c ) 360 o , d ) 45 o , e ) 135 o", + "Correct": "b", + "Explanation": "the measure of \\ pzq formed by the bottom edge of the shaded quadrilateral , zq , and this same edge after the rotation , zp , is approximately 90 . the transformation of the shaded quadrilateral to the unshaded quadrilateral is a clockwise rotation around point z through an an - gle equal to the measure of re ex angle pzq . the measure of \\ pzq added to the measure of re ex \\ pzq is equal to the measure of one complete rotation , or 360 . therefore , the measure of re ex angle pzq is approximately 360 o - 90 o or 270 o . thus the clockwise rotation around point z is through an angle of approximately 270 o correct answer b" + }, + { + "Answer": 196, + "Options": "a ) 225 , b ) 196 , c ) 266 , d ) 288 , e ) 261", + "Correct": "b", + "Explanation": "\"14 * 14 = 196 sq m answer : b\"" + }, + { + "Answer": 201, + "Options": "['a ) 201 m ( power ) 2', 'b ) 220 m ( power ) 2', 'c ) 211 m ( power ) 2', 'd ) 219 m ( power ) 2', 'e ) 205 m ( power ) 2']", + "Correct": "a", + "Explanation": "area of one square field = 10000 m ( power ) 2 10000 \u00d7 1 = 10000 side of this field = \u221a 10000 m = 100 m side of another square = 101 m difference of areas = [ 101 ( power ) 2 - 100 ( power ) 2 ] m ( power ) 2 [ 101 + 100 ] [ 101 - 100 ] m ( power ) 2 ( 201 ) ( 1 ) m 2 = 201 m ( power ) 2 answer is a ." + }, + { + "Answer": 10, + "Options": "a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 10", + "Correct": "e", + "Explanation": "\"if the width is w , then length and height would be w / 2 . so , w * w / 2 * w / 2 = 128 = > w ^ 3 = ( 2 ^ 3 ) * 64 = ( 2 ^ 3 ) * ( 4 ^ 3 ) = > w = 2 * 4 = 8 in . along the width of the cuboid , 8 cubes do n ' t touch the tin foil . so the actual width will be non - touching cubes + touching cubes = 8 + 2 = q = 10 ans e .\"" + }, + { + "Answer": 60, + "Options": "a ) 13 , b ) 33 , c ) 50 , d ) 51 , e ) 60", + "Correct": "e", + "Explanation": "\"yes , ensure that you understand the relation thoroughly ! cost per liter = k * fraction of spirit 60 cents is the cost of 2 liters of solution ( 1 part water , 1 part spirit ) . so cost per liter is 30 cents . fraction of spirit is 1 / 2 . 30 = k * ( 1 / 2 ) k = 60 cost per liter = 60 * ( 1 / 3 ) ( 1 part spirit , 2 parts water ) cost for 3 liters = 60 * ( 1 / 3 ) * 3 = 50 cents e . 60 cents\"" + }, + { + "Answer": 140, + "Options": "a ) 176 , b ) 190 , c ) 140 , d ) 278 , e ) 292", + "Correct": "c", + "Explanation": "\"1 / 2 * 14 * 20 = 140 answer : c\"" + }, + { + "Answer": 725.9999999999998, + "Options": "a ) 864 , b ) 726 , c ) 255 , d ) 287 , e ) 267", + "Correct": "b", + "Explanation": "\"a 3 = 1331 = > a = 11 6 a 2 = 6 * 11 * 11 = 726 answer : b\"" + }, + { + "Answer": 700, + "Options": "['a ) 450', 'b ) 600', 'c ) 700', 'd ) 2400', 'e ) 3200']", + "Correct": "c", + "Explanation": "answer c ) 9600 yards need 1200 lbs 1 yard will need 1200 / 9600 = 1 / 8 lbs 3600 yards will need 1 / 8 * 5600 yards = 700 lbs" + }, + { + "Answer": 125, + "Options": "a ) 125 cm 3 , b ) 400 cm 3 , c ) 250 cm 3 , d ) 625 cm 3 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : edge of cude = 20 / 4 = 5 cm volume = a * a * a = 5 * 5 * 5 = 125 cm cube option a\"" + }, + { + "Answer": 20.25, + "Options": "a ) 15.25 , b ) 18.25 , c ) 19.25 , d ) 20.25 , e ) 21.25", + "Correct": "d", + "Explanation": "\"since the mirror is 42 inches in all sides , it must be a square . area of a square is a = a ^ 2 ; 18 ^ 2 = 324 . area of rectangle is double of that 2 * 324 = 648 . now a = lw and we need find w so a / l = w ; 648 / 32 = 20.25 answer ! answer is d\"" + }, + { + "Answer": 2784, + "Options": "a ) 2784 , b ) 2287 , c ) 2977 , d ) 2668 , e ) 1298", + "Correct": "a", + "Explanation": "\"let the side of the square plot be a ft . a 2 = 144 = > a = 12 length of the fence = perimeter of the plot = 4 a = 48 ft . cost of building the fence = 48 * 58 = rs . 2784 . answer : a\"" + }, + { + "Answer": 45, + "Options": "['a ) 38 .', 'b ) 40 .', 'c ) 42 .', 'd ) 44 .', 'e ) 45 .']", + "Correct": "e", + "Explanation": "let the width = x x * 4 x = 900 x ^ 2 = 225 x = 15 length = 4 * 15 = 60 difference = 60 - 15 = 45 e is the answer" + }, + { + "Answer": 9, + "Options": "a ) 6 / \u03c0 , b ) 9 / \u03c0 , c ) 6 , d ) 9 , e ) 12", + "Correct": "d", + "Explanation": "\"given area of the base of a hemisphere is 3 = pi * r ^ 2 thus r = sqrt ( 3 / pi ) . surface area of whole sphere = 4 * pi * r ^ 2 . = 4 * pi * 3 / pi = 12 . since the hemisphere is half of a sphere the surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . but the total surface area = 6 + area of the base of a hemisphere . = 6 + 3 = 9 . answer is d ! !\"" + }, + { + "Answer": 600, + "Options": "['a ) 225', 'b ) 450', 'c ) 25 \u221a 2', 'd ) 200', 'e ) 600']", + "Correct": "e", + "Explanation": "square ab + bc = 70 : ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 4900 . since ( ac ) ^ 2 = ( ab ) ^ 2 + ( bc ) ^ 2 = 50 ^ 2 = 2500 , then ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 2500 + 2 * ab * bc = 4900 . 2500 + 2 * ab * bc = 4900 . ab * bc = 1200 . the area = 1 / 2 * ab * bc = 600 . answer : e ." + }, + { + "Answer": 103, + "Options": "a ) 64 , b ) 72 , c ) 86 , d ) 98 , e ) 103", + "Correct": "e", + "Explanation": "\"use the options . the options which after getting added to 27 shows a cube of a number could be right . here 64 + 22 = 86 72 + 22 = 94 86 + 22 = 108 98 + 22 = 120 103 + 22 = 125 - - - ( 5 * 5 * 5 ) so we have 103 as the answer ! e\"" + }, + { + "Answer": 140, + "Options": "a ) 120 , b ) 110 , c ) 130 , d ) 140 , e ) 150", + "Correct": "d", + "Explanation": "\"the triangle with sides 30 cm , 28 cm and 10 cm is right angled , where the hypotenuse is 30 cm . area of the triangle = 1 / 2 * 28 * 10 = 140 cm 2 answer : option d\"" + }, + { + "Answer": 2.9999999999999996, + "Options": "['a ) 9', 'b ) 6', 'c ) 4', 'd ) 3', 'e ) 2']", + "Correct": "d", + "Explanation": "let x be the side length of square a . then the area of square a is x ^ 2 . the area of square b is ( sqrt ( 3 ) x ) ^ 2 = 3 x ^ 2 . the answer is d ." + }, + { + "Answer": 120, + "Options": "['a ) 100', 'b ) 120', 'c ) 150', 'd ) 180', 'e ) none']", + "Correct": "b", + "Explanation": "solution other side = \u221a ( 17 ) 2 - ( 15 ) 2 = \u221a 289 - 225 = \u221a 64 = 8 m . \u2234 area = ( 15 x 8 ) m 2 = 120 m 2 . answer b" + }, + { + "Answer": 8, + "Options": "a ) 4 , b ) 7 , c ) 8 , d ) 13 , e ) 26", + "Correct": "c", + "Explanation": "\"this question can be solved algebraically or by testing the answers . we ' re told that a rectangle has an area of 120 and a perimeter of 46 . we ' re asked for the length of one of the shorter sides of the rectangle . since the answers are all integers , and the area is 120 , the shorter side will almost certainly be less than 10 ( since 10 x 10 = 100 , but we ' re not dealing with a square ) . answer b ( 7 ) does not divide evenly into 120 , let ' s test answer c : 8 if . . . the shorter side = 8 . . . the area = 120 . . . . 120 / 8 = 15 = the longer side perimeter = 8 + 8 + 15 + 15 = 46 c\"" + }, + { + "Answer": 600, + "Options": "['a ) 576 metres', 'b ) 589 metres', 'c ) 600 metres', 'd ) 700 metres', 'e ) none']", + "Correct": "c", + "Explanation": "solution let the length of the outer edges be x metres . then , length of the inner edge = ( x - 6 ) m . \u2234 x 2 - ( x - 6 ) 2 = 1764 \u2039 = \u203a x 2 - ( x 2 - 12 x + 36 ) = 1764 \u2039 = \u203a 12 x = 1800 \u2039 = \u203a x = 150 . \u2234 required perimeter = ( 4 x ) m \u2039 = \u203a ( 4 x 150 ) m = 600 m . answer c" + }, + { + "Answer": 60, + "Options": "a ) 158 , b ) 129 , c ) 150 , d ) 123 , e ) 60", + "Correct": "e", + "Explanation": "\"1 / 2 * 12 * 10 = 60 answer : e\"" + }, + { + "Answer": 1583.3626974092558, + "Options": "['a ) 1584', 'b ) 1854', 'c ) 1458', 'd ) 1485', 'e ) none of them']", + "Correct": "a", + "Explanation": "lateral surface area = 2 \u03c0 rh = 2 \u00d7 22 / 7 \u00d7 12 \u00d7 21 = 44 \u00d7 36 = 1584 m ( power 2 ) answer is a ." + }, + { + "Answer": 8, + "Options": "['a ) 8 cm', 'b ) 9 cm', 'c ) 10 cm', 'd ) 11 cm', 'e ) none']", + "Correct": "a", + "Explanation": "sol . let the radius of the cone be r cm . then , 1 / 3 \u220f * r \u00b2 * 6 = \u220f * 8 * 8 * 2 \u21d4 r \u00b2 = [ 8 * 8 * 2 * 3 / 6 ] = 64 \u21d4 r = 8 cm . answer a" + }, + { + "Answer": 32.24999999999998, + "Options": "a ) 32.25 % , b ) 40 % , c ) 37.50 % , d ) 36.75 % , e ) 32 %", + "Correct": "a", + "Explanation": "\"say both sides of the rectangle are equal to 100 ( so consider that we have a square ) . in this case the area is 100 * 100 = 10,000 . the area of new rectangle would be 115 * 115 = 13,225 , which is 32.25 % greater than the old area . answer : a .\"" + }, + { + "Answer": 0.4, + "Options": "a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 2 / 5", + "Correct": "e", + "Explanation": "the area of the right triangle is ( 1 / 2 ) * 4 * 10 = 20 . only the points ( a , b ) below the line y = x satisfy a - b > 0 . the part of the triangle which is below the line y = x has an area of ( 1 / 2 ) ( 4 ) ( 4 ) = 8 . p ( a - b > 0 ) = 8 / 20 = 2 / 5 the answer is e ." + }, + { + "Answer": 204, + "Options": "['a ) 256', 'b ) 266', 'c ) 204', 'd ) 224', 'e ) 324']", + "Correct": "c", + "Explanation": "a strip of 4 meters is covering the inner rectangular rug for all 4 sides . length of inner rug = 25 - ( 2 * 4 ) breadth of inner rug = 20 - ( 2 * 4 ) area of rug = 17 * 12 = 204 sq . mt \u00e2 nswer : c" + }, + { + "Answer": 43.99999999999999, + "Options": "a ) 30 % , b ) 44 % , c ) 50 % , d ) 55 % , e ) 60 %", + "Correct": "b", + "Explanation": "\"let original length = x meters original breadth = y meters original area = xy m ^ 2 new length = 120 x / 100 new breadth = 120 y / 100 = 6 y / 5 new area = 6 x / 5 * 6 y / 5 = 36 xy / 25 m ^ 2 increase percent = 11 xy / 25 * 1 / xy * 100 = 44 % answer is b\"" + }, + { + "Answer": 16, + "Options": "['a ) 22', 'b ) 16', 'c ) 11', 'd ) 12', 'e ) 10']", + "Correct": "b", + "Explanation": "there are 6 surfaces to the cube . in which opposite surfaces are painted brown and other 2 opposite surfaces are painted orange . then 4 edges of the cube have both the colors . since the big cube cut in to 64 smaller cubes , the 4 edges of the cube have both the colors . since the big cube cut into 64 smaller cubes , the 4 edges of the big cube has 4 \u00d7 4 = 16 smaller cubes have both brown and orange colors . answer = 16 answer : b" + }, + { + "Answer": 159.20000000000002, + "Options": "a ) 75 % , b ) 80 % , c ) 100 % , d ) 150 % , e ) 159.2 %", + "Correct": "e", + "Explanation": "\"let length of each side of square a be 10 area of a = 10 ^ 2 = 100 since , length of each side of square a is increased by 100 percent to make square b length of each side of square b = 2 * 10 = 20 area of b = 20 ^ 2 = 400 since , length of the side of square b is increased by 80 percent to make square c length of each side of square c = 1.8 * 20 = 36 area of c = 36 ^ 2 = 1296 difference in areas of c and cummulative areas of a and b = 1296 - ( 400 + 100 ) = 796 percent is the area of square c greater than the sum of the areas of squares a and b = ( 796 / 500 ) * 100 % = 159.2 % answer e\"" + }, + { + "Answer": 20, + "Options": "a ) 28 , b ) 29 , c ) 30 , d ) 20 , e ) 32", + "Correct": "d", + "Explanation": "\"try filling the numbers into the answer y x y = find the closest to 400 . answer d\"" + }, + { + "Answer": 140, + "Options": "a ) 144 m 2 , b ) 140 m 2 , c ) 108 m 2 , d ) 158 m 2 , e ) none of these", + "Correct": "b", + "Explanation": "\"area of the outer rectangle = 23 \u00e3 \u2014 16 = 368 m 2 area of the inner rectangle = 19 \u00e3 \u2014 12 = 228 m 2 required area = ( 368 \u00e2 \u20ac \u201c 228 ) = 140 m 2 answer b\"" + }, + { + "Answer": 50.26548245743669, + "Options": "['a ) 50.00 square meter', 'b ) 50.04 square meter', 'c ) 50.28 square meter', 'd ) 50.24 square meter', 'e ) 50.43 square meter']", + "Correct": "c", + "Explanation": "diameter = 8 meter . radius = diameter / 2 . = 8 / 2 . = 4 meter . area of a circle = \u00ef \u20ac r 2 . here , pi ( \u00ef \u20ac ) = 3.14 meter , radius ( r ) = 4 . area of a circle = 3.14 \u00e3 \u2014 4 \u00e3 \u2014 4 . . = 3.14 \u00e3 \u2014 16 . = 50.28 square meter answer : c" + }, + { + "Answer": 3.0000000000000004, + "Options": "['a ) 1', 'b ) 3 / 2', 'c ) 2', 'd ) 3', 'e ) 6']", + "Correct": "d", + "Explanation": "volume of prism = area of base * height = 1 / 2 * ( square root of 2 ) * ( square root of 2 ) * 3 = 3 answer : d" + }, + { + "Answer": 100, + "Options": "a ) 100 , b ) 662 , c ) 772 , d ) 882 , e ) 21", + "Correct": "a", + "Explanation": "\"10 * 10 = 100 sq m answer : a\"" + }, + { + "Answer": 5436, + "Options": "a ) s . 4529 , b ) s . 4586 , c ) s . 4597 , d ) s . 4530 , e ) s . 5436", + "Correct": "e", + "Explanation": "\"area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 6 = rs . 5436 answer : e\"" + }, + { + "Answer": 3, + "Options": "['a ) 2', 'b ) 3.5', 'c ) 3', 'd ) 4', 'e ) 5']", + "Correct": "c", + "Explanation": "area of the park = ( 60 x 40 ) m 2 = 2400 m 2 . area of the lawn = 2109 m 2 . area of the crossroads = ( 2400 - 2109 ) m 2 = 291 m 2 . let the width of the road be x metres . then , 60 x + 40 x - x 2 = 291 x 2 - 100 x + 291 = 0 ( x - 97 ) ( x - 3 ) = 0 x = 3 . c )" + }, + { + "Answer": 91, + "Options": "a ) 71 % , b ) 51 % , c ) 91 % , d ) 81 % , e ) 61 %", + "Correct": "c", + "Explanation": "\"r = 3 \u00ef \u20ac r 2 = 9 r = 10 \u00ef \u20ac r 2 = 100 100 \u00ef \u20ac \u00e2 \u20ac \u201c 9 \u00ef \u20ac = 91 100 - - - - ? = > 91 % . answer : c\"" + }, + { + "Answer": 160, + "Options": "a ) 120 , b ) 772 , c ) 288 , d ) 160 , e ) 2848", + "Correct": "d", + "Explanation": "\"the triangle with sides 39 cm , 32 cm and 10 cm is right angled , where the hypotenuse is 39 cm . area of the triangle = 1 / 2 * 32 * 10 = 160 cm 2 answer : d\"" + }, + { + "Answer": 120, + "Options": "a ) 297 cm 2 , b ) 384 cm 2 , c ) 120 cm 2 , d ) 267 cm 2 , e ) 186 cm 2", + "Correct": "c", + "Explanation": "\"area of a parallelogram = base * height = 12 * 10 = 120 cm 2 answer : c\"" + }, + { + "Answer": 17, + "Options": "['a ) 19 m', 'b ) 17 m', 'c ) 15 m', 'd ) 16 m', 'e ) 20 m']", + "Correct": "b", + "Explanation": "rectangular area = l \u00d7 b = 120 and perimeter = 2 ( l + b ) = 46 l + b = 23 ( l - b ) power 2 - 4 lb = ( 23 ) power 2 - 4 \u00d7 120 = ( 529 - 480 ) = 49 = l - b = 7 l + b = 23 , l - b = 7 , we get l = 15 , b = 8 diagonal = \u221a 152 + 82 \u221a 225 + 64 = > \u221a 289 = 17 m answer is b ." + }, + { + "Answer": 4096, + "Options": "a ) 4096 , b ) 4098 , c ) 5000 , d ) 5096 , e ) can not be determined", + "Correct": "a", + "Explanation": "\"explanatory answer the shape of the area used for growing cabbage has remained a square in both the years . let the side of the square area used for growing cabbage this year be x ft . therefore , the area of the ground used for cultivation this year = x 2 sq . ft . let the side of the square area used for growing cabbage last year be y ft . therefore , the area of the ground used for cultivation last year = y 2 sq . ft . as the number of cabbage grown has increased by 127 , the area would have increased by 127 sq ft because each cabbage takes 1 sq ft space . hence , x 2 - y 2 = 127 ( x + y ) ( x - y ) = 127 . 127 is a prime number and hence it will have only two factors . i . e . , 127 and 1 . therefore , 127 can be expressed as product of 2 numbers in only way = 127 * 1 i . e . , ( x + y ) ( x - y ) = 127 * 1 so , ( x + y ) should be 127 and ( x - y ) should be 1 . solving the two equations we get x = 64 and y = 63 . therefore , number of cabbage produced this year = x 2 = 642 = 4096 . alternative approach : use answer choices the area in both the years are squares of two numbers . that rules out choice b , c and d . as 4098,5000 and 5096 are not the square of any number . check choice a : if this year ' s produce is 4096 , last year ' s produce would have been 4096 - 127 = 3969 3969 is the square of 63 . so , 4096 is the answer . choice a\"" + }, + { + "Answer": 17254.942310250928, + "Options": "a ) 29963 sq m , b ) 28937 sq m , c ) 43162 sq m , d ) 27688 sq m , e ) 17248 sq m", + "Correct": "e", + "Explanation": "\"let the radii of the smaller and the larger circles be s m and l m respectively . 2 \u220f s = 528 and 2 \u220f l = 704 s = 528 / 2 \u220f and l = 704 / 2 \u220f difference between the areas = \u220f l ^ 2 - \u220f s ^ 2 = \u220f { 264 ^ 2 / \u220f ^ 2 - 352 ^ 2 / \u220f ^ 2 } = 264 ^ 2 / \u220f - 352 ^ 2 / \u220f = ( 264 - 352 ) ( 264 + 352 ) / \u220f = ( 88 ) ( 616 ) / ( 22 / 7 ) = 17248 sq m answer : e\"" + }, + { + "Answer": 4.999999999999999, + "Options": "a ) 3 : 1 , b ) 5 : 1 , c ) 3 : 5 , d ) 3 : 7 , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : let the edges be a and b of two cubes , then a 3 / b 3 = 125 / 1 = > ( a / b ) 3 = ( 5 / 1 ) 3 a / b = 5 / 1 = > a : b = 5 : 1 option b\"" + }, + { + "Answer": 156, + "Options": "a ) 120 cm 2 , b ) 156 cm 2 , c ) 178 cm 2 , d ) 189 cm 2 , e ) 176 cm 2", + "Correct": "b", + "Explanation": "\"the triangle with sides 28 cm , 26 cm and 12 cm is right angled , where the hypotenuse is 28 cm . area of the triangle = 1 / 2 * 26 * 12 = 156 cm 2 answer : b\"" + }, + { + "Answer": 10, + "Options": "a ) 5 , b ) 6 , c ) 10 , d ) 13 , e ) 28", + "Correct": "c", + "Explanation": "\"suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 160 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , number of tiles = ( r - 2 ) * ( c + 4 ) = 160 comparing both of them we get c * r = ( r - 2 ) * ( c + 4 ) = > 4 r - 2 c = 8 c = 2 r - 4 putting it in c * r = 160 ( 2 r - 4 ) * r = 160 2 r ^ 2 - 4 r - 160 = 0 r can not be negative so r = 10 and c = 16 so , answer will be c\"" + }, + { + "Answer": 2, + "Options": "['a ) 2 units', 'b ) 12 units', 'c ) 6.5 units', 'd ) 6 units', 'e ) 7.5 units']", + "Correct": "a", + "Explanation": "explanatory answer in a right angled triangle , the radius of the incircle = s - h , where ' s ' is the semi perimeter of the triangle and ' r ' is the radius of the inscribed circle . the semi perimeter of the triangle = a + b + c / 2 = 5 + 12 + 13 / 2 = 15 therefore , r = 15 - 13 = 2 units . choice a" + }, + { + "Answer": 330, + "Options": "['a ) 160', 'b ) 240', 'c ) 330', 'd ) 440', 'e ) 560']", + "Correct": "c", + "Explanation": "the number of jumbo tiles = x . the number of regular tiles = 2 x . assume the ratio of the dimensions of a regular tile is a : a - - > area = a ^ 2 . the dimensions of a jumbo tile is 3 a : 3 a - - > area = 9 a ^ 2 . the area of regular tiles = 2 x * a ^ 2 = 60 . the area of jumbo tiles = x * 9 a ^ 2 = 4.5 ( 2 x * a ^ 2 ) = 4.5 * 60 = 270 . total area = 60 + 270 = 330 . answer : c ." + }, + { + "Answer": 2735, + "Options": "a ) 2812 , b ) 8231 , c ) 2734 , d ) 2735 , e ) 4254", + "Correct": "d", + "Explanation": "\"a volume of 4 l can be kept in 1 hemisphere therefore , a volume of 10940 l can be kept in ( 10940 / 4 ) hemispheres ans . 2735 answer : d\"" + }, + { + "Answer": 2199.114857512855, + "Options": "['a ) 2200', 'b ) 1100', 'c ) 5500', 'd ) 3300', 'e ) 1050']", + "Correct": "a", + "Explanation": "1 / 3 \u03c0 rh = 1 / 3 \u00d7 22 / 7 \u00d7 100 \u00d7 21 = 2200 m ( power 3 ) answer is a ." + }, + { + "Answer": 112.04507993669432, + "Options": "['a ) 110', 'b ) 111', 'c ) 113', 'd ) 112', 'e ) none of them']", + "Correct": "d", + "Explanation": "let the length of the wire be h meters . then , \u220f ( 0.50 / ( 2 x 100 ) ) ^ 2 x h = 2.2 / 1000 = h = ( ( 2.2 / 1000 ) x ( 100 x 100 ) / ( 0.25 x 0.25 ) x ( 7 / 22 ) ) = 112 m . answer is d ." + }, + { + "Answer": 90, + "Options": "['a ) 90 , 85,60', 'b ) 85 , 75,60', 'c ) 90 , 75,70', 'd ) 90 , 75,60', 'e ) none']", + "Correct": "d", + "Explanation": "explanation : let length = 6 x , breadth = 5 x and height = 4 x in cm 2 ( 6 x \u00d7 5 x + 5 x \u00d7 4 x + 6 x \u00d7 4 x ) = 33300 148 x 2 = 33300 \u21d2 x 2 = 33300 / 148 = 225 \u21d2 x = 15 length = 90 cm , breadth = 75 cm and height = 60 cm correct option : d" + }, + { + "Answer": 2718, + "Options": "a ) s . 4528 , b ) s . 4520 , c ) s . 4527 , d ) s . 4530 , e ) s . 2718", + "Correct": "e", + "Explanation": "\"area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 3 = rs . 2718 answer : e\"" + }, + { + "Answer": 9, + "Options": "a ) 9 feet , b ) 12 feet , c ) 13 feet , d ) 15 feet , e ) 18 feet", + "Correct": "a", + "Explanation": "\"total circuit = 12 / 4 = 3 total feet squirrel travels = 3 * 3 = 9 feet answer : a\"" + }, + { + "Answer": 72, + "Options": "a ) 288 , b ) 72 , c ) 200 , d ) 112 , e ) 178", + "Correct": "b", + "Explanation": "\"d 2 / 2 = ( 12 * 12 ) / 2 = 72 answer : b\"" + }, + { + "Answer": 67.88571428571429, + "Options": "a ) 52.6 , b ) 52.9 , c ) 67.9 , d ) 52.1 , e ) 52.2", + "Correct": "c", + "Explanation": "\"54 / 360 * 22 / 7 * 12 * 12 = 67.9 m 2 answer : c\"" + }, + { + "Answer": 0.78125, + "Options": "['a ) a . 3 / 16', 'b ) 1 / 4', 'c ) c . 1 / 2', 'd ) 25 / 32', 'e ) 7 / 8']", + "Correct": "d", + "Explanation": "area of the rectangular rug = 2 * 7 = 14 fraction not covered by the rug = ( total area - rug area ) / total area = ( 64 - 14 ) / 64 = 25 / 32 = d" + }, + { + "Answer": 10, + "Options": "['a ) 2', 'b ) 5', 'c ) 6', 'd ) 7', 'e ) 10']", + "Correct": "e", + "Explanation": "4410 = 2 * 3 ^ 2 * 5 * 7 ^ 2 to be perfect square , we need to multiply by at least 2 * 5 = 10 . the answer is e ." + }, + { + "Answer": 6, + "Options": "['a ) 36', 'b ) 18', 'c ) 12', 'd ) 8', 'e ) 6']", + "Correct": "e", + "Explanation": "volume of a pyramid is given by v = 1 / 3 ah , where a is the area of the triangular base and h is the height of the pyramid . area of triangular base = 1 / 2 * 3 * 3 = 9 / 2 so , v = 1 / 3 * 9 / 2 * 4 = 6 option e" + }, + { + "Answer": 5.656854249492381, + "Options": "a ) 4 , b ) 5.656 , c ) 5 , d ) 6 , e ) 7", + "Correct": "b", + "Explanation": "\"side of triangle is a then perimeter = a + a + a . sqrt 2 ( right angle and pythagorus ) = 2 a + a . sqrt 2 = 8 + 8 sqrt 2 or , a . ( 2 + sqrt 2 ) = 8 ( 1 + sqrt 2 ) , a = 8 * ( 1 + sqrt 2 ) / 2 + sqrt 2 = 8 * 2.414 / 3.414 = 0.707 * 8 then hypotenuse = 5.656 b\"" + }, + { + "Answer": 32, + "Options": "a ) 34 , b ) 40 , c ) 68 , d ) 88 , e ) 32", + "Correct": "e", + "Explanation": "\"we have : l = 20 ft and lb = 120 sq . ft . so , b = 6 ft . length of fencing = ( l + 2 b ) = ( 20 + 12 ) ft = 32 ft . answer : e\"" + }, + { + "Answer": 307500, + "Options": "['a ) 3,360', 'b ) 307,500', 'c ) 621,500', 'd ) 704,000', 'e ) 2 , 816,000']", + "Correct": "b", + "Explanation": "one is 300 m by 500 m and the other is 250 m by 630 m : ( 300 * 500 ) + ( 250 * 630 ) = 150000 + 157500 307500 answer : b" + }, + { + "Answer": 32.98672286269283, + "Options": "a ) 23.56 , b ) 33.0 , c ) 23.55 , d ) 23.53 , e ) 23.57", + "Correct": "b", + "Explanation": "\"let the side of the square be a cm . parameter of the rectangle = 2 ( 22 + 20 ) = 84 cm parameter of the square = 84 cm i . e . 4 a = 84 a = 21 diameter of the semicircle = 21 cm circimference of the semicircle = 1 / 2 ( \u00e2 \u02c6 \u008f ) 21 = 1 / 2 ( 22 / 7 ) ( 21 ) = 66 / 2 = 33 cm answer : b\"" + }, + { + "Answer": 15, + "Options": "['a ) w = 15 and l = 20', 'b ) w = 25 and l = 30', 'c ) w = 35 and l = 40', 'd ) w = 45 and l = 50', 'e ) w = 55 and l = 60']", + "Correct": "a", + "Explanation": "l * w = 300 : area , l is the length and w is the width . 2 l + 2 w = 70 : perimeter l = 35 - w : solve for l ( 35 - w ) * w = 300 : substitute in the area equation w = 15 and l = 20 : solve for w and find l using l = 35 - w . correct answer a" + }, + { + "Answer": 0.43999999999999995, + "Options": "a ) 0.11 % , b ) 0.7 % , c ) 0.44 % , d ) 0.6 % , e ) 0.8 %", + "Correct": "c", + "Explanation": "\"let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 27 / 25 ) x ( 40 / 43 ) y = ( 913 / 909 ) ( xy ) error in measurement = ( 913 / 909 ) xy - xy = ( 4 / 909 ) xy error percentage = [ ( 4 / 909 ) xy ( 1 / xy ) 100 ] % = ( 11 / 25 ) % = 0.44 % . answer is c .\"" + }, + { + "Answer": 2688, + "Options": "['a ) 3220 m cube', 'b ) 4140 m cube', 'c ) 2688 m cube', 'd ) 4000 m cube', 'e ) none of these']", + "Correct": "c", + "Explanation": "explanation : l = ( 40 - 16 ) m = 24 m , [ because 8 + 8 = 16 ] b = ( 30 - 16 ) m = 14 m , h = 8 m . volume of the box = ( 24 x 14 x 8 ) m cube = 2688 m cube . option c" + }, + { + "Answer": 364, + "Options": "a ) 287 cm 2 , b ) 887 cm 2 , c ) 364 cm 2 , d ) 368 cm 2 , e ) 668 cm 2", + "Correct": "c", + "Explanation": "\"area of a parallelogram = base * height = 26 * 14 = 364 cm 2 answer : c\"" + }, + { + "Answer": 3, + "Options": "['a ) 4 : 1', 'b ) 2 : 1', 'c ) 7 : 1', 'd ) 5 : 1', 'e ) 3 : 1']", + "Correct": "e", + "Explanation": "volume of the cylinder = \u03c0 r ( power 2 ) h volume of the cone = 1 / 3 \u03c0 r ( power 2 ) h ( \u03c0 r ( power 2 ) h ) / ( 1 / 3 \u03c0 r ( power 2 ) h ) = 3 / 1 = 3 : 1 answer is e ." + }, + { + "Answer": 5, + "Options": "a ) 5 : 1 , b ) 3 : 1 , c ) 5 : 8 , d ) 3 : 2 , e ) 8 : 3", + "Correct": "a", + "Explanation": "\"d = 5 d d = d a \u221a 2 = 5 d a \u221a 2 = d a = 5 d / \u221a 2 a = d / \u221a 2 = > 5 : 1 answer : a\"" + }, + { + "Answer": 1728, + "Options": "a ) 1730 cm 2 , b ) 1728 cm 2 , c ) 1870 cm 2 , d ) 1890 cm 2 , e ) 668 cm 2", + "Correct": "b", + "Explanation": "\"area of a parallelogram = base * height = 48 * 36 = 1728 cm 2 answer : b\"" + }, + { + "Answer": 25, + "Options": "a ) 80 sq m , b ) 26 sq m , c ) 25 sq m , d ) 45 sq m , e ) 96 sq m", + "Correct": "c", + "Explanation": "\"5 * 5 = 25 sq m answer : c\"" + }, + { + "Answer": 40, + "Options": "a ) a ) 40 , b ) b ) 828 , c ) c ) 729 , d ) d ) 34 , e ) e ) 35", + "Correct": "a", + "Explanation": "\"explanation : area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 32 / 2 = 40 cm 2 answer : option a\"" + }, + { + "Answer": 20, + "Options": "a ) 8 m , b ) 10 m , c ) 12 m , d ) 20 m , e ) 17 m", + "Correct": "d", + "Explanation": "\"let the length of the hall be x m breadth of the hall = 1 x / 2 m area of the hall = length * breadth 800 = x * 1 x / 2 x \u00b2 = 1600 x = 40 difference between the length and breadth of the hall = x - 1 x / 2 = x / 2 = 40 / 2 = 20 m answer : d\"" + }, + { + "Answer": 56, + "Options": "a ) 48 , b ) 52 , c ) 54 , d ) 56 , e ) 46", + "Correct": "d", + "Explanation": "\"isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side , the longer side with side 17 will be divided into 3 parts = 11 , 3 and 3 ( making one square and two right triangles ) for the right triangle , height will be = ( 5 ^ 2 - 3 ^ 2 ) ^ 1 / 2 = 4 and the area of trapezoid = 1 / 2 ( b 1 + b 2 ) h = 1 / 2 * 28 * 4 = 56 d is the answer\"" + }, + { + "Answer": 648, + "Options": "a ) 287 cm 2 , b ) 887 cm 2 , c ) 384 cm 2 , d ) 268 cm 2 , e ) 648 cm 2", + "Correct": "e", + "Explanation": "\"area of a parallelogram = base * height = 36 * 18 = 648 cm 2 answer : e\"" + }, + { + "Answer": 59.975859750350594, + "Options": "['a ) 30 cm', 'b ) 60 cm', 'c ) 72 cm', 'd ) 132 cm .', 'e ) 142 cm .']", + "Correct": "b", + "Explanation": "length of wire = circumference of circle of radius 42 cm = ( 2 * 22 / 7 * 42 ) = 264 cm . therefore , perimeter of rectangle = 264 cm . let , length = 6 x cm & breadth = 5 x cm . therefore , 2 ( 6 x + 5 x ) = 264 or x = 12 . therefore , smaller side = 60 cm answer : b" + }, + { + "Answer": 327.90242451070714, + "Options": "a ) 327.9 , b ) 325.9 , c ) 347.7 , d ) 357.9 , e ) 327.9", + "Correct": "a", + "Explanation": "\"area of the rhombus = 1 / 2 * p * \u221a 4 ( a ) 2 - ( p ) 2 a = 22 ; p = 16 a = 1 / 2 * 16 * \u221a 4 ( 22 ) 2 - ( 16 ) 2 = 1 / 2 * 16 * \u221a 1936 - 256 = 1 / 2 * 16 * \u221a 1680 a = 327.9 answer : a\"" + }, + { + "Answer": 32.25, + "Options": "['a ) 52.65', 'b ) 56.25', 'c ) 50.75', 'd ) 32.25', 'e ) 52.75']", + "Correct": "d", + "Explanation": "a = 100 a 2 = 10000 a = 115 a 2 = 13225 - - - - - - - - - - - - - - - - 10000 - - - - - - - - - 3225 100 - - - - - - - ? = > 32.25 % answer : d" + }, + { + "Answer": 3, + "Options": "a ) 3 : 1 , b ) 3 : 2 , c ) 3 : 5 , d ) 3 : 7 , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : let the edges be a and b of two cubes , then a 3 / b 3 = 27 / 8 = > ( a / b ) 3 = ( 3 / 2 ) 3 a / b = 3 / 2 = > a : b = 3 : 2 option b\"" + }, + { + "Answer": 80, + "Options": "a ) 78 , b ) 80 , c ) 85 , d ) 88 , e ) 90", + "Correct": "b", + "Explanation": "\"least number of cubes will be required when the cubes that could fit in are biggest . 6 is the biggest number that could divide all three , 30 , 48 and 12 . thus side of cube must be 6 , and total number of cubes = 30 / 6 * 48 / 6 * 12 / 6 = 80 ans b .\"" + }, + { + "Answer": 3, + "Options": "['a ) 4 hours', 'b ) 11 hours', 'c ) 7 hours 15 minutes', 'd ) 3 hours', 'e ) 14 hours']", + "Correct": "d", + "Explanation": "answer is : d , 3 hours the volume of the puddle is irrelevant and only height matters since rain fell all over the city . thus , it takes only 30 / 10 = 3 hours of rain to fill the puddle" + }, + { + "Answer": 250, + "Options": "a ) 158 , b ) 129 , c ) 250 , d ) 123 , e ) 117", + "Correct": "c", + "Explanation": "\"1 / 2 * 20 * 25 = 250 answer : c\"" + }, + { + "Answer": 1520, + "Options": "a ) $ 1520 , b ) $ 1640 , c ) $ 1780 , d ) $ 1850 , e ) $ 1960", + "Correct": "a", + "Explanation": "\"the total surface area is 2 ( 2 * 4 + 4 * 5 + 2 * 5 ) = 76 square feet the total cost is 76 * $ 20 = $ 1520 the answer is a .\"" + }, + { + "Answer": 1812, + "Options": "a ) s . 4528 , b ) s . 1812 , c ) s . 4527 , d ) s . 4530 , e ) s . 4521", + "Correct": "b", + "Explanation": "\"area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 2 = rs . 1812 answer : b\"" + }, + { + "Answer": 16, + "Options": "a ) 5 square inches , b ) 10 square inches , c ) 16 square inches , d ) 25 square inches , e ) 350 square inches", + "Correct": "c", + "Explanation": "\"in the first case each can buy one pizza of $ 10 and one pizza of $ 20 . in square inches that would be ( 8 * 8 = 64 ) for the small pizza and ( 12 * 12 = 144 ) for the large pizza . in total sq inches that would be ( 64 + 144 ) * 2 = 416 sq inches . in the second case if they pool their money together they can buy 3 large pizzas . in terms of square inches that would be 3 * 144 = 432 sq inches . hence , the difference is 16 square inches more ( 432 - 416 ) . the correct answer is c\"" + }, + { + "Answer": 330, + "Options": "a ) 144 , b ) 131 , c ) 330 , d ) 390 , e ) 445", + "Correct": "c", + "Explanation": "\"there are 20 business exec and in each handshake 2 business execs are involved . hence 20 c 2 = 190 also , each of 20 exec will shake hand with every 7 other chairmen for total of 140 handshake . total = 190 + 140 = 330 ans : c\"" + }, + { + "Answer": 625, + "Options": "a ) 225 sq m , b ) 186 sq m , c ) 586 sq m , d ) 287 sq m , e ) 625 sq m", + "Correct": "e", + "Explanation": "\"25 * 25 = 625 sq m answer : e\"" + }, + { + "Answer": 2004, + "Options": "a ) 3008 , b ) 2004 , c ) 1008 , d ) 2016 , e ) 3000", + "Correct": "b", + "Explanation": "\"note that trapezoids axy d and bxy c are congruent , so the area of axy d is always 4008 / 2 = 2004 . correct answer b\"" + }, + { + "Answer": 66.84507609859604, + "Options": "['a ) 52.5', 'b ) 60.2', 'c ) 66.8', 'd ) 74.25', 'e ) 80.12']", + "Correct": "c", + "Explanation": "diameter of the circle = perimeter / \u00ef \u20ac = 52.5 x 7 / 22 = 16.70 perimeter of the square = 16.70 x 4 = 66.8 cm answer : c" + }, + { + "Answer": 15, + "Options": "a ) 25 , b ) 23 , c ) 22 , d ) 15 , e ) 18", + "Correct": "d", + "Explanation": "\"area of carol ' s rectangle = 24 * 5 = 120 let width of jordan ' s rectangle = w since , the areas are equal 8 w = 120 = > w = 15 answer d\"" + }, + { + "Answer": 120, + "Options": "a ) 120 cm 2 , b ) 130 cm 2 , c ) 312 cm 2 , d ) 315 cm 2 , e ) none of these", + "Correct": "a", + "Explanation": "\"the triangle with sides 26 cm , 24 cm and 10 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 24 * 10 = 120 cm 2 answer : a\"" + }, + { + "Answer": 420, + "Options": "a ) 520 , b ) 420 , c ) 320 , d ) 550 , e ) 450", + "Correct": "b", + "Explanation": "\"sol . 6 x * x = 7 * 4200 x = 70 length = 6 * 70 = 420 b\"" + }, + { + "Answer": 252, + "Options": "a ) 80 , b ) 96 , c ) 108 , d ) 120 , e ) 252", + "Correct": "e", + "Explanation": "\"imo : e here we have to select 5 points out of 10 points . order is not important so the answer will be 10 c 5 = 252 answer e\"" + }, + { + "Answer": 0.8888888888888888, + "Options": "['a ) 1 / 9 sq units .', 'b ) 4 / 9 sq units .', 'c ) 8 / 9 sq units .', 'd ) 7 / 9 sq units .', 'e ) 6 / 9 sq units .']", + "Correct": "c", + "Explanation": "area will be 2 / 3 * 4 / 3 = 8 / 9 sq units . answer : c" + }, + { + "Answer": 294, + "Options": "['a ) 24 a 8', 'b ) 24 a 4', 'c ) 24 a 1', 'd ) 24 a 2', 'e ) 294 a 2']", + "Correct": "e", + "Explanation": "6 a 2 = 6 * 7 a * 7 a = 294 a 2 answer : e" + }, + { + "Answer": 4, + "Options": "a ) 12 h , b ) 10 h , c ) 4 h , d ) 6 h , e ) none of these", + "Correct": "c", + "Explanation": "explanation area of field = 400 km 2 . then , each side of field = \u221a 400 = 20 km distance covered by the horse = perimeter of square field = 20 \u00d7 4 = 80 km \u2234 time taken by horse = distances / peed = 80 / 20 = 4 h answer c" + }, + { + "Answer": 34, + "Options": "['a ) 5 square inches', 'b ) 10 square inches', 'c ) 15 square inches', 'd ) 25 square inches', 'e ) 34 square inches']", + "Correct": "e", + "Explanation": "in the first case each can buy one pizza of $ 10 and one pizza of $ 20 . in square inches that would be ( 9 * 9 = 81 ) for the small pizza and ( 14 * 14 = 196 ) for the large pizza . in total sq inches that would be ( 81 + 196 ) * 2 = 554 sq inches . in the second case if they pool their money together they can buy 3 large pizzas . in terms of square inches that would be 3 * 196 = 588 sq inches . hence , the difference is 34 square inches more ( 588 - 554 ) . the correct answer is e" + }, + { + "Answer": 14, + "Options": "['a ) 2', 'b ) 5', 'c ) 6', 'd ) 7', 'e ) 14']", + "Correct": "e", + "Explanation": "solution : this problem is testing us on the rule that when we express a perfect square by its unique prime factors , every prime factor ' s exponent is an even number . let \u2019 s start by prime factorizing 3,150 . 3,150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2 3,150 = 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 ( notice that the exponents of both 2 and 7 are not even numbers . this tells us that 3,150 itself is not a perfect square . ) we also are given that 3,150 multiplied by f is the square of an integer . we can write this as : 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 x f = square of an integer according to our rule , we need all unique prime factors ' exponents to be even numbers . thus , we need one more 2 and one more 7 . therefore , y = 7 x 2 = 14 answer is e ." + }, + { + "Answer": 250, + "Options": "['a ) 200', 'b ) 225', 'c ) 240', 'd ) 250', 'e ) none']", + "Correct": "d", + "Explanation": "solution required % = [ \u03c0 x ( 5 ) 2 / 2 \u03c0 x 5 x 100 ] % \u2039 = \u203a 250 % . answer d" + }, + { + "Answer": 37.5, + "Options": "['a ) 37.2 %', 'b ) 37.5 %', 'c ) 30.2 %', 'd ) 37.7 %', 'e ) 33.2 %']", + "Correct": "b", + "Explanation": "explanation : 100 * 100 = 10000 110 * 125 = 13750 - - - - - - - - - - - 3750 10000 - - - - - - 3750 100 - - - - - - - ? = > 37.5 % answer : option b" + }, + { + "Answer": 20, + "Options": "['a ) 5 %', 'b ) 20 %', 'c ) 50 %', 'd ) 100 %', 'e ) 120 %']", + "Correct": "b", + "Explanation": "let x be the original length of one side . then the original area is x ^ 2 . the new square has sides of length sqrt ( 5 ) * x , so the area is 5 x ^ 2 . the area of the original square is 1 / 5 = 20 % times the area of the new square . the answer is b ." + }, + { + "Answer": 4, + "Options": "a ) 2 : 1 , b ) 3 : 1 , c ) 4 : 1 , d ) 6 : 1 , e ) 8 : 1", + "Correct": "c", + "Explanation": "\"let x be the length of the small cube ' s side . the total surface area of the small cube is 6 x ^ 2 . the total surface area of the large cube is 6 ( 2 x ) ^ 2 = 24 x ^ 2 . the ratio of surface areas is 4 : 1 . the answer is c .\"" + }, + { + "Answer": 48, + "Options": "['a ) 20', 'b ) 24', 'c ) 48', 'd ) 72', 'e ) 120']", + "Correct": "c", + "Explanation": "j = juan , f = jamal since j is always fixed , set j , set f relative to j , then see how many options there are : j f 4 3 2 1 = 24 or f j 4 3 2 1 = 24 24 + 24 = 48 \u2026 c answer : c" + }, + { + "Answer": 32, + "Options": "['a ) q = 16', 'b ) q = 32', 'c ) 64', 'd ) 128', 'e ) 512']", + "Correct": "b", + "Explanation": "weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )" + }, + { + "Answer": 189, + "Options": "a ) 144 , b ) 131 , c ) 115 , d ) 189 , e ) 45", + "Correct": "d", + "Explanation": "\"there are 14 business exec and in each handshake 2 business execs are involved . hence 14 c 2 = 91 also , each of 14 exec will shake hand with every 7 other chairmen for total of 98 handshake . total = 91 + 98 = 189 ans : d\"" + }, + { + "Answer": 0.005, + "Options": "a ) 0.005 , b ) 0.002 , c ) 0.001 , d ) 0.0005 , e ) 0.0002", + "Correct": "a", + "Explanation": "\"it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 5 then x = 5 / 1000 = 0.005 . the answer is a\"" + }, + { + "Answer": 47.5, + "Options": "a ) 42.25 cm 2 , b ) 57.5 cm 2 , c ) 42.5 cm 2 , d ) 47.5 cm 2 , e ) 52.5 cm 2", + "Correct": "d", + "Explanation": "\"the triangle with sides 21 cm , 19 cm and 5 cm is right angled , where the hypotenuse is 21 cm . area of the triangle = 1 / 2 * 19 * 5 = 47.5 cm 2 answer : d\"" + }, + { + "Answer": 120, + "Options": "['a ) 150 sq . cm', 'b ) 120 sq . cm', 'c ) 130 sq . cm', 'd ) 125 sq . cm', 'e ) 110 sq . cm']", + "Correct": "b", + "Explanation": "let abcd is a rhombus with diagonals ac and bd which intersect each other at o . ac = 24 \u21d2 ao = 12 let bo = x and ab = 13 cm ( given ) by pythagorean theorem c 2 = a 2 + b 2 13 2 = 12 2 + x 2 169 = 144 + x 2 x 2 = 169 \u2013 144 x 2 = 25 x = 5 cm bo = 5 cm diagonal bd = 2 x 5 = 10 cm . area = \u00bd x [ product of diagonals ] = \u00bd x 24 x 10 area = 120 sq . cm answer is b" + }, + { + "Answer": 6750, + "Options": "a ) 6350 , b ) 7357 , c ) 6328 , d ) 6750 , e ) 7560", + "Correct": "d", + "Explanation": "\"area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 2.5 * 2 ) 2 * 2.5 = > 675 675 * 10 = rs . 6750 answer : d\"" + }, + { + "Answer": 4500, + "Options": "a ) 100 , b ) 250 , c ) 4500 , d ) 1200 , e ) 5625", + "Correct": "c", + "Explanation": "\"6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 60 * 20 * 1 / 2 = 600 feet ^ 3 of water must be removed , which equals to 600 * 7.5 = 4500 gallons . answer : c .\"" + }, + { + "Answer": 3876, + "Options": "a ) 3944 , b ) 920 , c ) 7290 , d ) 3876 , e ) 3729", + "Correct": "d", + "Explanation": "\"explanation : let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 57 = rs . 3876 . answer : option d\"" + }, + { + "Answer": 160, + "Options": "a ) 100 , b ) 777 , c ) 998 , d ) 729 , e ) 160", + "Correct": "e", + "Explanation": "\"160 % answer : e\"" + }, + { + "Answer": 3600, + "Options": "a ) a ) 3820 , b ) b ) 930 , c ) c ) 9309 , d ) d ) 3600 , e ) e ) 8302", + "Correct": "d", + "Explanation": "\"explanation : area = ( l + b \u2013 d ) d ( 80 + 50 \u2013 10 ) 10 = > 1200 m 2 1200 * 3 = rs . 3600 answer : option d\"" + }, + { + "Answer": 50, + "Options": "a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60", + "Correct": "d", + "Explanation": "\"area of first rectangle is 15 * 20 = 300 hence area of second would be 6 x = 300 x x = 50 answer is d\"" + }, + { + "Answer": 8.3, + "Options": "a ) 3.5 % , b ) 2.4 % , c ) 8.3 % , d ) 5 % , e ) 2.6 %", + "Correct": "c", + "Explanation": "\"say both sides of the rectangle are equal to 100 ( so consider that we have a square ) . in this case the area is 100 * 100 = 10,000 . now , the area obtained with wrong measurements would be 114 * 95 = 10,830 , which is 8.3 % greater than the actual area . answer : c .\"" + }, + { + "Answer": 384, + "Options": "a ) 345 , b ) 384 , c ) 378 , d ) 398 , e ) 300", + "Correct": "b", + "Explanation": "\"number of cubes required = volume of box / volume of cube = 12 * 16 * 6 / 3 = 384 cubes answer : b\"" + }, + { + "Answer": 9, + "Options": "a ) 8 , b ) 9 , c ) 7 , d ) 62 , e ) 2", + "Correct": "b", + "Explanation": "\"2 x * x = 162 = > x = 9 answer : b\"" + }, + { + "Answer": 3, + "Options": "['a ) 2', 'b ) 3', 'c ) 6', 'd ) 12', 'e ) 24']", + "Correct": "b", + "Explanation": "the prime factorization of a square has to have even powers of all its prime factors . if the original number has a factor , say of 7 , then when it \u2019 s squared , the square will have a factor of 7 ^ 2 . another way to say that is : any positive integer all of whose prime factors have even powers must be a perfect square of some other integer . look at the prime factorization of 432 432 = ( 2 ^ 4 ) * ( 3 ^ 3 ) the factor of 2 already has an even power \u2014 - that \u2019 s all set . the factor of 3 currently has an odd power . if n = 3 , then 432 * n would have an even power of 2 and an even power of 3 ; therefore , it would be a perfect square . thus , n = 3 is a choice that makes 432 * n a perfect square . answer : b ." + }, + { + "Answer": 17, + "Options": "a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20", + "Correct": "b", + "Explanation": "integer powers of 2 = 2 , 2 ^ 2 , 2 ^ 3 , 2 ^ 4 , 2 ^ 5 , 2 ^ 6 , 2 ^ 7 etc . let , cube root of x is closest to 50 i . e . x is closest to cube of 50 = 50 * 50 * 50 = 125000 but x must be equivalent to an integer power of 2 2 ^ 10 = 1024 2 ^ 7 = 128 i . e . 2 ^ 17 = 128 * 1024 = 128000 ( approx . ) i . e . 2 ^ 18 = 256 * 1024 = 256000 ( approx . ) i . e . 2 ^ 16 = 64 * 1024 = 64000 ( approx . ) i . e . 2 ^ 17 which is closest to 125000 i . e . integer power of 2 must be 7 answer : option b" + }, + { + "Answer": 1.6, + "Options": "a ) 1.6 cm , b ) 2.4 cm , c ) 4.8 cm , d ) 2.16 cm , e ) 3.2 cm", + "Correct": "a", + "Explanation": "\"look at the diagram below : now , in case when qy is perpendicular to pr , two right triangles pqr and pqy are similar : qy : qp = qr : pr - - > qy : 2 = 8 : 10 - - > qy = 1.6 . answer : a .\"" + }, + { + "Answer": 180, + "Options": "a ) 180 cm 2 , b ) 112 cm 2 , c ) 776 cm 2 , d ) 666 cm 2 , e ) 886 cm 2", + "Correct": "a", + "Explanation": "\"the triangle with sides 28 cm , 24 cm and 15 cm is right angled , where the hypotenuse is 28 cm . area of the triangle = 1 / 2 * 24 * 15 = 180 cm 2 answer : a\"" + }, + { + "Answer": 30, + "Options": "a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 32", + "Correct": "d", + "Explanation": "\"area of first rectangle is 8 * 15 = 120 hence area of second would be 4 x = 120 x x = 30 answer is d\"" + }, + { + "Answer": 40, + "Options": "a ) 87 cm 2 , b ) 28 cm 2 , c ) 98 cm 2 , d ) 26 cm 2 , e ) 40 cm 2", + "Correct": "e", + "Explanation": "\"area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 32 / 2 = 40 cm 2 answer : e\"" + }, + { + "Answer": 78.75, + "Options": "a ) 22 , b ) 75 , c ) 78 , d ) 54 , e ) 23", + "Correct": "c", + "Explanation": "\"area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 4.5 * 35 / 2 = 78.75 cm 2 answer : c\"" + }, + { + "Answer": 1080, + "Options": "a ) 54 , b ) 64 , c ) 81 , d ) 1080 , e ) 120", + "Correct": "d", + "Explanation": "\"volume of larger cube = 216 = 6 ^ 3 side of larger cube = 6 volume of smaller cube = 1 - - > side of smaller cube = 1 surface area of larger cube = 6 * 6 ^ 2 = 216 surface area of 27 smaller cubes = 216 * 6 * 1 = 1296 difference = 1296 - 216 = 1080 answer : d\"" + }, + { + "Answer": 50265.482457436694, + "Options": "a ) 10000 , b ) 50000 , c ) 80000 , d ) 85000 , e ) 90000", + "Correct": "b", + "Explanation": "\"answer should be b . v = \\ pir ^ 2 h = \\ pi * 40 ^ 2 * 10 = approximately 50000\"" + }, + { + "Answer": 19.999999999999996, + "Options": "a ) 20 % , b ) 18 % , c ) 36 % , d ) 64 % , e ) none of these", + "Correct": "a", + "Explanation": "\"if area of a circle decreased by x % then the radius of a circle decreases by ( 100 \u2212 10 \u221a 100 \u2212 x ) % = ( 100 \u2212 10 \u221a 100 \u2212 36 ) % = ( 100 \u2212 10 \u221a 64 ) % = 100 - 80 = 20 % answer a\"" + }, + { + "Answer": 6.146341463414634, + "Options": "['a ) 4.1 cm', 'b ) 5.1 cm', 'c ) 6.1 cm', 'd ) 7.1 cm', 'e ) 8.1 cm']", + "Correct": "c", + "Explanation": "semi - perimeter of the triangle = ( a + b + c ) / 2 = ( 41 + 28 + 15 ) / 2 = 84 / 2 = 42 cm therefore , area of the triangle = \u221a ( s ( s - a ) ( s - b ) ( s - c ) ) = \u221a ( 42 ( 42 - 41 ) ( 42 - 28 ) ( 42 - 15 ) ) cm \u00b2 = \u221a ( 42 \u00d7 1 \u00d7 27 \u00d7 14 ) cm \u00b2 = \u221a ( 3 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 2 \u00d7 2 \u00d7 7 \u00d7 7 ) cm \u00b2 = 3 \u00d7 3 \u00d7 2 \u00d7 7 cm \u00b2 = 126 cm \u00b2 now , area of triangle = 1 / 2 \u00d7 b \u00d7 h therefore , h = 2 a / b = ( 2 \u00d7 126 ) / 41 = 252 / 41 = 6.1 cm answer : option c" + }, + { + "Answer": 12, + "Options": "['a ) 76', 'b ) 55', 'c ) 44', 'd ) 12', 'e ) 91']", + "Correct": "d", + "Explanation": "ans : { a 1 , a 2 } , { a 2 , a 3 } , { a 3 , a 4 } , { a 4 , a 5 } , { a 5 , a 6 } , { a 6 , a 7 } \u2026 , { a 35 , a 36 } , { a 36 , a 1 } from the above arrangement , if we separate a 3 , a 6 , a 9 , . . . . . a 36 . total 12 persons the reamining persons must have shaked hand with atleast one person . so answer is 12 . answer : d" + }, + { + "Answer": 375, + "Options": "a ) 250 , b ) 300 , c ) 375 , d ) 550 , e ) 750", + "Correct": "c", + "Explanation": "\"area = 0.5 x 25 x 30 = 375 cm \u00e2 \u00b2 answer : c\"" + }, + { + "Answer": 9, + "Options": "a ) 5 , b ) 6 , c ) 8 , d ) 9 , e ) 10", + "Correct": "d", + "Explanation": "number of diagonals in any polygon can be found using this formula : n ( n - 3 ) / 2 here n = 6 no . of diagonals = 6 ( 6 - 3 ) / 2 = 9 ans d" + }, + { + "Answer": 120, + "Options": "['a ) 90', 'b ) 100', 'c ) 120', 'd ) 130', 'e ) 140']", + "Correct": "c", + "Explanation": "sol . x * 4 x = 3 * 1200 x = 30 length = 4 * 30 = 120 c" + }, + { + "Answer": 0.6666666666666666, + "Options": "a ) 4 / 6 , b ) 5 / 4 , c ) 3 / 2 , d ) 5 / 7 , e ) 2 / 3", + "Correct": "a", + "Explanation": "\"we are basically given that the triangles are similar . in two similar triangles , the ratio of their areas is the square of the ratio of their sides and also , the square of the ratio of their corresponding heights . therefore , area / area = height ^ 2 / height ^ 2 = 16 / 36 - - > height / height = 4 / 6 . answer : a .\"" + }, + { + "Answer": 34, + "Options": "['a ) 2', 'b ) 4', 'c ) 34', 'd ) 38', 'e ) 40']", + "Correct": "c", + "Explanation": "pythogoras will help here ! let the sides be x and diagonal be d then d ^ 2 = 2 x ^ 2 and area = x ^ 2 now plug in the given diagonal values to find x values and then subtract the areas ans will be 18 ^ 2 / 2 - 16 ^ 2 / 2 = 68 / 2 = 34 ans c ." + }, + { + "Answer": 0.0003, + "Options": "a ) 0.005 , b ) 0.002 , c ) 0.001 , d ) 0.0003 , e ) 0.0002", + "Correct": "d", + "Explanation": "it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 0.3 then x = 0.3 / 1000 = 0.0003 . the answer is d" + }, + { + "Answer": 10, + "Options": "a ) 1 , b ) 2 , c ) 10 , d ) 8 , e ) 16", + "Correct": "c", + "Explanation": "\"as per the question - - width is negligible now , let l be the length of the fence = 2 pir l = 1 / 5 ( pir ^ 2 ) pir ^ 2 = 10 pir r = 10 answer : c\"" + }, + { + "Answer": 11, + "Options": "a ) 11 , b ) 5 , c ) 10 , d ) 15 , e ) 20", + "Correct": "a", + "Explanation": "\"longest chord of a circle is the diameter of the circle diameter = 2 * radius if diameter of the circle is given as 22 = 2 * 11 so radius of the circle = 11 correct answer - a\"" + }, + { + "Answer": 8.041666666666668, + "Options": "['a ) 8 cm', 'b ) 9 cm', 'c ) 10 cm', 'd ) 11 cm', 'e ) 7 cm']", + "Correct": "a", + "Explanation": "a , b , c are sides of triangle , ad is the median , ad ^ 2 = ab ^ 2 - bd ^ 2 then ad = 12 , the centriod median divides into 2 : 1 ratio so 12 will be divide into 2 : 1 ratio so 8 is radius . so ans is 8 cm answer : a" + }, + { + "Answer": 380.132711084365, + "Options": "a ) 354 cm 2 , b ) 380 m 2 , c ) 350 m 2 , d ) 407 m 2 , e ) none of these", + "Correct": "b", + "Explanation": "\"area of the shaded portion = 1 \u2044 4 \u00d7 \u03c0 \u00d7 ( 22 ) 2 = 380 m 2 answer b\"" + }, + { + "Answer": 79.99999999999993, + "Options": "a ) 90 , b ) 75 , c ) 70 , d ) 80 , e ) 85", + "Correct": "d", + "Explanation": "( 4 / 5 - 3 / 4 ) cylinder is filled by 4 bottles 0.8 - 0.75 = 0.05 cylinder is filled by 4 bottles 1 cylinder is filled by 4 / 0.05 = 80 bottles answer : d" + }, + { + "Answer": 21, + "Options": "['a ) 21', 'b ) 22', 'c ) 23', 'd ) 24', 'e ) 25']", + "Correct": "a", + "Explanation": "perfect squares divisiors are 1 , 2 ^ 2 & 2 ^ 4 only sum of divisors of 544 which are perfect squares = 1 + 2 ^ 2 + 2 ^ 4 = 21 answer : a" + }, + { + "Answer": 164, + "Options": "a ) 84 , b ) 124 , c ) 164 , d ) 180 , e ) 120", + "Correct": "c", + "Explanation": "\"explanation : surface area = [ 2 ( 10 x 4 + 4 x 3 + 10 x 3 ) ] cm 2 = 164 cm 2 answer : c\"" + }, + { + "Answer": 56, + "Options": "a ) 17 , b ) 18 , c ) 54 , d ) 56 , e ) 864", + "Correct": "d", + "Explanation": "\"least number of cubes will be required when the cubes that could fit in are biggest . 5 is the biggest number that could divide all three , 35 , 20 and 10 . thus side of cube must be 5 , and total number of cubes = 35 / 5 * 20 / 5 * 10 / 5 = 56 ans d it is .\"" + }, + { + "Answer": 384, + "Options": "a ) 298 cm 2 , b ) 384 cm 2 , c ) 279 cm 2 , d ) 297 cm 2 , e ) 278 cm 2", + "Correct": "b", + "Explanation": "\"area of a parallelogram = base * height = 24 * 16 = 384 cm 2 answer : b\"" + }, + { + "Answer": 3, + "Options": "['a ) 1', 'b ) 2', 'c ) 3', 'd ) 4', 'e ) 5']", + "Correct": "c", + "Explanation": "volume of given ice cream = ( pie ) * 6 \u00b2 * 15 = 540 ( pie ) dividing to 10 children volume given to a child = 54 ( pie ) let r be radius and h be the height of the cone , then ( pie ) r \u00b2 h / 3 + 2 ( pie ) r \u00b3 / 3 = 54 ( pie ) also given h = 4 r 4 r \u00b3 / 3 + 2 r \u00b3 / 3 = 54 2 r \u00b3 = 54 r \u00b3 = 27 r = 3 answer : c" + }, + { + "Answer": 22, + "Options": "['a ) 21', 'b ) 22', 'c ) 23', 'd ) 24', 'e ) 20']", + "Correct": "b", + "Explanation": "7 th one is exactly opposite represents half of circle . with 7 and 18 total members are 12 for remaing half = 12 * 2 - 2 ( 7 th and 18 th ( already taken ) ) = 22 answer : b" + }, + { + "Answer": 4.020725758589058, + "Options": "a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 9", + "Correct": "a", + "Explanation": "\"if sides are 7 , vol = 7 ^ 3 = 343 80 % = 274.4 , 90 % = 308.7 so vol above water , between 68.6 and 34.3 - - > too big if side are 4 , vol = 64 80 % = 51.2 , 90 % = 57.6 vol above water between 12.8 and 6.4 so 4 should be the answer . check option c , if sides are 5 , vol = 125 80 % = 100 , . 90 % = 112.5 vol above water between 12.5 - 25 ( sides are 4 cubic centimeters ) a\"" + }, + { + "Answer": 408, + "Options": "a ) 400 m 2 , b ) 404 m 2 , c ) 408 m 2 , d ) 401 m 2 , e ) 412 m 2", + "Correct": "c", + "Explanation": "\"surface area of a cuboid = 2 ( lb + bh + lh ) = 2 ( 10 * 9 + 9 * 6 + 10 * 6 ) = 2 ( 90 + 54 + 60 ) = 2 * 204 = 408 m 2 answer : c\"" + }, + { + "Answer": 24, + "Options": "['a ) 8 \u221a 2', 'b ) 9 \u221a 3', 'c ) 18', 'd ) 16 \u221a 2', 'e ) 24']", + "Correct": "e", + "Explanation": "area of shaded figure = area of square - ( area of triangle aef + area of triangle fbc + area of triangle edc ) = 8 * 8 - ( 1 / 2 * 4 * 4 + 1 / 2 * 4 * 8 + 1 / 2 * 4 * 8 ) = 24 . answer e ." + }, + { + "Answer": 960, + "Options": "a ) 960 cm 2 , b ) 240 cm 2 , c ) 480 cm 2 , d ) 45 cm 2 , e ) 250 cm 2", + "Correct": "a", + "Explanation": "\"area of a parallelogram = base * height = 60 * 16 = 960 cm 2 answer : a\"" + }, + { + "Answer": 11550, + "Options": "['a ) 11647', 'b ) 11550', 'c ) 12654', 'd ) 26537', 'e ) 32651']", + "Correct": "b", + "Explanation": "b 11550 there is just one way to find it out and that is the generic computing method . the number of squares and rectangles formed = ( summation of column numbers ) = ( 1 + 2 + 3 + . . . . . . + 19 + 20 ) * ( 1 + 2 + 3 + . . . . . . + 9 + 10 ) = 210 * 55 = 11550" + }, + { + "Answer": 48, + "Options": "['a ) 32 cm', 'b ) 48 cm', 'c ) 50 cm', 'd ) 28 cm', 'e ) 30 cm']", + "Correct": "b", + "Explanation": "ratio of sides = 1 / 2 : 1 / 3 : 1 / 4 = 6 : 4 : 3 largest side = 104 * 6 / 13 = 48 cm answer is b" + }, + { + "Answer": 576, + "Options": "a ) 576 cm 2 , b ) 384 cm 2 , c ) 672 cm 2 , d ) 267 cm 2 , e ) 286 cm 2", + "Correct": "a", + "Explanation": "\"area of a parallelogram = base * height = 32 * 18 = 576 cm 2 answer : a\"" + }, + { + "Answer": 11, + "Options": "a ) 15 , b ) 11 , c ) 28 , d ) 91 , e ) none of these", + "Correct": "b", + "Explanation": "let the number be x . then , x + x 2 = 132 ( x + 12 ) ( x - 11 ) = 0 x = 11 answer : b" + }, + { + "Answer": 49, + "Options": "['a ) 44', 'b ) 45', 'c ) 46', 'd ) 47', 'e ) 49']", + "Correct": "e", + "Explanation": "67 x 67 = 4489 4489 - 4440 = 49 if added to 49 get perfect square answer = e" + }, + { + "Answer": 40, + "Options": "['a ) 48', 'b ) 40', 'c ) 24', 'd ) 18', 'e ) 12']", + "Correct": "b", + "Explanation": "for example our cube have a side 1 meter , so we have 1 cubical meter in this cube and this cubical meter weigth 5 pounds if we take cube with side 2 meters we will have 8 cubical meters in this cube 8 meters * 5 pounds = 40 pounds so answer is b and similar but more theoretical approach : if we have sides a and b than they have equal ration with their areas : a / b = a ^ 2 / b ^ 2 and they have equal ration with their volumes : a / b = a ^ 3 / b ^ 3 we have two sides 1 / 2 so their volume will be in ratio 1 / 8 weight of one cube * volume of another cube 5 * 8 = 40 so answer is b" + }, + { + "Answer": 40, + "Options": "['a ) 32', 'b ) 36', 'c ) 40', 'd ) 44', 'e ) 48']", + "Correct": "c", + "Explanation": "let x be the length of one side of the square garden . x ^ 2 = 8 x + 20 x ^ 2 - 8 x - 20 = 0 ( x - 10 ) ( x + 2 ) = 0 x = 10 , - 2 p = 4 ( 10 ) = 40 the answer is c ." + }, + { + "Answer": 2945, + "Options": "a ) 2812 , b ) 8231 , c ) 2734 , d ) 4222 , e ) 2945", + "Correct": "e", + "Explanation": "\"a volume of 4 l can be kept in 1 hemisphere therefore , a volume of 11780 l can be kept in ( 11780 / 4 ) hemispheres ans . 2945 answer : e\"" + }, + { + "Answer": 0.0002, + "Options": "a ) 0.005 , b ) 0.002 , c ) 0.001 , d ) 0.0005 , e ) 0.0002", + "Correct": "e", + "Explanation": "\"it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 0.2 then x = 0.2 / 1000 = 0.0002 . the answer is e\"" + }, + { + "Answer": 10.2, + "Options": "a ) 3.5 % , b ) 2.4 % , c ) 10.2 % , d ) 5 % , e ) 2.6 %", + "Correct": "c", + "Explanation": "\"say both sides of the rectangle are equal to 100 ( so consider that we have a square ) . in this case the area is 100 * 100 = 10,000 . now , the area obtained with wrong measurements would be 116 * 95 = 11,020 , which is 10.2 % greater than the actual area . answer : c .\"" + }, + { + "Answer": 98, + "Options": "['a ) 98', 'b ) 99', 'c ) 100', 'd ) 101', 'e ) 102']", + "Correct": "a", + "Explanation": "125 1 * 1 * 1 small cubes = 5 * 5 * 5 cubes because hallow in inner we do n ' t have 3 * 3 * 3 cubes so 125 - 27 = 98 cubes required answer : a" + }, + { + "Answer": 288, + "Options": "a ) 423 cm 2 , b ) 122 cm 2 , c ) 420 cm 2 , d ) 251 cm 2 , e ) 288 cm 2", + "Correct": "e", + "Explanation": "\"area of a parallelogram = base * height = 18 * 16 = 288 cm 2 answer : e\"" + }, + { + "Answer": 300, + "Options": "a ) 450 , b ) 600 , c ) 750 , d ) 2400 , e ) 300", + "Correct": "e", + "Explanation": "\"answer e ) 9600 yards need 1200 lbs 1 yard will need 800 / 9600 = 1 / 12 lbs 3600 yards will need 1 / 12 * 3600 yards = 300 lbs\"" + }, + { + "Answer": 480, + "Options": "['a ) 420', 'b ) 430', 'c ) 280', 'd ) 360', 'e ) 480']", + "Correct": "e", + "Explanation": "sol . 8 x * x = 9 * 3200 x = 60 length = 8 * 60 = 480 e" + }, + { + "Answer": 7, + "Options": "a ) 7 h , b ) 10 h , c ) 8 h , d ) 6 h , e ) none of these", + "Correct": "a", + "Explanation": "explanation area of field = 1225 km 2 . then , each side of field = \u221a 1225 = 35 km distance covered by the horse = perimeter of square field = 35 \u00d7 4 = 140 km \u2234 time taken by horse = distances / peed = 140 / 20 = 7 h answer a" + }, + { + "Answer": 3, + "Options": "['a ) 3 hours', 'b ) 4 hours 15 minutes', 'c ) 6 hours', 'd ) 2 hours 5 minutes', 'e ) 8 hours']", + "Correct": "a", + "Explanation": "answer is : a , 3 hours the volume of the drum is irrelevant and only height matters since rain fell all over the city . thus , it takes only 15 / 5 = 3 hours of rain to fill the drum" + }, + { + "Answer": 125.00000000000001, + "Options": "a ) 125 , b ) 155 , c ) 130 , d ) 120 , e ) 100", + "Correct": "a", + "Explanation": "\"r = 5 h = 5 \u03c0 * 5 * 5 * 5 = 125 \u03c0 cc answer : a\"" + }, + { + "Answer": 98, + "Options": "a ) 33 , b ) 45 , c ) 66 , d ) 77 , e ) 98", + "Correct": "e", + "Explanation": "\"r = 7 h = 5 \u03c0 * 7 * 7 * 5 = 98 \u03c0 cc answer : e\"" + }, + { + "Answer": 128, + "Options": "a ) 128 , b ) 289 , c ) 200 , d ) 112 , e ) 178", + "Correct": "a", + "Explanation": "\"d 2 / 2 = ( 16 * 16 ) / 2 = 128 answer : a\"" + }, + { + "Answer": 530.929158456675, + "Options": "a ) 124 cm \u00b2 , b ) 531 cm \u00b2 , c ) 354 cm \u00b2 , d ) 584 cm \u00b2 , e ) 594 cm \u00b2", + "Correct": "b", + "Explanation": "\"area of circle = \u03c0 r \u00b2 = 22 / 7 \u00d7 13 \u00d7 13 cm \u00b2 = 531 cm \u00b2 answer : b\"" + }, + { + "Answer": 5236, + "Options": "a ) 4830 , b ) 5236 , c ) 6420 , d ) 8960 , e ) 7960", + "Correct": "b", + "Explanation": "\"clearly , l = ( 48 - 14 ) m = 34 m , b = ( 36 - 14 ) m = 22 m , h = 8 m . volume of the box = ( 34 x 22 x 7 ) m 3 = 5236 m 3 . answer : option b\"" + }, + { + "Answer": 600, + "Options": "['a ) 600', 'b ) 450', 'c ) 350', 'd ) 500', 'e ) 620']", + "Correct": "a", + "Explanation": "area of the rhombus = 1 / 2 d 1 d 2 = ( 1 / 2 \u00e3 \u2014 40 \u00e3 \u2014 30 ) cm ( power ) 2 = 40 \u00e3 \u2014 15 = 600 cm ( power ) 2 answer is a ." + }, + { + "Answer": 212, + "Options": "a ) 212 , b ) 200 , c ) 220 , d ) 230 , e ) 240", + "Correct": "a", + "Explanation": "\"let no of sits in vip enclosure is x then x * 40 + 15 ( 320 - x ) = 7500 or 25 x = 7500 - 4800 , x = 2700 / 25 = 108 vip = 108 general 212 a\"" + }, + { + "Answer": 76, + "Options": "['a ) 74 m', 'b ) 75 m', 'c ) 76 m', 'd ) 77 m', 'e ) 78 m']", + "Correct": "c", + "Explanation": "let l and b are the length and width of the original rectangle . since , l * b = 360 sq . m - ( 1 ) now , a / c to the problem ( l + 10 ) * ( b - 6 ) = 360 sq . m therefore , b = 6 ( 1 + l / 10 ) - ( 2 ) l * l + 10 l - 600 = 0 { by using equations 1 and 2 } thereafter , ( l - 20 ) ( l + 30 ) = 0 hence , l = 20 m b = 18 m { by using equation 2 } now , perimeter of the original rectangle = 2 ( l + b ) = 2 ( 20 + 18 ) = 76 m answer : c" + }, + { + "Answer": 0.5800000000000001, + "Options": "a ) 0.11 % , b ) 0.7 % , c ) 0.4 % , d ) 0.6 % , e ) 0.58 %", + "Correct": "e", + "Explanation": "\"let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 61 / 57 ) x ( 47 / 50 ) y = ( 867 / 862 ) ( xy ) error in measurement = ( 867 / 862 ) xy - xy = ( 5 / 862 ) xy error percentage = [ ( 5 / 862 ) xy ( 1 / xy ) 100 ] % = ( 29 / 50 ) % = 0.58 % . answer is e .\"" + }, + { + "Answer": 3, + "Options": "['a ) 3', 'b ) 4', 'c ) 5', 'd ) 6', 'e ) 7']", + "Correct": "a", + "Explanation": "nos . are 2025 , 2116 , 2209 answers is 3 answer : a" + }, + { + "Answer": 30, + "Options": "a ) 22 , b ) 30 , c ) 77 , d ) 54 , e ) 23", + "Correct": "b", + "Explanation": "\"area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 3 * 20 / 2 = 30 cm 2 answer : b\"" + }, + { + "Answer": 24.99999999999999, + "Options": "['a ) 5', 'b ) 25', 'c ) 50', 'd ) 150', 'e ) 625']", + "Correct": "b", + "Explanation": "volume of a cube = side ^ 3 125 = side ^ 3 so side = 5 area of one side of the cube = side ^ 2 = 5 ^ 2 = 25 correct answer - b" + }, + { + "Answer": 25.000000000000004, + "Options": "['a ) 5', 'b ) 10', 'c ) 15', 'd ) 20', 'e ) 25']", + "Correct": "e", + "Explanation": "volume of prism = area of base * height = 1 / 2 * ( square root of 5 ) * ( square root of 5 ) * 10 = 25 answer : e" + }, + { + "Answer": 2.5, + "Options": "a ) 4 : 5 , b ) 1 : 3 , c ) 2.5 : 1 , d ) 3.5 : 1 , e ) 3 : 2", + "Correct": "c", + "Explanation": "\"d = 2.5 d d = d a \u221a 2 = 2.5 d a \u221a 2 = d a = 2.5 d / \u221a 2 a = d / \u221a 2 = > 2.5 : 1 answer : c\"" + }, + { + "Answer": 53.999999999999964, + "Options": "a ) 54 , b ) 8 , c ) 16 , d ) 24 , e ) 34", + "Correct": "a", + "Explanation": "no . of small cubes will have only one face painted = ( x - 2 ) 2 * 6 here x = side of the small cube = 5 therfore ( x - 2 ) 2 * 6 = 54 answer : a" + }, + { + "Answer": 21, + "Options": "['a ) 14 cms', 'b ) 21 cms', 'c ) 42 cms', 'd ) none of these', 'e ) can not be determined']", + "Correct": "b", + "Explanation": "solution largest size of the tile . h . c . f of 378 cm and 525 cm = 21 cms . answer b" + }, + { + "Answer": 4800, + "Options": "a ) 4500 , b ) 4000 , c ) 4800 , d ) 4600 , e ) 4320", + "Correct": "c", + "Explanation": "\"area of the rhombus = 1 / 2 d 1 d 2 = ( 1 / 2 \u00e3 \u2014 80 \u00e3 \u2014 120 ) cm ( power ) 2 = 80 \u00e3 \u2014 60 = 4800 cm ( power ) 2 answer is c .\"" + }, + { + "Answer": 270, + "Options": "a ) 180 cm , b ) 220 cm , c ) 240 cm , d ) 270 cm , e ) 300 cm", + "Correct": "d", + "Explanation": "\"we have 45 for first triangle , when we join mid - points of first triangle we get the second equilateral triangle then the length of second one is 22.5 and continues . so we have 45 , 22.5 , 11.25 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 45 / 1 - ( 1 / 2 ) = 90 equilateral triangle perimeter is 3 a = 3 * 90 = 270 . so option d .\"" + }, + { + "Answer": 361, + "Options": "a ) 324 , b ) 361 , c ) 400 , d ) 441 , e ) 484", + "Correct": "b", + "Explanation": "\"we know that the perimeter of square = 4 \u00e3 \u2014 side side = 19 cm therefore , perimeter = 4 \u00e3 \u2014 19 cm = 76 cm now , area of the square = ( side \u00e3 \u2014 side ) sq . units = 19 \u00e3 \u2014 19 cm \u00e2 \u00b2 = 361 cm \u00e2 \u00b2 answer : b\"" + }, + { + "Answer": 35, + "Options": "a ) 22 , b ) 38 , c ) 35 , d ) 29 , e ) 18", + "Correct": "c", + "Explanation": "explanation : a triangle is formed by joining any three non - collinear points in pairs . there are 7 non - collinear points the number of triangles formed = \\ inline { \\ color { black } 7 c _ { 3 } } = 35 answer : c ) 35" + }, + { + "Answer": 4, + "Options": "['a ) 2', 'b ) 3', 'c ) 4', 'd ) 5', 'e ) 6']", + "Correct": "c", + "Explanation": "an eqilateral triangle means all sides are equal ; therefore , base = side . the equation is ; base - area + perimeter = b - a + p = b - 1 / 2 bh + 3 b , and b = 2 . so , 2 - 2 / 2 h + 6 = 4 , and 8 - h = 4 . by plugging in the answers we can test the answers quickly ; then , 4 is the only possible answer . answer : c" + }, + { + "Answer": 612, + "Options": "a ) 198 cm 2 , b ) 384 cm 2 , c ) 510 cm 2 , d ) 612 cm 2 , e ) 680 cm 2", + "Correct": "d", + "Explanation": "\"area of a parallelogram = base * height = 34 * 18 = 612 cm 2 answer : d\"" + }, + { + "Answer": 8, + "Options": "['a ) 2', 'b ) 4', 'c ) 8', 'd ) 16', 'e ) none of the above']", + "Correct": "c", + "Explanation": "the answer is c it takes 3 distinct points to define a circle . only 2 are given here . the two points essentially identify a single chord of the circle c . since no other information is provided , however , the radius of the circle can essentially be anything . all this information tell us is that the radius isgreater 8 c" + }, + { + "Answer": 60, + "Options": "a ) 107 , b ) 70 , c ) 78 , d ) 60 , e ) 111", + "Correct": "d", + "Explanation": "\"number of cubes required = volume of box / volume of cube = 10 * 18 * 4 / 12 = 60 cubes answer : d\"" + }, + { + "Answer": 27, + "Options": "['a ) 20 sq . ft', 'b ) 27 sq . ft', 'c ) 37 sq . ft', 'd ) 47 sq . ft', 'e ) 57 sq . ft']", + "Correct": "b", + "Explanation": "other side = 15 2 - 9 2 2 2 ft = 225 - 81 4 4 ft = 144 4 ft = 6 ft . area of closet = ( 6 x 4.5 ) sq . ft = 27 sq . ft . b )" + }, + { + "Answer": 18, + "Options": "['a ) 18', 'b ) 77', 'c ) 625', 'd ) 276', 'e ) 191']", + "Correct": "a", + "Explanation": "explanation : ( or ) { \\ color { black } l ^ { 2 } + b ^ { 2 } = 41 } also , { \\ color { black } ( l + b ) ^ { 2 } = l ^ { 2 } + b ^ { 2 } + 2 lb } = 41 + 40 = 81 ( l + b ) = 9 . perimeter = 2 ( l + b ) = 18 cm . answer : a ) 18" + }, + { + "Answer": 4, + "Options": "a ) 3 : 8 , b ) 3 : 6 , c ) 3 : 7 , d ) 4 : 1 , e ) 3 : 3", + "Correct": "d", + "Explanation": "\"d = 4 d d = d a \u221a 2 = 4 d a \u221a 2 = d a = 4 d / \u221a 2 a = d / \u221a 2 = > 4 : 1 answer : d\"" + }, + { + "Answer": 30, + "Options": "['a ) 36 cm 2', 'b ) 35 cm 2', 'c ) 30 cm 2', 'd ) 32 cm 2', 'e ) 31 cm 2']", + "Correct": "c", + "Explanation": "the triangle with sides 13 cm , 12 cm and 5 cm is right angled , where the hypotenuse is 13 cm . area of the triangle = 1 / 2 * 12 * 5 = 30 cm 2 answer : c" + }, + { + "Answer": 126, + "Options": "['a ) 80', 'b ) 96', 'c ) 108', 'd ) 126', 'e ) 132']", + "Correct": "d", + "Explanation": "imo : d here we have to select 4 points out of 9 points . order is not important so the answer will be 9 c 4 = 126 answer d" + }, + { + "Answer": 100, + "Options": "a ) 200 % , b ) 300 % , c ) 100 % , d ) 500 % , e ) 350 %", + "Correct": "c", + "Explanation": "\"height of = > 100 % so increased by 100 % answer c\"" + }, + { + "Answer": 20, + "Options": "['a ) 16', 'b ) 20', 'c ) 18', 'd ) 22', 'e ) 21']", + "Correct": "b", + "Explanation": "think of an aluminum can can . if you took off the bottom and top and cut a slit down the length , it would flatten to a rectangle . the dimensions of the rectangle are the height of the can and the circumference of the circle . since you know both , use pythagoreans theorem or properties of 3 - 4 - 5 triangles to solve for the hypothenuse , 20 . ( correct answer b )" + }, + { + "Answer": 150, + "Options": "['a ) 25', 'b ) 50', 'c ) 100', 'd ) 150', 'e ) 200']", + "Correct": "d", + "Explanation": "two sides each = x the third = 2 x and the wall length is thus 2 x too x * 2 x = 2 x ^ 2 = 1250 ie x ^ 2 = 625 ie x = 25 l = 50 w = 25 total length of fence = 2 * 25 + 50 = 100 my answer is c" + }, + { + "Answer": 125, + "Options": "['a ) 100', 'b ) 2', 'c ) 5', 'd ) 125', 'e ) 80']", + "Correct": "d", + "Explanation": "the ratio is a 13 : a 23 = 1000 : 8 then number small cubes requiered is 1000 / 8 = 125 so the answre is d" + }, + { + "Answer": 3000, + "Options": "a ) 3008 , b ) 2002 , c ) 1008 , d ) 2016 , e ) 3000", + "Correct": "e", + "Explanation": "\"note that trapezoids axy d and bxy c are congruent , so the area of axy d is always 6000 / 2 = 3000 . correct answer e\"" + }, + { + "Answer": 360, + "Options": "['a ) 560 sq . units', 'b ) 360 sq . units', 'c ) 260 sq . units', 'd ) 460 sq . units', 'e ) 160 sq . units']", + "Correct": "b", + "Explanation": "given that the area of the square = 1225 sq . units = > side of square = \u221a 1296 = 36 units the radius of the circle = side of the square = 35 units length of the rectangle = 2 / 5 * 35 = 14 units given that breadth = 10 units area of the rectangle = lb = 36 * 10 = 360 sq . units answer : b" + }, + { + "Answer": 4, + "Options": "a ) 14 , b ) 8 , c ) 12 , d ) 4 , e ) 18", + "Correct": "d", + "Explanation": "\"let length of rectangle = l 4 ^ 2 = l * 4 = > l = 16 / 4 = 4 answer d\"" + }, + { + "Answer": 45, + "Options": "a ) 5 square meters , b ) 36 square meters , c ) 42 square meters , d ) 45 square meters , e ) 120 square meters", + "Correct": "d", + "Explanation": "\"300 - 180 = 120 sq m of the wallpaper overlaps ( in either two layers or three layers ) if 36 sq m has two layers , 120 - 30 = 90 sq m of the wallpaper overlaps in three layers . 90 sq m makes two extra layers hence the area over which it makes two extra layers is 45 sq m . answer ( d ) .\"" + }, + { + "Answer": 60, + "Options": "['a ) 45', 'b ) 50', 'c ) 60', 'd ) 70', 'e ) 80']", + "Correct": "c", + "Explanation": "we see 68 ^ 2 - 32 ^ 2 = ( 68 + 32 ) * ( 68 - 32 ) = 100 * 36 = 60 ^ 2 now ( 1 / 2 ) * 60 * 32 = 960 ( match with given options ) ( i . e area of a right angled triangle whose sides are 32 , 60,68 ) third side = 60 answer : c" + }, + { + "Answer": 16, + "Options": "['a ) $ 1', 'b ) $ 2', 'c ) $ 4', 'd ) $ 8', 'e ) $ 16']", + "Correct": "e", + "Explanation": "let x be the radius of b and 2 h be the height of b . therefore , radius of n = 2 x and height = h vol of b = 3.14 * x ^ 2 * 2 h vol of a = 3.14 * 4 x ^ 2 * h cost to fill half of b = $ 4 - - > cost to fill full b = $ 8 - - > 3.14 * x ^ 2 * 2 h = 8 - - > 3.14 * x ^ 2 * h = 4 - - > 4 * ( 3.14 * x ^ 2 * h ) = $ 16 ans e" + }, + { + "Answer": 270, + "Options": "a ) 120 cm 2 , b ) 765 cm 2 , c ) 216 cm 2 , d ) 270 cm 2 , e ) 275 cm 2", + "Correct": "d", + "Explanation": "\"the triangle with sides 39 cm , 36 cm and 15 cm is right angled , where the hypotenuse is 39 cm . area of the triangle = 1 / 2 * 36 * 15 = 270 cm 2 answer : d\"" + }, + { + "Answer": 1.6000000000000003, + "Options": "['a ) $ 1.60', 'b ) $ 16.00', 'c ) $ 96.00', 'd ) $ 108.00', 'e ) $ 196.00']", + "Correct": "a", + "Explanation": "total surface area = 6 a ^ 2 = 6 * 10 * 10 = 600 each quart covers 20 sqr ft thus total number of quarts = 600 / 1200 = 0.5 cost will be 0.5 * 3.2 = $ 1.6 ans : a" + }, + { + "Answer": 64, + "Options": "['a ) 8 cc', 'b ) 9 cc', 'c ) 2 cc', 'd ) 4 cc', 'e ) 64 cc']", + "Correct": "e", + "Explanation": "6 a 2 = 96 = 6 * 16 a = 4 = > a 3 = 64 cc answer : e" + }, + { + "Answer": 42, + "Options": "a ) 38 . , b ) 40 . , c ) 42 . , d ) 44 . , e ) 46 .", + "Correct": "c", + "Explanation": "\"let the width = x x * 4 x = 784 x ^ 2 = 196 x = 14 length = 4 * 14 = 56 difference = 56 - 14 = 42 c is the answer\"" + }, + { + "Answer": 144, + "Options": "['a ) 161 m \u00e2 \u00b2 .', 'b ) 144 m \u00e2 \u00b2 .', 'c ) 166 m \u00e2 \u00b2 .', 'd ) 169 m \u00e2 \u00b2 .', 'e ) 273 m \u00e2 \u00b2 .']", + "Correct": "b", + "Explanation": "perimeter of square = 48 m but perimeter of square = 4 \u00e3 \u2014 side therefore , 4 \u00e3 \u2014 side = 48 m therefore , side = 48 / 4 m = 12 m now , the area of the square = ( side \u00e3 \u2014 side ) therefore , area of the square = 12 \u00e3 \u2014 12 m \u00e2 \u00b2 = 144 m \u00e2 \u00b2 . answer : option b" + }, + { + "Answer": 54, + "Options": "a ) 52 , b ) 54 , c ) 55 , d ) 65 , e ) 48", + "Correct": "b", + "Explanation": "\"area of tile = 25 * 16 = 400 area of floor = 180 * 120 = 21600 no of tiles = 21600 / 400 = 54 so , the no of tile = 54 answer : b\"" + }, + { + "Answer": 26, + "Options": "a ) 11 , b ) 17 , c ) 26 , d ) 101 , e ) 1322", + "Correct": "c", + "Explanation": "\"let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 2028 3 b 2 = 2028 b 2 = 676 = 26 ( b > 0 ) b = 26 m . answer : c\"" + }, + { + "Answer": 40, + "Options": "['a ) 40', 'b ) 41', 'c ) 42', 'd ) 43', 'e ) 44']", + "Correct": "a", + "Explanation": "isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side , the longer side with side 13 will be divided into 3 parts = 7 , 3 and 3 ( making one square and two right triangles ) for the right triangle , height will be = ( 5 ^ 2 - 3 ^ 2 ) ^ 1 / 2 = 4 and the area of trapezoid = 1 / 2 ( b 1 + b 2 ) h = 1 / 2 * 20 * 4 = 40 a" + }, + { + "Answer": 5, + "Options": "['a ) 21 .', 'b ) 28 .', 'c ) 5 .', 'd ) 49 .', 'e ) 52 .']", + "Correct": "c", + "Explanation": "delta x will give us the dimension of one side of the parallelogram = 5 - 4 = 1 unit delta y will give us the dimension of the other side of parallelogram = 9 - 4 = 5 unit area of parallelogram = 1 * 5 = 5 answer is c" + }, + { + "Answer": 152, + "Options": "a ) 112 cu cm , b ) 136 cu cm , c ) 164 cu cm , d ) 180 cu cm , e ) 152 cu cm", + "Correct": "e", + "Explanation": "\"sol . surface area = [ 2 ( 8 x 6 + 6 x 2 + 8 x 2 ) ] = ( 2 x 76 ) = 152 cu cm answer e\"" + }, + { + "Answer": 6.4, + "Options": "a ) 3.5 % , b ) 6.4 % , c ) 3 % , d ) 5 % , e ) 2.6 %", + "Correct": "b", + "Explanation": "\"say both sides of the rectangle are equal to 100 ( so consider that we have a square ) . in this case the area is 100 * 100 = 10,000 . now , the area obtained with wrong measurements would be 112 * 95 = 10,640 , which is 6.4 % greater than the actual area . answer : b .\"" + }, + { + "Answer": 43.99999999999999, + "Options": "a ) 33 , b ) 37 , c ) 44 , d ) 99 , e ) 277", + "Correct": "c", + "Explanation": "\"explanation : let original length = x metres and original breadth = y metres . original area = xy increased length = and increased breadth = new area = the difference between the original area and new area is : increase % = = 44 % ] answer : c ) 44 %\"" + }, + { + "Answer": 4500, + "Options": "a ) a ) 3820 , b ) b ) 930 , c ) c ) 9309 , d ) d ) 4500 , e ) e ) 8302", + "Correct": "d", + "Explanation": "\"explanation : area = ( l + b \u2013 d ) d ( 100 + 60 \u2013 10 ) 10 = > 1500 m 2 1500 * 3 = rs . 4500 answer : option d\"" + }, + { + "Answer": 275, + "Options": "['a ) 550', 'b ) 275', 'c ) 50', 'd ) 300', 'e ) 250']", + "Correct": "b", + "Explanation": "piece one as p 1 , and piece two as p 2 . p 2 + 50 = p 1 as eq . a p 1 + p 2 = 600 as eq . b substitute eq . a into eq . b , resulting in ( p 2 + 50 ) + p 2 = 600 mm . group like terms , p 2 + p 2 = 600 - 50 ( 2 * p 2 / 2 ) = 550 / 2 solves to p 2 = 275 . ansewr is b ." + }, + { + "Answer": 84, + "Options": "a ) 84 , b ) 88 , c ) 112 , d ) 116 , e ) 120", + "Correct": "a", + "Explanation": "\"area of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 12 + 12 = 24 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 24 * 7 = 84 a is the answer\"" + }, + { + "Answer": 527.7875658030853, + "Options": "a ) 150 , b ) 170 , c ) 48 , d ) 528 , e ) 600", + "Correct": "d", + "Explanation": "\"\u03c0 * 12 * 14 = 528 answer : d\"" + }, + { + "Answer": 14, + "Options": "['a ) 4', 'b ) 4 \u221a 2', 'c ) 14', 'd ) 8 \u221a 2', 'e ) can not be determined from the information provided']", + "Correct": "c", + "Explanation": "ans c . . 14 . . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 4 or yz = 7 * \\ sqrt { 2 } . . therefore hyp = xy = 14" + }, + { + "Answer": 5938.804937425641, + "Options": "a ) 2399 , b ) 3888 , c ) 2999 , d ) 5940 , e ) 2888", + "Correct": "d", + "Explanation": "\"explanation : area = ( 13.86 x 10000 ) sq . m = 138600 sq . m circumference = cost of fencing = rs . ( 1320 x 4.50 ) = rs . 5940 . answer : d ) 5940\"" + }, + { + "Answer": 125, + "Options": "a ) 120 , b ) 110 , c ) 130 , d ) 140 , e ) 125", + "Correct": "e", + "Explanation": "\"the triangle with sides 26 cm , 25 cm and 10 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 25 * 10 = 125 cm 2 answer : option e\"" + }, + { + "Answer": 165, + "Options": "a ) 188 cm 2 , b ) 165 cm 2 , c ) 168 cm 2 , d ) 198 cm 2 , e ) 987 cm 2", + "Correct": "b", + "Explanation": "\"1 / 2 * 22 ( 9 + 6 ) = 165 cm 2 answer : b\"" + }, + { + "Answer": 180, + "Options": "a ) 281 , b ) 284 , c ) 288 , d ) 255 , e ) 180", + "Correct": "e", + "Explanation": "\"area of a parallelogram = base * height = 18 * 10 = 180 cm 2 answer : e\"" + }, + { + "Answer": 31.41592653589793, + "Options": "a ) 77.14 cm , b ) 47.14 cm , c ) 84.92 cm , d ) 94.94 cm , e ) 31.42 cm", + "Correct": "e", + "Explanation": "\"let the side of the square be a cm . parameter of the rectangle = 2 ( 24 + 16 ) = 80 cm parameter of the square = 80 cm i . e . 4 a = 80 a = 20 diameter of the semicircle = 20 cm circimference of the semicircle = 1 / 2 ( \u220f ) ( 20 ) = 1 / 2 ( 22 / 7 ) ( 20 ) = 440 / 14 = 31.42 cm to two decimal places answer : e\"" + }, + { + "Answer": 495, + "Options": "['a ) 334', 'b ) 377', 'c ) 495', 'd ) 766', 'e ) 261']", + "Correct": "c", + "Explanation": "explanation : for any set of 4 points we get a cyclic quadrilateral . number of ways of choosing 4 points out of 12 points is \\ inline { \\ color { black } 12 c _ 4 { } } = 495 . therefore , we can draw 495 quadrilaterals answer : c ) 495" + }, + { + "Answer": 36, + "Options": "['a ) 36 %', 'b ) 37 %', 'c ) 35 %', 'd ) 38 %', 'e ) 39 %']", + "Correct": "a", + "Explanation": "for 5 cm - > pi * r ^ 2 - - > 3.14 * 5 ^ 2 - > 78.539 for 4 cm - > pi * r ^ 2 - - > 3.14 * 4 ^ 2 - > 50.265 % change - > ( 1 - 50.265 / 78.539 ) * 100 = 36 ie 36 % answer : a" + }, + { + "Answer": 1160, + "Options": "a ) 1160 , b ) 1251 , c ) 1102 , d ) 1352 , e ) 1450", + "Correct": "a", + "Explanation": "\"let the side of the square plot be a ft . a 2 = 25 = > a = 5 length of the fence = perimeter of the plot = 4 a = 20 ft . cost of building the fence = 20 * 58 = rs . 1160 . answer : a\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 5 , c ) 10 , d ) 15 , e ) 20", + "Correct": "a", + "Explanation": "\"longest chord of a circle is the diameter of the circle diameter = 2 * radius if diameter of the circle is given as 24 = 2 * 12 so radius of the circle = 12 correct answer - a\"" + }, + { + "Answer": 0.5625, + "Options": "a ) 3 / 4 , b ) 9 / 16 , c ) 16 / 3 , d ) 4 / 3 , e ) 3 / 16", + "Correct": "b", + "Explanation": "\"the area of rectangle a is ab . c = 4 a / 3 and d = 4 b / 3 . the area of rectangle b is cd = 16 ab / 9 . the ratio of rectangle a ' s area to rectangle b ' s area is ab / ( 16 ab / 9 ) = 9 / 16 . the answer is b .\"" + }, + { + "Answer": 38, + "Options": "['a ) 38', 'b ) 36', 'c ) 40', 'd ) 56', 'e ) 64']", + "Correct": "a", + "Explanation": "perimeter of square = p side of square = p / 4 area of square = ( p ^ 2 ) / 16 = a given that a = 2 p + 14.25 ( p ^ 2 ) / 16 = 2 p + 9 p ^ 2 = 32 p + 228 p ^ 2 - 32 p - 228 = 0 p ^ 2 - 38 p + 6 p - 228 = 0 p ( p - 38 ) + 6 ( p + 38 ) = 0 ( p - 38 ) ( p + 6 ) = 0 p = 38 or - 6 discarding negative value , p = 38 answer is a" + }, + { + "Answer": 1640, + "Options": "a ) $ 880 , b ) $ 1050 , c ) $ 1280 , d ) $ 1460 , e ) $ 1640", + "Correct": "e", + "Explanation": "\"the total surface area is 2 ( 2 * 3 + 3 * 7 + 2 * 7 ) = 82 square feet the total cost is 82 * $ 20 = $ 1640 the answer is e .\"" + }, + { + "Answer": 12, + "Options": "['a ) 30', 'b ) 24', 'c ) 12', 'd ) 8', 'e ) 9']", + "Correct": "c", + "Explanation": "n = side of big cube / side of small cube and no . of smaller cubes with two surfaces painted is ( n - 2 ) * 12 ( 3 - 2 ) * 12 = 12 ans answer : c" + }, + { + "Answer": 89.83333333333333, + "Options": "['a ) 89.8 cm \u00b3', 'b ) 92.5 cm \u00b3', 'c ) 132.8 cm \u00b3', 'd ) 144.5 cm \u00b3', 'e ) none']", + "Correct": "a", + "Explanation": "sol . volume of the block = ( 10 * 5 * 2 ) cm \u00b3 . volume of the cone carved out = [ 1 / 3 * 22 / 7 * 3 * 3 * 7 ] cm \u00b3 = 66 cm \u00b3 \u2234 wood wasted = ( 100 - 66 ) % = 34 % . answer a" + }, + { + "Answer": 4.235294117647059, + "Options": "['a ) 17', 'b ) 45 / 78', 'c ) 72 / 17', 'd ) 17 / 72', 'e ) 72']", + "Correct": "c", + "Explanation": "the wording is a bit confusing , though basically we are told that 1 / r = 1 / 8 + 1 / 9 , from which it follows that r = 72 / 17 . answer : c ." + }, + { + "Answer": 21, + "Options": "a ) 21 , b ) 56.25 , c ) 50.75 , d ) 42.75 , e ) 52.75", + "Correct": "a", + "Explanation": "\"a = 100 a 2 = 10000 a = 110 a 2 = 12100 - - - - - - - - - - - - - - - - 10000 - - - - - - - - - 2100 100 - - - - - - - ? = > 21 % answer : a\"" + }, + { + "Answer": 40, + "Options": "['a ) 10', 'b ) 20', 'c ) 40', 'd ) 60', 'e ) 80']", + "Correct": "c", + "Explanation": "dimensions of newly formed rectangle , length = 8 + 4 = 12 cm breadth = 8 cm perimeter of the new rectangle = 2 x ( 12 = 8 ) = 40 cm answer : c" + }, + { + "Answer": 5184, + "Options": "a ) 4830 , b ) 5184 , c ) 6420 , d ) 8960 , e ) 7960", + "Correct": "b", + "Explanation": "\"clearly , l = ( 48 - 12 ) m = 36 m , b = ( 36 - 12 ) m = 24 m , h = 8 m . volume of the box = ( 36 x 24 x 12 ) m 3 = 5184 m 3 . answer : option b\"" + }, + { + "Answer": 5, + "Options": "a ) 3 cm , b ) 5 cm , c ) 6 cm , d ) 8 cm , e ) none", + "Correct": "b", + "Explanation": "\"solution 4 \u00ee r 2 = 2 \u00ee 5 x 10 \u00e2 \u2021 \u2019 r 2 = ( 5 x 10 / 2 ) \u00e2 \u2021 \u2019 25 \u00e2 \u2021 \u2019 r = 5 cm . answer b\"" + }, + { + "Answer": 360, + "Options": "a ) 180 cm , b ) 220 cm , c ) 240 cm , d ) 270 cm , e ) 360 cm", + "Correct": "e", + "Explanation": "\"we have 60 for first triangle , when we join mid - points of first triangle we get the second equilateral triangle then the length of second one is 30 and continues . so we have 60 , 30,15 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 60 / 1 - ( 1 / 2 ) = 120 equilateral triangle perimeter is 3 a = 3 * 120 = 360 . so option e .\"" + }, + { + "Answer": 340, + "Options": "a ) 320 cm 2 , b ) 360 cm 2 , c ) 340 cm 2 , d ) 310 cm 2 , e ) 300 cm 2", + "Correct": "c", + "Explanation": "\"the triangle with sides 36 cm , 34 cm and 20 cm is right angled , where the hypotenuse is 36 cm . area of the triangle = 1 / 2 * 34 * 20 = 340 cm 2 answer : c\"" + }, + { + "Answer": 0.64, + "Options": "a ) 5 / 4 , b ) 25 / 16 , c ) 4 / 5 , d ) 16 / 25 , e ) 16 / 5", + "Correct": "d", + "Explanation": "\"the area of rectangle a is ab . c = 5 a / 4 and d = 5 b / 4 . the area of rectangle b is cd = 25 ab / 16 . the ratio of rectangle a ' s area to rectangle b ' s area is ab / ( 25 ab / 16 ) = 16 / 25 . the answer is d .\"" + }, + { + "Answer": 40, + "Options": "['a ) 20 m', 'b ) 24 m', 'c ) 28 m', 'd ) 40 m', 'e ) 43 m']", + "Correct": "d", + "Explanation": "perimeter of square = 4 * side perimeter of first square = 24 m . side of first square = \u2234 area of first square = perimeter of second square = 32 m . side of second square = \u2234 area of second square = sum of the areas of two squares = 36 + 64 = 100 m 2 \u2234 side of square = \u2234 perimeter of square = 4 * 10 = 40 m . d" + }, + { + "Answer": 180, + "Options": "['a ) 120 l', 'b ) 180 l', 'c ) 240 l', 'd ) 300 l', 'e ) 360 l']", + "Correct": "b", + "Explanation": "pi \u2217 r ^ 2 \u2217 h = 60 double the radius . . . . . pi \u2217 ( 2 r ) ^ 2 \u2217 h = pi \u2217 4 \u2217 r ^ 2 \u2217 h = 4 \u2217 60 = 240 important . . we are looking at the increase so 240 - 60 = 180 answer : b" + }, + { + "Answer": 0.4, + "Options": "['a ) 1 / 6', 'b ) 1 / 5', 'c ) 3 / 10', 'd ) 1 / 3', 'e ) 4 / 10']", + "Correct": "e", + "Explanation": "a square with an area of 4 has a perimeter of 8 . for the area to be > 4 , the longer piece must be > 8 . the wire must be cut within 2 meters from either end . the probability of this is 4 / 10 = 2 / 5 . the answer is e ." + }, + { + "Answer": 0.1111111111111111, + "Options": "a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 5 , e ) 1 / 3", + "Correct": "a", + "Explanation": "\"if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 8,12 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives s = 1 / 9 . a\"" + }, + { + "Answer": 8, + "Options": "a ) 10 feet , b ) 8 feet , c ) 13 feet , d ) 15 feet , e ) 18 feet", + "Correct": "b", + "Explanation": "\"total circuit = 16 / 4 = 4 total feet squirrel travels = 4 * 2 = 8 feet answer : b\"" + }, + { + "Answer": 4, + "Options": "a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) none of the above", + "Correct": "b", + "Explanation": "\"it takes 3 distinct points to define a circle . only 2 are given here . the two points essentially identify a single chord of the circle c . since no other information is provided , however , the radius of the circle can essentially be anything . all this information tell us is that the radius isgreater 4 b\"" + }, + { + "Answer": 400.4747183031658, + "Options": "a ) 410.47 , b ) 403.47 , c ) 420.47 , d ) 400.47 , e ) 300.47", + "Correct": "d", + "Explanation": "\"area of the rhombus = 1 / 2 * p * \u221a 4 ( a ) 2 - ( p ) 2 a = 24 ; p = 18 a = 1 / 2 * 18 * \u221a 4 ( 24 ) 2 - ( 18 ) 2 = 1 / 2 * 18 * \u221a 2304 - 324 = 1 / 2 * 18 * \u221a 1980 a = 400.47 answer : d\"" + }, + { + "Answer": 14, + "Options": "a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 14", + "Correct": "e", + "Explanation": "solution : this problem is testing us on the rule that when we express a perfect square by its unique prime factors , every prime factor ' s exponent is an even number . let \u2019 s start by prime factorizing 3150 . 3150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2 3150 = 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 ( notice that the exponents of both 2 and 7 are not even numbers . this tells us that 3150 itself is not a perfect square . ) we also are given that 3150 multiplied by g is the square of an integer . we can write this as : 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 x g = square of an integer according to our rule , we need all unique prime factors ' exponents to be even numbers . thus , we need one more 2 and one more 7 . therefore , g = 7 x 2 = 14 answer is e ." + }, + { + "Answer": 0.5625, + "Options": "['a ) 9 / 16', 'b ) 8 / 16', 'c ) 7 / 16', 'd ) 6 / 16', 'e ) 5 / 16']", + "Correct": "a", + "Explanation": "area of tri ( ade ) / area of tri ( abc ) = de ^ 2 / bc ^ 2 since tri ( ade ) - tri ( abc ) area of tri ( ade ) / area of tri ( abc ) = 9 / 25 area of tri ( abc ) / area of tri ( ade ) = 25 / 9 area of tri ( abc ) = area of tri ( ade ) + area of trap ( bcde ) ( area of tri ( ade ) + area of trap ( bcde ) ) / area of tri ( ade ) = 25 / 9 1 + area of trap ( bcde ) / area of tri ( ade ) = 25 / 9 take 1 on both sides area of trap ( bcde ) / area of tri ( ade ) = ( 25 / 9 ) - 1 = 16 / 9 since question is asking for area of tri ( ade ) / area of trap ( bcde ) = 9 / 16 answer : a" + }, + { + "Answer": 18.999999999999993, + "Options": "['a ) 22', 'b ) 19', 'c ) 877', 'd ) 26', 'e ) 271']", + "Correct": "b", + "Explanation": "explanation : let old radius = 10 units . new radius is diminshed by 10 % . so new radius = 90 % ( 10 ) = 9 units . old area = \u03c0 \u00d7 r 2 = 100 \u03c0 new area = \u03c0 \u00d7 92 = 81 \u03c0 change = 19 \u03c0 / 100 \u03c0 \u00d7 100 = 19 % answer : b" + }, + { + "Answer": 4, + "Options": "['a ) 2 : 1', 'b ) 1 : 2', 'c ) 2 : 3', 'd ) 1 : 4', 'e ) 4 : 1']", + "Correct": "e", + "Explanation": "lenth of the diagonals be 2 x and x units . areas are 1 / 2 \u00d7 ( 2 x ) power 2 and ( 1 / 2 \u00d7 ( xpower 2 ) ) required ratio = 1 / 2 \u00d7 4 x 2 : 1 / 2 x 2 = 4 : 1 answer is e ." + }, + { + "Answer": 300, + "Options": "['a ) 189 cm 2', 'b ) 300 cm 2', 'c ) 127 cm 2', 'd ) 177 cm 2', 'e ) 187 cm 2']", + "Correct": "b", + "Explanation": "1 / 2 * 40 ( 9 + 6 ) = 300 cm 2 answer : b" + }, + { + "Answer": 120, + "Options": "a ) 120 cm , b ) 767 cm , c ) 88 cm , d ) 666 cm , e ) 776 cm", + "Correct": "a", + "Explanation": "\"area of each slab = 72 / 50 m 2 = 1.44 m 2 length of each slab \u221a 1.44 = 1.2 m = 120 cm\"" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 5 , c ) 6 , d ) 8 , e ) 10", + "Correct": "a", + "Explanation": "\"ans is ` ` b ' ' . for max volume of cylinder ( pi * r ^ 2 * h ) we need to max out r ^ 2 * h . we do n ' t know what the dimensions of the crate refer to . so to maximize the above eqn , radius may be of 9 , 10,12 one of the base area ( 8 x 12 , 14 x 12 or 8 x 14 ) r is maximum for base 14 x 12 and 12 can be maximum value so r = 10 / 2 = 6 a\"" + }, + { + "Answer": 10, + "Options": "['a ) 10', 'b ) 11', 'c ) 12', 'd ) 9', 'e ) 8']", + "Correct": "a", + "Explanation": "see the values row wise 5 6 n 7 11 6 + n 7 + n 11 + 6 + n 6 + n + 7 + n 60 hence 11 + 6 + n + 6 + n + 7 + n = 60 n = 10 answer : a" + }, + { + "Answer": 2743.999999999999, + "Options": "a ) 24 , b ) 48 , c ) 64 , d ) 2744 , e ) 100", + "Correct": "d", + "Explanation": "\"volume = 343 = side ^ 3 i . e . side of cube = 7 new cube has dimensions 14 , 14 , and 14 as all sides are twice of teh side of first cube volume = 14 * 14 * 14 = 2744 square feet answer : option d\"" + }, + { + "Answer": 99, + "Options": "a ) 64 , b ) 72 , c ) 86 , d ) 98 , e ) 99", + "Correct": "e", + "Explanation": "\"use the options . the options which after getting added to 26 shows a cube of a number could be right . here 64 + 26 = 90 72 + 26 = 98 86 + 26 = 112 98 + 26 + 124 99 + 26 = 125 - - - ( 5 * 5 * 5 ) so we have 99 as the answer ! e\"" + }, + { + "Answer": 12.000000000000002, + "Options": "a ) 4 , b ) 4 \u221a 2 , c ) 12 , d ) 8 \u221a 2 , e ) can not be determined from the information provided", + "Correct": "c", + "Explanation": "\"ans c . . 12 . . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 36 or yz = 3 * \\ sqrt { 2 } . . therefore hyp = xy = 12\"" + }, + { + "Answer": 160250, + "Options": "['a ) 150,200', 'b ) 140,300', 'c ) 100,300', 'd ) 160,250', 'e ) 100,200']", + "Correct": "d", + "Explanation": "let length l = 25 x and breadth b = 16 x area of the square = 200 ^ 2 = 40000 16 x * 25 x = 40000 400 x ^ 2 = 40000 x ^ 2 = 100 x = 10 length = 25 * 10 = 250 breadth = 16 * 10 = 160 answer : d" + }, + { + "Answer": 125, + "Options": "['a ) 5', 'b ) 125', 'c ) 4', 'd ) 100', 'e ) 24']", + "Correct": "b", + "Explanation": "the ratio between larger and smaller is 6 a 12 : 6 a 22 = 600 : 24 a 12 : a 22 = 100 : 4 a 1 : a 2 = 10 : 2 then length of cube is 10 and 2 so make a cube with length 10 , we have to 5 small cubes each in length , breadth and height . so total 125 cubes are required . then the answer is b" + }, + { + "Answer": 117.62122895040181, + "Options": "['a ) 118.67', 'b ) 116.67', 'c ) 117.67', 'd ) 120.56', 'e ) 120.57']", + "Correct": "c", + "Explanation": "req . area = \u00ef \u20ac [ ( 16.2 ) 2 \u00e2 \u20ac \u201c ( 15 ) 2 ] = 22 \u00e2 \u0081 \u201e 7 \u00e3 \u2014 ( 31.2 \u00e3 \u2014 1.2 ) [ since a 2 - b 2 = ( a + b ) ( a - b ) ] = ( 22 \u00e3 \u2014 31.2 \u00e3 \u2014 1.2 ) / 7 = 117.67 sq m answer c" + }, + { + "Answer": 480, + "Options": "['a ) 488', 'b ) 429', 'c ) 418', 'd ) 480', 'e ) 410']", + "Correct": "d", + "Explanation": "262 \u2013 102 = 242 d 1 = 20 d 2 = 48 1 / 2 * 20 * 48 = 480 answer : d" + }, + { + "Answer": 145, + "Options": "a ) 75 % , b ) 80 % , c ) 145 % , d ) 150 % , e ) 180 %", + "Correct": "c", + "Explanation": "\"let length of each side of square a be 10 area of a = 10 ^ 2 = 100 since , length of each side of square a is increased by 100 percent to make square b length of each side of square b = 2 * 10 = 20 area of b = 20 ^ 2 = 400 since , length of the side of square b is increased by 75 percent to make square c length of each side of square c = 1.75 * 20 = 35 area of c = 35 ^ 2 = 1225 difference in areas of c and cummulative areas of a and b = 1225 - ( 400 + 100 ) = 725 percent is the area of square c greater than the sum of the areas of squares a and b = ( 725 / 500 ) * 100 % = 145 % answer c\"" + }, + { + "Answer": 153.93804002589985, + "Options": "['a ) 237', 'b ) 154', 'c ) 2376', 'd ) 198', 'e ) 171']", + "Correct": "b", + "Explanation": "explanation : the diameter is equal to the shortest side of the rectangle . so radius = 14 / 2 = 7 cm . answer : b ) 154" + }, + { + "Answer": 876, + "Options": "a ) rs . 692 , b ) rs . 768 , c ) rs . 876 , d ) rs . 972 , e ) none", + "Correct": "c", + "Explanation": "\"solution surface area of the cube = ( 6 \u00d7 82 ) sq . ft = 384 sq . ft . quantity of paint required = ( 384 / 16 ) kg \u2039 = \u203a 24 kg . cost of painting = rs . ( 36.50 \u00d7 24 ) = rs . 876 . answer c\"" + }, + { + "Answer": 50.26548245743669, + "Options": "a ) 24 cm \u00b2 , b ) 44 cm \u00b2 , c ) 50 cm \u00b2 , d ) 84 cm \u00b2 , e ) 94 cm \u00b2", + "Correct": "c", + "Explanation": "\"area of circle = \u03c0 r \u00b2 = 22 / 7 \u00d7 4 \u00d7 4 cm \u00b2 = 50 cm \u00b2 answer : c\"" + }, + { + "Answer": 25.132741228718345, + "Options": "a ) 32 m 3 , b ) 25.1 m 3 , c ) 40 m 3 , d ) 44 m 3 , e ) none", + "Correct": "b", + "Explanation": "\"solution volume = \u03c0 r 2 h \u2039 = \u203a ( 22 / 7 \u00d7 1 \u00d7 1 \u00d7 8 ) m 3 \u2039 = \u203a 25.1 m 3 . answer b\"" + }, + { + "Answer": 7, + "Options": "a ) 3 : 7 , b ) 3 : 5 , c ) 3 : 8 , d ) 7 : 1 , e ) 3 : 5", + "Correct": "d", + "Explanation": "\"d = 7 d d = d a \u221a 2 = 7 d a \u221a 2 = d a = 7 d / \u221a 2 a = d / \u221a 2 = > 7 : 1 answer : d\"" + }, + { + "Answer": 0.7538461538461538, + "Options": "a ) 0.25 , b ) 0.5 , c ) 0.75 , d ) 0.1 , e ) 0.3", + "Correct": "c", + "Explanation": "\"i guess it ' s mean that square b is placed within square aentirely . since , the perimeter of b is 16 , then its side is 16 / 4 = 4 and the area is 4 ^ 2 = 16 ; empty space between the squares is 65 - 16 = 48 square centimeters , so if a random point is in this area then it wo n ' t be within square b : p = favorable / total = 48 / 64 = 0.75 . answer : c\"" + }, + { + "Answer": 76, + "Options": "a ) 34 , b ) 40 , c ) 68 , d ) 76 , e ) 92", + "Correct": "d", + "Explanation": "\"given that length and area , so we can find the breadth . length x breadth = area 20 x breadth = 560 breadth = 28 feet area to be fenced = 2 b + l = 2 ( 28 ) + 20 = 76 feet answer : d\"" + }, + { + "Answer": 20, + "Options": "['a ) 90', 'b ) 85', 'c ) 70', 'd ) 35', 'e ) 20']", + "Correct": "e", + "Explanation": "number of diagonals in any polygon can be found using this formula : n ( n - 3 ) / 2 here n = 8 no . of diagonals = 8 ( 8 - 3 ) / 2 = 20 ans e" + }, + { + "Answer": 108, + "Options": "a ) 432 , b ) 108 , c ) 252 , d ) 992 , e ) 212", + "Correct": "b", + "Explanation": "\"2 ( 3 x + x ) = 48 l = 18 b = 6 lb = 18 * 6 = 108 answer : b\"" + }, + { + "Answer": 60, + "Options": "a ) 76 , b ) 88 , c ) 60 , d ) 55 , e ) 35", + "Correct": "c", + "Explanation": "\"area of a triangle = r * s where r is the in radius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 48 / 2 = 60 cm 2 answer : c\"" + }, + { + "Answer": 1760, + "Options": "a ) 1800 , b ) 1760 , c ) 1400 , d ) 2600 , e ) 3600", + "Correct": "b", + "Explanation": "let the side of the square plot be a ft . a 2 = 484 = > a = 22 length of the fence = perimeter of the plot = 4 a = 88 ft . cost of building the fence = 88 * 20 = rs . 1760 . answer : b" + }, + { + "Answer": 47.77142857142857, + "Options": "a ) 30 m 2 , b ) 40 m 2 , c ) 47.7 m 2 , d ) 50 m 2 , e ) 55 m 2", + "Correct": "c", + "Explanation": "\"38 / 360 * 22 / 7 * 12 * 12 = 47.7 m 2 answer : c\"" + }, + { + "Answer": 750, + "Options": "a ) 120 cm 2 , b ) 750 cm 2 , c ) 216 cm 2 , d ) 197 cm 2 , e ) 275 cm 2", + "Correct": "b", + "Explanation": "\"the triangle with sides 65 cm , 60 cm and 25 cm is right angled , where the hypotenuse is 65 cm . area of the triangle = 1 / 2 * 60 * 25 = 750 cm 2 answer : b\"" + }, + { + "Answer": 64, + "Options": "['a ) 77 cm', 'b ) 88 cm', 'c ) 64 cm', 'd ) 11 cm', 'e ) 18 cm']", + "Correct": "c", + "Explanation": "let breadth = x cm , then , length = 3 x cm x 2 + ( 3 x ) 2 = ( 810 \u2212 \u2212 \u221a ) 2 = > 10 x 2 = 640 = > x = 8 x 2 + ( 3 x ) 2 = ( 810 ) 2 = > 10 x 2 = 640 = > x = 8 so , length = 24 cm and breadth = 8 cm perimeter = 2 ( l + b ) = 2 ( 24 + 8 ) = 64 cm answer : c" + }, + { + "Answer": 64, + "Options": "['a ) 32', 'b ) 64', 'c ) 25', 'd ) 16', 'e ) none']", + "Correct": "b", + "Explanation": "solution : let the original length of the rectangle be 20 unit and breadth be 10 unit . then original area = length * breadth = 20 * 10 = 200 square unit . 40 % decrease in each side , then length = ( 20 - 40 % of 20 ) = 12 unit . breadth = ( 10 - 40 % of 10 ) = 6 unit . now , area = 12 * 6 = 72 square unit . decrease in area = 200 - 72 = 128 square unit . % decrease in area = ( 128 / 200 ) * 100 = 64 % mind calculation method : let the original area be 100 square unit . 100 = = = 40 % \u2193 ( decrease in length ) = = = > 60 = = = 40 % \u2193 = = = ( decrease in breadth ) = = = > 36 . diminished in area = 100 - 36 = 64 % answer : option b" + }, + { + "Answer": 17, + "Options": "['a ) 7', 'b ) 21', 'c ) 19', 'd ) 15', 'e ) 17']", + "Correct": "e", + "Explanation": "x ^ 2 \u00e2 \u20ac \u201c x = 272 = > x = 17 answer e" + }, + { + "Answer": 5806.831494371739, + "Options": "a ) 2399 , b ) 3888 , c ) 2999 , d ) 5808 , e ) 2888", + "Correct": "d", + "Explanation": "\"explanation : area = ( 13.86 x 10000 ) sq . m = 138600 sq . m circumference = cost of fencing = rs . ( 1320 x 4.40 ) = rs . 5808 . answer : d ) 5808\"" + }, + { + "Answer": 88, + "Options": "a ) 277 , b ) 266 , c ) 150 , d ) 88 , e ) 212", + "Correct": "d", + "Explanation": "\"1 / 2 * 11 * 16 = 88 answer : d\"" + }, + { + "Answer": 32, + "Options": "['a ) 10 cm', 'b ) 15 cm', 'c ) 32 cm', 'd ) 35 cm', 'e ) 20 cm']", + "Correct": "c", + "Explanation": "perimeter of triangle = a + b + c perimeter = 7 cm + 10 cm + 15 cm = 32 cm answer : c ." + }, + { + "Answer": 0.7142857142857143, + "Options": "a ) 4 / 5 , b ) 5 / 4 , c ) 3 / 2 , d ) 5 / 7 , e ) 2 / 3", + "Correct": "d", + "Explanation": "\"we are basically given that the triangles are similar . in two similar triangles , the ratio of their areas is the square of the ratio of their sides and also , the square of the ratio of their corresponding heights . therefore , area / area = height ^ 2 / height ^ 2 = 25 / 49 - - > height / height = 5 / 7 . answer : d .\"" + }, + { + "Answer": 30, + "Options": "['a ) 20', 'b ) 30', 'c ) 40', 'd ) 50', 'e ) 60']", + "Correct": "b", + "Explanation": "if each side is 120 feet . . then total perimeter is 150 * 4 = 600 poles every 20 feet hence no of poles = 600 / 20 = 30 answer : b" + }, + { + "Answer": 10.995574287564276, + "Options": "a ) 23.56 , b ) 23.59 , c ) 23.55 , d ) 23.53 , e ) 11.0", + "Correct": "e", + "Explanation": "\"let the side of the square be a cm . parameter of the rectangle = 2 ( 8 + 6 ) = 28 cm parameter of the square = 28 cm i . e . 4 a = 28 a = 7 diameter of the semicircle = 7 cm circimference of the semicircle = 1 / 2 ( \u00e2 \u02c6 \u008f ) 7 = 1 / 2 ( 22 / 7 ) ( 7 ) = 11 cm answer : e\"" + }, + { + "Answer": 11, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", + "Correct": "d", + "Explanation": "\"let t be the number of trees . then the length required for trees on the sidewalk will be 1 * t = t to maximize the number of trees , the number of 14 feet spaces between trees should be 1 less than total number of trees . for example , if there are 3 trees , then there should be 2 spaces between them . so the number of 14 feet spaces will be t - 1 . then , the length of sidewalk required for 14 feet spaces will be 14 * ( t - 1 ) it is given that total lenght of sidewalk is 166 feet . or 14 ( t - 1 ) + t = 151 or 14 t - 14 + t = 151 or 15 t = 165 or t = 11 answer : - d\"" + }, + { + "Answer": 56, + "Options": "a ) 48 , b ) 56 , c ) 60 , d ) 56 , e ) 192", + "Correct": "d", + "Explanation": "\"say length of garden is l meters . then ( l * 12 ) = 16 * 12 [ given area is same . area = l * b ] therefore l works out to 16 meters . perimeter of garden = 2 * ( 16 + 12 ) = 56 meter . answer is d\"" + }, + { + "Answer": 945, + "Options": "a ) 875 , b ) 945 , c ) 1425 , d ) 2025 , e ) 2500", + "Correct": "b", + "Explanation": "\"there ' s a direct formula for this . number of diagonals in a regular polygon = [ n * ( n - 3 ) ] / 2 , n = number of sides of the regular polygon . here , n = 45 . plugging it in , we get 945 diagonals ! answer ( b ) .\"" + }, + { + "Answer": 24, + "Options": "['a ) 36', 'b ) 32', 'c ) 24', 'd ) 21', 'e ) 15']", + "Correct": "c", + "Explanation": "27 cubic centimetre cubes gives side = 3 cm so if : l * w * h is 9 * 12 * 8 , then max . cube we can have are 3 * 4 * 2 = 24 l * w * h is 9 * 8 * 12 , then max . cube we can have are 3 * 2 * 4 = 24 l * w * h is 12 * 8 * 9 , then max . cube we can have are 4 * 2 * 3 = 24 l * w * h is 12 * 9 * 8 , then max . cube we can have are 4 * 3 * 2 = 24 l * w * h is 8 * 12 * 9 , then max . cube we can have are 2 * 4 * 3 = 24 l * w * h is 8 * 9 * 12 , then max . cube we can have are 2 * 3 * 4 = 24 in all cases we get t = 24 cubes . ans . c" + }, + { + "Answer": 96, + "Options": "a ) 24 a 8 , b ) 24 a 4 , c ) 96 a 2 , d ) 24 a 2 , e ) 24 a 7", + "Correct": "c", + "Explanation": "\"6 a 2 = 6 * 4 a * 4 a = 96 a 2 answer : c\"" + }, + { + "Answer": 35.42, + "Options": "a ) 35.22 , b ) 33.52 , c ) 35.42 , d ) 36.22 , e ) 38.42", + "Correct": "c", + "Explanation": "\"100 * 100 = 10000 111 * 122 = 13542 - - - - - - - - - - - - 3542 10000 - - - - - - - 3542 100 - - - - - - - - - - 35.42 answer c\"" + }, + { + "Answer": 385, + "Options": "a ) 160 , b ) 240 , c ) 385 , d ) 440 , e ) 560", + "Correct": "c", + "Explanation": "\"the number of jumbo tiles = x . the number of regular tiles = 2 x . assume the ratio of the dimensions of a regular tile is a : a - - > area = a ^ 2 . the dimensions of a jumbo tile is 3 a : 3 a - - > area = 9 a ^ 2 . the area of regular tiles = 2 x * a ^ 2 = 70 . the area of jumbo tiles = x * 9 a ^ 2 = 4.5 ( 2 x * a ^ 2 ) = 4.5 * 70 = 315 . total area = 70 + 315 = 385 answer : c .\"" + }, + { + "Answer": 8473.409170212508, + "Options": "a ) 2996 sq m , b ) 2897 sq m , c ) 4312 sq m , d ) 5768 sq m , e ) 8470 sq m", + "Correct": "e", + "Explanation": "\"let the radii of the smaller and the larger circles be s m and l m respectively . 2 \u220f s = 132 and 2 \u220f l = 352 s = 132 / 2 \u220f and l = 352 / 2 \u220f difference between the areas = \u220f l ^ 2 - \u220f s ^ 2 = \u220f { 66 ^ 2 / \u220f ^ 2 - 132 ^ 2 / \u220f ^ 2 } = 66 ^ 2 / \u220f - 132 ^ 2 / \u220f = ( 66 - 132 ) ( 66 + 132 ) / \u220f = ( 110 ) ( 242 ) / ( 22 / 7 ) = 8470 sq m answer : e\"" + }, + { + "Answer": 12, + "Options": "['a ) 12 cm 2', 'b ) 16 cm 2', 'c ) 20 cm 2', 'd ) 24 cm', 'e ) none of these']", + "Correct": "a", + "Explanation": "in a rectangle , ( perimeter ) 2 / 4 = ( diagonal ) 2 + 2 \u00d7 area \u21d2 ( 14 ) 2 / 4 = 5 ( 2 ) + 2 \u00d7 area 49 = 25 + 2 \u00d7 area \u2234 area = 49 \u2212 25 / 2 = 24 / 2 = 12 cm 2 answer a" + }, + { + "Answer": 495, + "Options": "a ) 160 , b ) 240 , c ) 360 , d ) 495 , e ) 560", + "Correct": "d", + "Explanation": "\"the number of jumbo tiles = x . the number of regular tiles = 2 x . assume the ratio of the dimensions of a regular tile is a : a - - > area = a ^ 2 . the dimensions of a jumbo tile is 3 a : 3 a - - > area = 9 a ^ 2 . the area of regular tiles = 2 x * a ^ 2 = 90 . the area of jumbo tiles = x * 9 a ^ 2 = 4.5 ( 2 x * a ^ 2 ) = 4.5 * 90 = 405 . total area = 90 + 405 = 495 answer : d .\"" + }, + { + "Answer": 516, + "Options": "['a ) 816', 'b ) 516', 'c ) 716', 'd ) 216', 'e ) 916']", + "Correct": "b", + "Explanation": "lateral surface = 4 a ( power ) 2 4 \u00d7 12 ( power ) 2 = 4 \u00d7 144 = > 516 m ( power ) 2 answer is b ." + }, + { + "Answer": 124.93242414866094, + "Options": "['a ) a 125', 'b ) b 120', 'c ) c 70', 'd ) d 40', 'e ) e 10']", + "Correct": "a", + "Explanation": "l = 120 / 12 = 10 ft w = 108 / 12 = 9 ft area of paper = 90 area of cube = 10 * side ^ 2 side of cube = 5 v of cube = 125" + }, + { + "Answer": 599.9999999999998, + "Options": "a ) 864 , b ) 556 , c ) 255 , d ) 600 , e ) 267", + "Correct": "d", + "Explanation": "\"a 3 = 1000 = > a = 10 6 a 2 = 6 * 10 * 10 = 600 answer : d\"" + }, + { + "Answer": 43.982297150257104, + "Options": "['a ) 40 m 3', 'b ) 42 m 3', 'c ) 44 m 3', 'd ) 46 m 3', 'e ) none of these']", + "Correct": "c", + "Explanation": "explanation : volume = \u03c0 r 2 hvolume = ( 22 / 7 \u2217 1 \u2217 1 \u2217 14 ) m 3 = 44 m 3 option c" + }, + { + "Answer": 48, + "Options": "a ) 23 , b ) 32 , c ) 34 , d ) 43 , e ) 48", + "Correct": "e", + "Explanation": "\"explanation : a / 18 = 8 * 8 = > a = 8 * 8 * 18 x * 2 x = 8 * 8 * 18 x = 24 = > 2 x = 48 answer : option e\"" + }, + { + "Answer": 750, + "Options": "['a ) 750', 'b ) 850', 'c ) 950', 'd ) 1050', 'e ) none of the above']", + "Correct": "a", + "Explanation": "let the dimensions of the box be , length = 5 * a , breadth = 5 * ( a + 1 ) , height = 5 * ( a + 2 ) hence , volume = 5 * 5 * 5 * a * ( a + 1 ) * ( a + 2 ) among any 3 consecutive positive integers , we will either have ( a number that is divisible by both 23 ) or ( a number divisible by 2 and another number divisible by 3 ) . volume = multiple of ( 125 * 2 * 3 ) 750 = 125 * 2 * 3 answer : a" + }, + { + "Answer": 24, + "Options": "['a ) 36', 'b ) 32', 'c ) 24', 'd ) 21', 'e ) 15']", + "Correct": "c", + "Explanation": "27 cubic centimetre cubes gives side = 3 cm so if : l * w * h is 9 * 12 * 8 , then max . cube we can have are 3 * 4 * 2 = 24 l * w * h is 9 * 8 * 12 , then max . cube we can have are 3 * 2 * 4 = 24 l * w * h is 12 * 8 * 9 , then max . cube we can have are 4 * 2 * 3 = 24 l * w * h is 12 * 9 * 8 , then max . cube we can have are 4 * 3 * 2 = 24 l * w * h is 8 * 12 * 9 , then max . cube we can have are 2 * 4 * 3 = 24 l * w * h is 8 * 9 * 12 , then max . cube we can have are 2 * 3 * 4 = 24 in all cases we get q = 24 cubes . ans . c" + }, + { + "Answer": 9, + "Options": "a ) 0 % , b ) 20 % increase , c ) 20 % decrease , d ) 9 % decrease , e ) insufficient data", + "Correct": "d", + "Explanation": "\"( 13 / 10 ) * ( 7 / 10 ) = 91 / 100 of original area 91 / 100 is a 9 % decrease from 100 / 100 - > d\"" + }, + { + "Answer": 3944, + "Options": "['a ) rs . 3944', 'b ) rs . 3942', 'c ) rs . 3987', 'd ) rs . 3929', 'e ) rs . 3938']", + "Correct": "a", + "Explanation": "let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 58 = rs . 3944 . answer : a" + }, + { + "Answer": 72, + "Options": "['a ) a ) 160 degree', 'b ) b ) 168 degree', 'c ) c ) 191 degree', 'd ) d ) 72 degree', 'e ) e ) 204 degree']", + "Correct": "d", + "Explanation": "let the common ratio be x . . so m = 2 x and f = 3 x and total = 5 x 1 of m = 2 x and 1 of f = 3 x . . total preferring that carrer = 5 x now 5 x = 360 , so x = 360 / 5 = 72 . . so x * 8 / 3 = 72 * 8 / 3 = 192 d" + }, + { + "Answer": 143.5, + "Options": "a ) 143.5 , b ) 154 , c ) 160 , d ) 148.75 , e ) 142.25", + "Correct": "a", + "Explanation": "\"if we take a square with side length x and draw a diagonal , we get two isosceles right triangles . if we focus on one such right triangle , we see that the legs have length x . square 24 - inch flat - screen television the diagonal ( hypotenuse ) = 24 so , we can apply the pythagorean theorem to get x \u00b2 + x \u00b2 = 24 \u00b2 simplify : 2 x \u00b2 = 24 \u00b2 divide both sides by 2 to get : x \u00b2 = 24 \u00b2 / 2 since the area of the square = x \u00b2 , we can see that the area of this square is 24 \u00b2 / 2 square 17 - inch flat - screen television the diagonal ( hypotenuse ) = 17 so , we can apply the pythagorean theorem to get x \u00b2 + x \u00b2 = 17 \u00b2 simplify : 2 x \u00b2 = 17 \u00b2 divide both sides by 2 to get : x \u00b2 = 17 \u00b2 / 2 since the area of the square = x \u00b2 , we can see that the area of this square is 17 \u00b2 / 2 difference in areas = 24 \u00b2 / 2 - 17 \u00b2 / 2 = 288 - 144.5 i . e = 143.5 a\"" + }, + { + "Answer": 1240, + "Options": "a ) $ 1100 , b ) $ 1240 , c ) $ 1360 , d ) $ 1480 , e ) $ 1550", + "Correct": "b", + "Explanation": "\"the total surface area is 2 ( 2 * 3 + 3 * 5 + 2 * 5 ) = 62 square feet the total cost is 62 * $ 20 = $ 1240 the answer is b .\"" + }, + { + "Answer": 71.9822971502571, + "Options": "['a ) 55', 'b ) 86', 'c ) 25', 'd ) 72', 'e ) 35']", + "Correct": "d", + "Explanation": "perimeter of a circle = 2 pi * r perimeter of a semicircle = pi * r + 2 r aprox perimiter = 3.14 * 14 + 2 * 14 = 71.96 approximately 72 answer d" + }, + { + "Answer": 50, + "Options": "a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90", + "Correct": "a", + "Explanation": "\"let l be the length and w be the width . l = ( 7 / 5 ) w perimeter : 2 l + 2 w = 240 , 2 ( 7 / 5 ) w + 2 w = 240 solve the above equation to find : w = 50 m and l = 70 m . correct answer a ) 50\"" + }, + { + "Answer": 20, + "Options": "a ) 35 , b ) 40 , c ) 25 , d ) 18 , e ) 20", + "Correct": "e", + "Explanation": "\"area of tile = 45 * 50 = 2250 area of floor = 250 * 180 = 45000 no of tiles = 45000 / 2250 = 20 so , the no of tile = 20 answer : e\"" + }, + { + "Answer": 10, + "Options": "['a ) 30 cm', 'b ) 10 cm', 'c ) 50 cm', 'd ) 90 cm', 'e ) 70 cm']", + "Correct": "b", + "Explanation": "the volume of a rectangular prism is given by area of base ? height the rate at which the tank is being filled is 1 liter per minute which we need to convert 1 liter = 1 dm 3 but 1 dm = 10 cm . hence 1 liter = ( 10 cm ) 3 = 1000 cm 3 the height h of the water is related to the volume by volume = area of base * h in one minute the volume increases by 1 liter or 1000 cm 3 and the height increases by h = volume / area of base = 1000 cm 3 / 100 cm 2 = 10 cm correct answer b" + }, + { + "Answer": 30, + "Options": "a ) 38 . , b ) 30 . , c ) 42 . , d ) 44 . , e ) 46 .", + "Correct": "b", + "Explanation": "\"let the width = x x * 3 x = 675 x ^ 2 = 225 x = 15 length = 3 * 15 = 45 difference = 45 - 15 = 30 b is the answer\"" + }, + { + "Answer": 0.8, + "Options": "a ) 0.2 % , b ) 0.4 % , c ) 0.6 % , d ) 0.8 % , e ) 1 %", + "Correct": "d", + "Explanation": "\"let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 105 / 100 ) * x * ( 96 / 100 ) * y = ( 504 / 500 ) ( xy ) error in measurement = ( 504 / 500 ) xy - xy = ( 4 / 500 ) xy error % = [ ( 4 / 500 ) xy * ( 1 / xy ) * 100 ] % = ( 4 / 5 ) % = 0.8 % . answer d 0.8 %\"" + }, + { + "Answer": 58, + "Options": "a ) 48 m 2 , b ) 40 m 2 , c ) 50 m 2 , d ) 58 m 2 , e ) 62 m 2", + "Correct": "d", + "Explanation": "\"surface area of a cuboid = 2 ( lb + bh + lh ) = 2 ( 5 * 4 + 4 * 1 + 5 * 1 ) = 2 ( 20 + 4 + 5 ) = 2 * 29 = 58 m 2 answer : d\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 8 , c ) 6 , d ) 10 , e ) 16", + "Correct": "a", + "Explanation": "\"1 ) draw a simple cube 2 ) draw 9 squares on each face of the cube ( so that it looks like a rubik ' s cube ) - this is what the cube will look like when it ' s cut into 27 equal smaller cubes . 3 ) remember that the outside of the cube is the part that ' s painted . . . . the mini - cubes with 2 painted sides are all on the edge of the cube , in themiddleof the edge . there are 4 in front , 4 in back and 4 more on thestripthat runs around the left / top / right / bottom of the cube . v = 4 + 4 + 4 = 12 . answer a\"" + }, + { + "Answer": 28, + "Options": "a ) 28 cm 2 , b ) 27 cm 2 , c ) 29 cm 2 , d ) 25 cm 2 , e ) 35 cm 2", + "Correct": "a", + "Explanation": "\"area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.0 * 28 / 2 = 28 cm 2 answer : a\"" + }, + { + "Answer": 5, + "Options": "a ) 3 , b ) 6 , c ) 5 , d ) 9 , e ) 1", + "Correct": "c", + "Explanation": "s = ( 1 + 2 + 7 ) / 2 = 5 answer : c" + }, + { + "Answer": 1320, + "Options": "a ) 1276 , b ) 1200 , c ) 2832 , d ) 1299 , e ) 1320", + "Correct": "e", + "Explanation": "\"explanation : l * 30 = 1200 \u00e8 l = 40 40 + 30 + 50 = 120 120 * 11 = 1320 answer : option e\"" + }, + { + "Answer": 2, + "Options": "['a ) 4', 'b ) 5', 'c ) 6', 'd ) 7', 'e ) 2']", + "Correct": "e", + "Explanation": "first calculate the surface area of the rectangle by multiplying the length and width of the rectangle together , then multiply by 2 to get both sides of the rectangle . this calculates to 12 inches . find the surface area of the sides of the rectangular cube . multiply the height by the length of the rectangle . multiply the answer by 2 ( for the 2 sides on the rectangular cube ) . this calculates to 3 inches . then multiply the width of the rectangle by the height . multiply the answer by 2 ( for the 2 sides on the rectangular cube ) . this calculates to 2 inches . add the totals together to get the rectangular cube surface area of 17 inches . since a square cube has 6 sides , divide the surface area by 6 . this calculates to 2.833 inches as the surface area of each side of the cube . the square root of 2.833 is 1.683 . rounding to the nearest whole number that makes each side of the cube measuring 2 inches . the correct answer is ( e ) ." + }, + { + "Answer": 130, + "Options": "a ) 120 , b ) 110 , c ) 130 , d ) 140 , e ) 150", + "Correct": "c", + "Explanation": "\"the triangle with sides 30 cm , 26 cm and 10 cm is right angled , where the hypotenuse is 30 cm . area of the triangle = 1 / 2 * 26 * 10 = 130 cm 2 answer : option c\"" + }, + { + "Answer": 300, + "Options": "['a ) 100 m', 'b ) 125 m', 'c ) 150 m', 'd ) 278 m', 'e ) 300 m']", + "Correct": "e", + "Explanation": "sol . area of the field = total cost / rate = ( 333.18 / 25.6 ) hectares = 13.5 hectares ( 13.5 x 10000 ) m ^ 2 = 135000 m ^ 2 . let altitude = x metres and base = 3 x metres . then , ( 1 / 2 ) * 3 x * x = 135000 < = > x ^ 2 = 90000 < = > x = 300 . base = 900 m and altitude = 300 m . ans : e" + }, + { + "Answer": 29.25, + "Options": "a ) 22 , b ) 35 , c ) 77 , d ) 54 , e ) 29", + "Correct": "e", + "Explanation": "\"area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 1.5 * 39 / 2 = 29 cm 2 answer : e\"" + }, + { + "Answer": 1800, + "Options": "['a ) 1276', 'b ) 1200', 'c ) 2832', 'd ) 1800', 'e ) 1236']", + "Correct": "d", + "Explanation": "explanation : l * 30 = 1200 \u00e8 l = 40 40 + 30 + 50 = 120 120 * 15 = 1800 answer : option d" + }, + { + "Answer": 90, + "Options": "a ) 30 , b ) 45 , c ) 90 , d ) 120 , e ) 180", + "Correct": "c", + "Explanation": "\"area = 0.5 x 12 x 15 = 90 cm \u00e2 \u00b2 answer : c\"" + }, + { + "Answer": 71.99999999999999, + "Options": "['a ) 12', 'b ) 96', 'c ) 50', 'd ) 72', 'e ) 144']", + "Correct": "d", + "Explanation": "the biggest rectangle would be a square , whose diagonal is 12 ( 6 + 6 ) if side of square is a , 144 = a ^ 2 + a ^ 2 = 2 a ^ 2 so area of square = a ^ 2 = 144 / 2 = 72 answer : d" + }, + { + "Answer": 1, + "Options": "a ) 0 % , b ) 20 % increase , c ) 20 % decrease , d ) 1 % decrease , e ) insufficient data", + "Correct": "d", + "Explanation": "\"explanatory answer whenever you encounter problems like this , use a numerical example and then proceed . for ease of computation , it is safe in most cases , to assume the length to be 100 units and the width to be 100 units . ( remember , a square is a rectangle too and the problem works the same way when you assume different values for length and width . computation becomes a bit tedious with different values for length and width ) area of a rectangle = length * width = 100 * 100 = 10,000 sq units . when the length increases by 10 % , the new length becomes 110 units . and as the width decreases by 10 % , new width becomes 90 units . therefore , new area = 110 * 90 = 9900 sq units . new area is 100 sq units lesser than the original area . % change in area = ( ( change in area ) / ( original area ) ) * 100 = ( 100 / 10,000 ) * 100 = 1 % decrease in area the correct choice is ( d )\"" + }, + { + "Answer": 4456.443887106987, + "Options": "['a ) 4457', 'b ) 4567', 'c ) 4235', 'd ) 4547', 'e ) 4675']", + "Correct": "a", + "Explanation": "explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . \u03c0 r 2 = 175600 \u21d4 ( r ) 2 = ( 175600 x ( 7 / 22 ) ) \u21d4 r = 236.37 m . circumference = 2 \u03c0 r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 3 ) = rs . 4457 . answer : option a" + }, + { + "Answer": 44, + "Options": "a ) 22 , b ) 32 , c ) 44 , d ) 55 , e ) 56", + "Correct": "c", + "Explanation": "\"we can divide the trapezoid into two triangles and a rectangle sides of triangle , t 1 - - > h 1 = 5 , b 1 = 3 , s 1 = root ( 25 - 9 ) = 4 = s 2 of triangle t 2 area of triangle = ( 1 / 2 ) * 4 * 3 = 6 side of the rectangle = 8 * 4 = 32 total area of the trapezoid = 32 + 6 + 6 = 44 answer : c\"" + }, + { + "Answer": 2.01, + "Options": "['a ) 2.21 %', 'b ) 2.07 %', 'c ) 2.08 %', 'd ) 2.01 %', 'e ) 2.11 %']", + "Correct": "d", + "Explanation": "r = 100 r = 101 r 2 = 10000 r 2 = 10201 10000 - - - - 201 100 - - - - ? = > 2.01 % answer : d" + }, + { + "Answer": 300, + "Options": "['a ) 126', 'b ) 156', 'c ) 190', 'd ) 300', 'e ) 260']", + "Correct": "d", + "Explanation": "sol . let width = x , length = ( 10 + x ) perimeter = 2 ( x + ( 10 + x ) ) = 2 ( 2 x = 10 ) & 2 ( 2 x + 10 ) * 6.5 = 1950 x = 70 required perimeter = 2 ( 70 + 80 ) = 300 d" + }, + { + "Answer": 226.19467105846502, + "Options": "['a ) 226.3', 'b ) 226.2', 'c ) 228.2', 'd ) 227', 'e ) 226']", + "Correct": "a", + "Explanation": "req . area = \u00ef \u20ac [ ( 19 ) 2 \u00e2 \u20ac \u201c ( 17 ) 2 ] = 22 \u00e2 \u0081 \u201e 7 \u00e3 \u2014 ( 36 \u00e3 \u2014 2 ) [ since a 2 - b 2 = ( a + b ) ( a - b ) ] = ( 22 \u00e3 \u2014 36 \u00e3 \u2014 2 ) / 7 = 226.3 sq m answer a" + }, + { + "Answer": 42.25, + "Options": "['a ) 42.25 sq cm', 'b ) 45.25 sq cm', 'c ) 43.25 sq cm', 'd ) 50.25 sq cm', 'e ) 52.25 sq cm']", + "Correct": "a", + "Explanation": "though there might be some technicalities concerning the termnearest ( as 6.5 is equidistant from both 6 and 7 ) the answer still should be a : 6.5 ^ 2 = 42.25 . answer : a" + }, + { + "Answer": 64, + "Options": "['a ) 14', 'b ) 47', 'c ) 54', 'd ) 180', 'e ) 64']", + "Correct": "e", + "Explanation": "area = length x breadth 480 = 40 x breadth so , breadth = 12 units fencing required is - breadth + breadth + length 12 + 12 + 40 = > 64 feet answer must be ( e ) 64" + }, + { + "Answer": 5, + "Options": "['a ) 3 \u221a 2', 'b ) 5', 'c ) 5 \u221a 2', 'd ) \u221a ( 67 )', 'e ) \u221a ( 73 )']", + "Correct": "b", + "Explanation": "height of cone = 3 radius of base = 4 so the distance from the apex of c to any point on the circumference of the base of c will be a right angled triangle hence the distance is sqrt ( 3 ^ 2 + 4 ^ 2 ) = 5 answer : b" + }, + { + "Answer": 3650, + "Options": "a ) 2510 , b ) 3650 , c ) 2530 , d ) 2515 , e ) 2520", + "Correct": "b", + "Explanation": "\"length = breadth + 23 . therefore , 4 \u00d7 breadth + 2 \u00d7 23 = 246 m \u21d2 breadth = 50 m length = 50 + 23 = 73 m area = 73 \u00d7 50 = 3650 m 2 answer is b .\"" + }, + { + "Answer": 10, + "Options": "['a ) 7', 'b ) 8', 'c ) 9', 'd ) 10', 'e ) 11']", + "Correct": "d", + "Explanation": "10 units as other 2 sides will be 15,15 units . answer : d" + }, + { + "Answer": 863.9999999999997, + "Options": "['a ) 864', 'b ) 209', 'c ) 278', 'd ) 276', 'e ) 280']", + "Correct": "a", + "Explanation": "a 3 = 1728 = > a = 12 6 a 2 = 6 * 12 * 12 = 864 answer : a" + }, + { + "Answer": 0.6666666666666666, + "Options": "['a ) 4 / 5', 'b ) 5 / 4', 'c ) 3 / 2', 'd ) 5 / 7', 'e ) 2 / 3']", + "Correct": "e", + "Explanation": "we are basically given that the triangles are similar . in two similar triangles , the ratio of their areas is the square of the ratio of their sides and also , the square of the ratio of their corresponding heights . therefore , area / area = height ^ 2 / height ^ 2 = 4 / 9 - - > height / height = 2 / 3 . answer : e ." + }, + { + "Answer": 5120, + "Options": "a ) 4830 , b ) 5120 , c ) 6420 , d ) 8960 , e ) none", + "Correct": "b", + "Explanation": "\"explanation clearly , l = ( 48 \u2013 16 ) m = 32 m , b = ( 36 - 16 ) m = 20 m , h = 8 m . volume of the box = ( 32 x 20 x 8 ) m 3 = 5120 m 3 . answer b\"" + }, + { + "Answer": 120, + "Options": "a ) 329 , b ) 288 , c ) 120 , d ) 238 , e ) 31", + "Correct": "c", + "Explanation": "\"1 / 2 * 12 * 20 = 120 answer : c\"" + }, + { + "Answer": 480, + "Options": "a ) 180 cm , b ) 220 cm , c ) 240 cm , d ) 270 cm , e ) 480 cm", + "Correct": "e", + "Explanation": "\"we have 80 for first triangle , when we join mid - points of first triangle we get the second equilateral triangle then the length of second one is 40 and continues . so we have 80 , 40,20 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 80 / 1 - ( 1 / 2 ) = 160 equilateral triangle perimeter is 3 a = 3 * 160 = 480 . so option e .\"" + }, + { + "Answer": 43200, + "Options": "a ) 43,200 , b ) 19,600 , c ) 20,000 , d ) 20,400 , e ) 20,800", + "Correct": "a", + "Explanation": "\"you can avoid a lot of work in this problem by recognizing that , with the info provided , the diagonal forms a triangle inside the rectangle with sides that have a 3 : 4 : 5 ratio . diagonal = 200 2 x + 2 y = 560 , or x + y = 280 a ^ 2 + b ^ 2 = c ^ 2 for each the sides of the triangle using the ratio 3 : 4 : 5 for sides , and knowing c = 300 , you can deduce the following a = 180 b = 240 180 x 240 = 43,200 a is the answer .\"" + }, + { + "Answer": 3848.4510006474966, + "Options": "['a ) 3600', 'b ) 2646', 'c ) 3850', 'd ) 4215', 'e ) 5205']", + "Correct": "c", + "Explanation": "radius of required circle = 35 cm its area = 22 / 7 \u00d7 35 \u00d7 35 110 \u00d7 35 = 3850 cm ( power ) 2 answer is c ." + }, + { + "Answer": 0.6, + "Options": "['a ) 1 / 4', 'b ) 3 / 8', 'c ) 1 / 2', 'd ) 3 / 5', 'e ) 2']", + "Correct": "d", + "Explanation": "one side surface area of a cube = x * x = x ^ 2 total 6 sides = 6 x ^ 2 as for the rectangular , height ( h ) and width ( w ) are same as cube , x . only length = 2 x . l x h = 2 x * x = 2 x ^ 2 - - - - > 4 sides = 2 x ^ 2 * 4 = 8 x ^ 2 w * h = x * x = x ^ 2 - - - - - - > 2 sides = x ^ 2 * 2 = 2 x ^ 2 total 6 sides = 8 x ^ 2 + 2 x ^ 2 = 10 x ^ 2 ratio of cube area to rectangular area e = 6 x ^ 2 / 10 x ^ 2 - - - - > 6 / 10 - - - - > 3 / 5 ( d )" + }, + { + "Answer": 66, + "Options": "a ) 38 . , b ) 40 . , c ) 66 . , d ) 44 . , e ) 46 .", + "Correct": "c", + "Explanation": "\"answer is c : 66 let w be the width , so length is 7 w . therefore : w * 7 w = 847 , solving for , w = 11 , so 7 w - w = 6 w = 6 * 11 = 66\"" + }, + { + "Answer": 4775.921532301596, + "Options": "a ) 2996 sq m , b ) 4774 sq m , c ) 4312 sq m , d ) 2768 sq m , e ) 2786 sq m", + "Correct": "b", + "Explanation": "\"let the radii of the smaller and the larger circles be s m and l m respectively . 2 \u220f s = 660 and 2 \u220f l = 704 s = 660 / 2 \u220f and l = 704 / 2 \u220f difference between the areas = \u220f l ^ 2 - \u220f s ^ 2 = \u220f { 330 ^ 2 / \u220f ^ 2 - 352 ^ 2 / \u220f ^ 2 } = 330 ^ 2 / \u220f - 352 ^ 2 / \u220f = ( 330 - 352 ) ( 330 + 352 ) / \u220f = ( 22 ) ( 682 ) / ( 22 / 7 ) = 4774 sq m answer : b\"" + }, + { + "Answer": 7, + "Options": "a ) 4 , b ) 7 , c ) 8 , d ) 13 , e ) 26", + "Correct": "b", + "Explanation": "\"this question can be solved algebraically or by testing the answers . we ' re told that a rectangle has an area of 91 and a perimeter of 40 . we ' re asked for the length of one of the shorter sides of the rectangle . since the answers are all integers , and the area is 91 , the shorter side will almost certainly be less than 10 ( since 10 x 10 = 100 , but we ' re not dealing with a square ) . let ' s test answer b : 7 if . . . the shorter side = 7 . . . the area = 91 . . . . 91 / 7 = 13 = the longer side perimeter = 7 + 7 + 13 + 13 = 40 b\"" + }, + { + "Answer": 90, + "Options": "a ) 189 cm 2 , b ) 150 cm 2 , c ) 127 cm 2 , d ) 177 cm 2 , e ) 90 cm 2", + "Correct": "e", + "Explanation": "\"1 / 2 * 20 ( 5 + 4 ) = 90 cm 2 answer : e\"" + }, + { + "Answer": 10, + "Options": "a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 10", + "Correct": "e", + "Explanation": "\"for max volume of cylinder ( pi * r ^ 2 * h ) we need to max out r ^ 2 * h . we do n ' t know what the dimensions of the crate refer to . . therefore for max vol base should be 20 x 20 i . e . of radius 20 / 2 = 10 e\"" + }, + { + "Answer": 50, + "Options": "['a ) 40 cm', 'b ) 45 cm', 'c ) 50 cm', 'd ) 52 cm', 'e ) 57 cm']", + "Correct": "c", + "Explanation": "explanation : let x and y be the length and breadth of the rectangle respectively . then , x - 4 = y + 3 or x - y = 7 - - - - ( 1 ) area of the rectangle = xy ; area of the square = ( x - 4 ) ( y + 3 ) ( x - 4 ) ( y + 3 ) = xy < = > 3 x - 4 y = 12 - - - - ( 2 ) solving 1 & 2 , we get x = 16 and y = 9 . perimeter of the rectangle = 2 ( x + y ) = [ 2 ( 16 + 9 ) ] cm = 50 cm . answer : option c" + }, + { + "Answer": 50.28571428571428, + "Options": "a ) 53 m 2 , b ) 51 m 2 , c ) 50.2 m 2 , d ) 45 m 2 , e ) 40 m 2", + "Correct": "c", + "Explanation": "\"40 / 360 * 22 / 7 * 12 * 12 = 50.2 m 2 answer : c\"" + }, + { + "Answer": 160, + "Options": "a ) 160 , b ) 288 , c ) 150 , d ) 238 , e ) 31", + "Correct": "a", + "Explanation": "\"1 / 2 * 16 * 20 = 160 answer : a\"" + }, + { + "Answer": 88, + "Options": "['a ) 56', 'b ) 88', 'c ) 112', 'd ) 116', 'e ) 120']", + "Correct": "b", + "Explanation": "ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 8 + 8 = 16 length of 2 nd diagonal = 5.5 + 5.5 = 11 area = 1 / 2 * 16 * 11 = 88 b is the answer" + }, + { + "Answer": 24, + "Options": "['a ) 12', 'b ) 80', 'c ) 59', 'd ) 24', 'e ) 25']", + "Correct": "d", + "Explanation": "explanation : h 2 = ( 10 ) 2 - ( 8 ) 2 - ( 6 ) 2 - > h = 6 1 / 2 * 8 * 6 = 24 answer is d" + }, + { + "Answer": 0.20987654320987653, + "Options": "['a ) 17 / 64', 'b ) 17 / 81', 'c ) 16 / 25', 'd ) 3 / 5', 'e ) 6 / 25']", + "Correct": "b", + "Explanation": "i guess it ' s mean that square b is placed within square aentirely . since , the perimeter of b is 32 , then its side is 32 / 4 = 8 and the area is 4 ^ 2 = 64 ; empty space between the squares is 81 - 64 = 17 square centimeters , so if a random point is in this area then it wo n ' t be within square b : p = favorable / total = 17 / 81 . answer : b" + }, + { + "Answer": 14, + "Options": "['a ) 14 metres', 'b ) 5 metres', 'c ) 7.5 metres', 'd ) data inadequate', 'e ) none of these']", + "Correct": "a", + "Explanation": "l \u00d7 b = 24 \u00d7 b \u2234 l = 24 m and l \u2013 b = 10 \u2234 b = 24 \u2013 10 = 14 m answer a" + }, + { + "Answer": 1200, + "Options": "['a ) s . 1350', 'b ) s . 1327', 'c ) s . 1200', 'd ) s . 1397', 'e ) s . 1927']", + "Correct": "c", + "Explanation": "area = ( l + b + 2 d ) 2 d = ( 75 + 40 + 2.5 * 2 ) 2 * 2.5 = > 600 600 * 2 = rs . 1200 answer : c" + }, + { + "Answer": 10, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", + "Correct": "c", + "Explanation": "\"100 kg - 1 cubic meter ; 100,000 g - 1 cubic meter ; 100,000 g - 1 , 000,000 cubic centimeters ; 1 g - 1 , 000,000 / 100,000 = 10 / 1 = 10 cubic centimeters . answer : c .\"" + }, + { + "Answer": 24, + "Options": "a ) 48 , b ) 32 , c ) 24 , d ) 18 , e ) 12", + "Correct": "c", + "Explanation": "\"for example our cube have a side 1 meter , so we have 1 cubical meter in this cube and this cubical meter weigth 3 pounds if we take cube with side 2 meters we will have 8 cubical meters in this cube 8 meters * 3 pounds = 24 pounds so answer is c and similar but more theoretical approach : if we have sides a and b than they have equal ration with their areas : a / b = a ^ 2 / b ^ 2 and they have equal ration with their volumes : a / b = a ^ 3 / b ^ 3 we have two sides 1 / 2 so their volume will be in ratio 1 / 8 weight of one cube * volume of another cube 3 * 8 = 24 so answer is c\"" + }, + { + "Answer": 10, + "Options": "a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 10", + "Correct": "e", + "Explanation": "\"if the width is w , then length and height would be w / 2 . so , w * w / 2 * w / 2 = 128 = > w ^ 3 = ( 2 ^ 3 ) * 64 = ( 2 ^ 3 ) * ( 4 ^ 3 ) = > w = 2 * 4 = 8 in . along the width of the cuboid , 8 cubes do n ' t touch the tin foil . so the actual width will be non - touching cubes + touching cubes = 8 + 2 = p = 10 ans e .\"" + }, + { + "Answer": 72, + "Options": "['a ) 48 degrees', 'b ) 54 degrees', 'c ) 72 degrees', 'd ) 84 degrees', 'e ) 72 degrees']", + "Correct": "e", + "Explanation": "its a regular 10 sided so divide the globe by 10 . = 360 / 10 = 36 36 would be the angle at o . angles at a and b are equivalent , so 36 + 2 x = 180 2 x = 144 x = 72 angles oab and oba will be 72 degrees each . e" + }, + { + "Answer": 144, + "Options": "a ) 43 , b ) 144 , c ) 68 , d ) 87 , e ) 92", + "Correct": "b", + "Explanation": "\"sol . monthly rent per square feet = 3600 / ( 20 * 15 ) = 12 & annual rent per square feet = 12 * 12 = 144 answer : b\"" + }, + { + "Answer": 43.982297150257104, + "Options": "a ) 32 m 3 , b ) 36 m 3 , c ) 40 m 3 , d ) 44 m 3 , e ) none", + "Correct": "d", + "Explanation": "\"sol . volume = \u03c0 r 2 h = ( 22 / 7 x 1 x 1 x 14 ) m 3 = 44 m 3 . answer d\"" + }, + { + "Answer": 17.692307692307693, + "Options": "a ) 17.64 % , b ) 33.33 % , c ) 40 % , d ) 75 % , e ) none of these", + "Correct": "a", + "Explanation": "explanation : solution : ( 30 / ( 140 + 30 ) * 100 ) % = 17.64 % answer : a" + }, + { + "Answer": 9261, + "Options": "['a ) 8500 cm 3', 'b ) 9000 cm 3', 'c ) 9250 cm 3', 'd ) 9261 cm 3', 'e ) none']", + "Correct": "d", + "Explanation": "solution surface area = ( 34398 / 13 ) \u2039 = \u203a 2646 cm 3 \u2039 = \u203a 6 a 2 = 2646 \u2039 = \u203a a 2 = 441 \u2039 = \u203a a = 21 . so , volume = ( 21 x 21 x 21 ) cm 3 = 9261 cm 3 . answer d" + }, + { + "Answer": 1693.3184402848983, + "Options": "['a ) 1694 m 2', 'b ) 1700 m 2', 'c ) 1598 m 2', 'd ) 1500 m 2', 'e ) none of thes']", + "Correct": "a", + "Explanation": "radius of a circular grass lawn ( without path ) = 35 m \u2234 area = \u03c0 r 2 = \u03c0 ( 35 ) 2 radius of a circular grass lawn ( with path ) = 35 + 7 = 42 m \u2234 area = \u03c0 r 2 = \u03c0 ( 42 ) 2 \u2234 area of path = \u03c0 ( 42 ) 2 \u2013 \u03c0 ( 35 ) 2 = \u03c0 ( 422 \u2013 352 ) = \u03c0 ( 42 + 35 ) ( 42 \u2013 35 ) answer a" + }, + { + "Answer": 3780, + "Options": "a ) 3780 , b ) 5120 , c ) 6420 , d ) 8960 , e ) 7960", + "Correct": "a", + "Explanation": "\"clearly , l = ( 48 - 6 ) m = 42 m , b = ( 36 - 6 ) m = 30 m , h = 8 m . volume of the box = ( 42 x 30 x 3 ) m 3 = 3780 m 3 . answer : option a\"" + }, + { + "Answer": 114, + "Options": "['a ) 113', 'b ) 114', 'c ) 115', 'd ) 116', 'e ) 117']", + "Correct": "b", + "Explanation": "the total volume ( in terms of number of cubes ) of the solid = 3 * 9 * 5 = 135 the total volume ( in terms of number of cubes ) of the hollow = ( 3 - 2 ) * ( 9 - 2 ) * ( 5 - 2 ) = 21 so number of cubes required = 135 - 21 = 114 answer : b" + }, + { + "Answer": 5, + "Options": "['a ) 4', 'b ) 9', 'c ) 3', 'd ) 5', 'e ) 7']", + "Correct": "d", + "Explanation": "2880 = 20 * 144 ( because w . k . t 144 is perfect square ) = 2 * 10 * 144 = 2 * 2 * 5 * 144 = 4 * 5 * 144 ( here 4 and 144 are perfect square ) so the smallest number is 5 answer : d" + }, + { + "Answer": 100, + "Options": "a ) 64 , b ) 72 , c ) 86 , d ) 98 , e ) 100", + "Correct": "e", + "Explanation": "\"use the options . the options which after getting added to 25 shows a cube of a number could be right . here 64 + 25 = 89 72 + 25 = 97 86 + 25 = 111 98 + 25 = 123 100 + 25 = 125 - - - ( 5 * 5 * 5 ) so we have 100 as the answer ! e\"" + }, + { + "Answer": 0.4666666666666667, + "Options": "['a ) 9 / 30', 'b ) 14 / 30', 'c ) 4 / 9', 'd ) 3 / 5', 'e ) 6 / 25']", + "Correct": "b", + "Explanation": "i guess it ' s mean that square b is placed within rectangle a entirely . since , the perimeter of b is 16 , then its side is 16 / 4 = 4 and the area is 4 ^ 2 = 16 ; empty space between the squares is 30 - 16 = 14 square centimeters , so if a random point is in this area then it wo n ' t be within square b : p = favorable / total = 14 / 30 . answer : b ." + }, + { + "Answer": 135, + "Options": "a ) 135 , b ) 125 , c ) 120 , d ) 110 , e ) 140", + "Correct": "a", + "Explanation": "\"if i calculate it using the formulae , # diagonals = n ( n - 3 ) / 2 each vertex sends of n - 3 diagonals n = 19 - 1 then 18 * ( 18 - 3 ) / 2 = 135 correct option : a\"" + }, + { + "Answer": 800, + "Options": "['a ) 600', 'b ) 900', 'c ) 800', 'd ) 500', 'e ) 400']", + "Correct": "c", + "Explanation": "arear = 1 / 2 \u00d7 ( diagonal ) ( power ) 2 = ( 1 / 2 \u00d7 40 \u00d7 40 ) m ( power ) 2 = 1600 / 2 = 800 m ( power ) 2 answer is c ." + }, + { + "Answer": 220, + "Options": "['a ) 180 sq . units', 'b ) 11 sq . units', 'c ) 110 sq . units', 'd ) 140 sq . units', 'e ) 220 sq . units']", + "Correct": "e", + "Explanation": "given that the area of the square = 16 sq . units = > side of square = \u00e2 \u02c6 \u0161 16 = 4 units the radius of the circle = side of the square = 4 units length of the rectangle = 5 * 4 = 20 units given that breadth = 11 units area of the rectangle = lb = 20 * 11 = 220 sq . units answer : e" + }, + { + "Answer": 7737.769850454057, + "Options": "['a ) 7744', 'b ) 8844', 'c ) 5544', 'd ) 4444', 'e ) 3444']", + "Correct": "a", + "Explanation": "length of wire = 2 pier = 2 * ( 22 / 7 ) * 56 = 352 cm side of the square = 352 / 4 = 88 cm area of the square = 88 * 88 = 7744 sq cm answer : a" + }, + { + "Answer": 45, + "Options": "['a ) 17 m', 'b ) 45 m', 'c ) 54 m', 'd ) 77 m', 'e ) 34 m']", + "Correct": "b", + "Explanation": "1 m 2 - - - - 1 / 2 ? - - - - - 600 = > 1200 m 2 4 x * 3 x = 1200 = > x = 10 answer : b" + }, + { + "Answer": 23.84226894136092, + "Options": "a ) 20 % , b ) 18 % , c ) 24 % , d ) 64 % , e ) none of these", + "Correct": "c", + "Explanation": "\"if area of a circle decreased by x % then the radius of a circle decreases by ( 100 \u2212 10 \u221a 100 \u2212 x ) % = ( 100 \u2212 10 \u221a 100 \u2212 42 ) % = ( 100 \u2212 10 \u221a 58 ) % = 100 - 76 = 24 % answer c\"" + }, + { + "Answer": 125, + "Options": "a ) 120 , b ) 122 , c ) 124 , d ) 128 , e ) 126", + "Correct": "e", + "Explanation": "\"length = 9 feet breadth = 37 \u2212 92 = 14 feet area = 9 \u00d7 14 = 126 square feet answer is e .\"" + }, + { + "Answer": 0.8, + "Options": "a ) 0.8 % , b ) 0.2 % , c ) 0.4 % , d ) 0.9 % , e ) 0.6 %", + "Correct": "a", + "Explanation": "\"let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 105 / 100 * x ) * ( 96 / 100 * y ) = 504 / 500 * xy . error in measurement = 504 / 500 * xy ) - xy = 4 / 500 * xy . error % = [ 4 / 500 * xy * 1 / xy * 100 ] % = 4 / 5 = 0.8 % . answer is a\"" + }, + { + "Answer": 97, + "Options": "a ) 44 ft , b ) 97 ft , c ) 22 ft , d ) 11 ft , e ) 66 ft", + "Correct": "b", + "Explanation": "\"given that length and area , so we can find the breadth . length x breadth = area 80 x breadth = 680 breadth = 8.5 feet area to be fenced = 2 b + l = 2 ( 8.5 ) + 80 = 97 feet answer : b ) 97 ft\"" + }, + { + "Answer": 49, + "Options": "['a ) 49 rounds', 'b ) 42 rounds', 'c ) 54 rounds', 'd ) 52 rounds', 'e ) none of these']", + "Correct": "a", + "Explanation": "explanation : let the required number of rounds be x more radius , less rounds ( indirect proportion ) hence we can write as radius 14 : 20 } : : x : 70 \u21d2 14 \u00d7 70 = 20 x \u21d2 14 \u00d7 7 = 2 x \u21d2 x = 7 \u00d7 7 = 49 . answer : option a" + }, + { + "Answer": 4313.735577562732, + "Options": "['a ) 2898 sq m', 'b ) 1788 sq m', 'c ) 4312 sq m', 'd ) 7656 sq m', 'e ) 1786 sq m']", + "Correct": "c", + "Explanation": "let the radii of the smaller and the larger circles be s m and l m respectively . 2 \u220f s = 264 and 2 \u220f l = 352 s = 264 / 2 \u220f and l = 352 / 2 \u220f difference between the areas = \u220f l 2 - \u220f s 2 = \u220f { 1762 / \u220f 2 - 1322 / \u220f 2 } = 1762 / \u220f - 1322 / \u220f = ( 176 - 132 ) ( 176 + 132 ) / \u220f = ( 44 ) ( 308 ) / ( 22 / 7 ) = ( 2 ) ( 308 ) ( 7 ) = 4312 sq m answer : c" + }, + { + "Answer": 82, + "Options": "a ) 80 yards , b ) 82 yards , c ) 84 yards , d ) 85 yards , e ) 90 yards", + "Correct": "b", + "Explanation": "the definition of a rhombus states that every side is of equal length . this definition is the key to solving this question . 1 ) we state that the hypotenuse of either side triangle is x . for this solution , i will be working with the left triangle . 2 ) we state that the bottom and top sides of the rhombus are also x , due to the definition of a rhombus . 3 ) we will define the bottom of the left triangle as y . that is , for the rectangle bottom itself , we can define it as 25 = y + x , where x is a side for the rhombus and y is the bottom part of the left triangle . 4 ) from ( 1 ) , we know that x = 202 + y 2 \u2212 \u2212 \u2212 \u2212 \u2212 \u2212 \u2212 \u221a 202 + y 2 . 5 ) from ( 3 ) , we know x = 25 - y . 6 ) from ( 4 ) and ( 5 ) , we have the equation 202 + y 2 \u2212 \u2212 \u2212 \u2212 \u2212 \u2212 \u2212 \u221a = 25 \u2212 y 202 + y 2 = 25 \u2212 y 7 ) solving for y , we get 4.5 . 8 ) 25 - 4.5 = 20.5 = x 9 ) since all sides of the rhombus are the same , 20.5 * 4 = 41 * 2 = 82 . the answer is b , 82" + }, + { + "Answer": 4800, + "Options": "a ) s . 3988 , b ) s . 4800 , c ) s . 3228 , d ) s . 3922 , e ) s . 3928", + "Correct": "b", + "Explanation": "\"area = ( l + b \u2013 d ) d ( 110 + 60 \u2013 10 ) 10 = > 1600 m 2 1600 * 3 = rs . 4800 answer : b\"" + }, + { + "Answer": 2.5, + "Options": "a ) 2.5 cm , b ) 3.6 cm , c ) 5 cm , d ) 6.43 cm , e ) 7.56 cm", + "Correct": "a", + "Explanation": "\"increase in volume = volume of the cube = 5 * 5 * 5 cm ^ 3 rise in water level = volume / area = 5 * 5 * 5 / 10 * 5 = 2.5 cm answer is a\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "imo it should be c that is c reason : formed an equation . . . bat = b ball = c 2 b + 4 c = 180 1 b + 6 c = 190 solving both we get b that is bat = 40 and c that is ball = 25 new equation 195 to be divided in equal 3 b + 3 c = 195 3 * 40 + 3 * 25 = 195 120 + 75 = 195" + }, + { + "Answer": 876, + "Options": "a ) rs . 962 , b ) rs . 672 , c ) rs . 546 , d ) rs . 876 , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : surface area of a cube = 6 x 82 = 384 sq . ft quantity of paint required = ( 384 / 16 ) = 24 kg cost of painting = 36.5 x 24 = rs . 876 answer : d\"" + }, + { + "Answer": 140, + "Options": "['a ) 140 sq . units', 'b ) 158 sq . units', 'c ) 187 sq . units', 'd ) 607 sq . units', 'e ) 815 sq . units']", + "Correct": "a", + "Explanation": "given that the area of the square = 1225 sq . units = > side of square = \u221a 1225 = 35 units the radius of the circle = side of the square = 35 units length of the rectangle = 2 / 5 * 35 = 14 units given that breadth = 10 units area of the rectangle = lb = 14 * 10 = 140 sq . units answer : a" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 12", + "Correct": "a", + "Explanation": "\"we can find the radius of all the three cases of cylinders . the only crux to find the answer faster is that : voulme is pi * r ^ 2 * h . the volume is a function of r ^ 2 . so r has to be the highest to find the largest volume . so r = 2 for the surface 8 * 12 face . volume = 8 pi answer a\"" + }, + { + "Answer": 2718, + "Options": "a ) s . 4528 , b ) s . 4520 , c ) s . 4527 , d ) s . 4530 , e ) s . 2718", + "Correct": "e", + "Explanation": "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 3 = rs . 2718 answer : e" + }, + { + "Answer": 2, + "Options": "['a ) x / 2', 'b ) x', 'c ) 2 x', 'd ) 4 x', 'e ) 3 x']", + "Correct": "c", + "Explanation": "x ^ 2 = 1 / 2 \u00e3 \u0192 \u00e2 \u20ac \u201d x \u00e3 \u0192 \u00e2 \u20ac \u201d h or h = 2 x ^ 2 / x = 2 x answer : c" + }, + { + "Answer": 60, + "Options": "['a ) 12 square meters', 'b ) 5 square meters', 'c ) 44 square meters', 'd ) 60 square meters', 'e ) 22 square meters']", + "Correct": "d", + "Explanation": "area of a rectangle : a = w \u00d7 h d ) 60 square meters" + }, + { + "Answer": 27, + "Options": "a ) 10 feet , b ) 12 feet , c ) 27 feet , d ) 15 feet , e ) 18 feet", + "Correct": "c", + "Explanation": "\"total circuit = 27 / 3 = 9 total feet squirrel travels = 9 * 3 = 27 feet answer : c\"" + }, + { + "Answer": 25, + "Options": "a ) 23.57 , b ) 23.54 , c ) 23.5 , d ) 24.55 , e ) 25.14", + "Correct": "e", + "Explanation": "\"let the side of the square be a cm . perimeter of the rectangle = 2 ( 18 + 14 ) = 64 cm perimeter of the square = 64 cm i . e . 4 a = 64 a = 16 diameter of the semicircle = 16 cm circumference of the semicircle = 1 / 2 ( \u220f ) ( 16 ) = 1 / 2 ( 22 / 7 ) ( 16 ) = 25.14 cm to two decimal places answer : e\"" + }, + { + "Answer": 18.999999999999993, + "Options": "['a ) 10 %', 'b ) 19 %', 'c ) 20 %', 'd ) 36 %', 'e ) 30 %']", + "Correct": "b", + "Explanation": "let initial radius = a then , area = \u03c0 a ^ 2 . new radius = 90 % of a = 9 a / 10 . new area = \u03c0 * 81 a ^ 2 / 100 = 81 / 100 \u03c0 a ^ 2 reduce in area = [ \u03c0 a ^ 2 - 81 / 100 \u03c0 a ^ 2 ] = 19 / 100 \u03c0 a ^ 2 % reduce = [ ( 19 * \u03c0 a ^ 2 / 100 ) * ( 1 * 100 / \u03c0 a ^ 2 ) ] % = 19 % answer b" + }, + { + "Answer": 36, + "Options": "['a ) 28', 'b ) 36', 'c ) 40', 'd ) 56', 'e ) 84']", + "Correct": "b", + "Explanation": "you can also solve this via using the given numbers in the answer choices ! of course you need to be aware of the basic properties as outlined by the other posts above ( a = x ^ 2 and p = 4 x ) starting with d you will notice that x = 14 is way too big for your area ( 14 ^ 2 ) and will not satisfy : 6 a = 6 ( 2 p + 9 ) or a = 2 p + 9 - - > eliminate d and e now pick b ( its either too big , then its a , or too small then you know its c or it is b itsself ) and picking b indeed solves the problem ! ( 36 / 4 - - > 9 ; a = 9 ^ 2 = 81 and 81 = 2 x 36 + 9 )" + }, + { + "Answer": 53, + "Options": "a ) 50 , b ) 51 , c ) 52 , d ) 53 , e ) 54", + "Correct": "d", + "Explanation": "\"the number of males is 148 - 92 = 56 . the number of males with advanced degrees is 56 - 31 = 25 . the number of females with advanced degrees is 78 - 25 = 53 . the answer is d .\"" + }, + { + "Answer": 896, + "Options": "a ) 200 , b ) 384 , c ) 345 , d ) 244 , e ) 896", + "Correct": "e", + "Explanation": "\"area of a parallelogram = base * height = 28 * 32 = 896 cm 2 answer : option e\"" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 4 \u221a 2 , c ) 8 , d ) 8 \u221a 2 , e ) can not be determined from the information provided", + "Correct": "a", + "Explanation": "\"ans a . . 10 . . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 25 or yz = 5 * \\ sqrt { 2 } . . therefore hyp = xy = 10\"" + }, + { + "Answer": 30, + "Options": "['a ) 15 cm', 'b ) 20 cm', 'c ) 25 cm', 'd ) 30 cm', 'e ) none of these']", + "Correct": "d", + "Explanation": "explanation : we know the product of diagonals is 1 / 2 * ( product of diagonals ) let one diagonal be d 1 and d 2 so as per question 1 / 2 \u2217 d 1 \u2217 d 2 = 150 1 / 2 \u2217 10 \u2217 d 2 = 150 d 2 = 150 / 5 = 30 option d" + }, + { + "Answer": 75, + "Options": "['a ) 75', 'b ) 79', 'c ) 72', 'd ) 70', 'e ) 80']", + "Correct": "a", + "Explanation": "original area = \u03c0 r ( power ) 2 new area = \u03c0 ( r / 2 ) ( power ) 2 = ( \u03c0 r ( power ) 2 ) / 4 reduction in area = [ ( \u03c0 r ( power ) 2 - ( \u03c0 r ( power ) 2 ) / 4 ] 2 = ( 3 \u03c0 r ( power ) 2 ) / 4 reduction percent = ( ( 3 \u03c0 r ( power ) 2 ) / 4 \u00d7 1 / ( \u03c0 r ( power ) 2 \u00d7 100 ) % = 75 % answer is a ." + }, + { + "Answer": 2, + "Options": "a ) 0.1 , b ) 0 , c ) 1 , d ) 2 , e ) 3", + "Correct": "d", + "Explanation": "\"500 kg - 1 cubic meter ; 500,000 g - 1 cubic meter ; 500,000 g - 1 , 000,000 cubic centimeters ; 1 g - 1 , 000,000 / 500,000 = 10 / 5 = 2 cubic centimeters . answer : d .\"" + }, + { + "Answer": 4687.5, + "Options": "a ) 100 , b ) 250 , c ) 750 , d ) 1200 , e ) 4687.5", + "Correct": "e", + "Explanation": "\"6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 50 * 25 * 1 / 2 = 625 feet ^ 3 of water must be removed , which equals to 625 * 7.5 = 4687.5 gallons . answer : e .\"" + }, + { + "Answer": 36, + "Options": "['a ) 18', 'b ) 27', 'c ) 36', 'd ) 48', 'e ) 64']", + "Correct": "c", + "Explanation": "triangle area = root ( 3 ) s ^ 2 / 4 area of 3 squares together = 3 s ^ 2 root ( 3 ) s ^ 2 / 4 + 3 s ^ 2 = 48 + 4 root ( 3 ) root ( 3 ) / 4 s ^ 2 = 4 root ( 3 ) s ^ 2 = 16 = > s = 4 there are 3 sides of each square = 3 ( 4 ) ( 3 ) = 36 option c" + }, + { + "Answer": 4.04, + "Options": "['a ) 4.00 %', 'b ) 4.04 %', 'c ) 4.16 %', 'd ) 4.30 %', 'e ) 5 %']", + "Correct": "b", + "Explanation": "100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 102 x 102 ) cm 2 . ( a 2 - a 1 ) = [ ( 102 ) 2 - ( 100 ) 2 ] = ( 102 + 100 ) x ( 102 - 100 ) = 404 cm 2 . percentage error = 404 x 100 % = 4.04 % 100 x 100 b" + }, + { + "Answer": 6, + "Options": "a ) 4 m 2 , b ) 6 m 2 , c ) 18 m 2 , d ) 19 m 2 , e ) 12 m 2", + "Correct": "b", + "Explanation": "\"1 / 2 * 3 * 4 = 6 m 2 answer : b\"" + }, + { + "Answer": 511.99999999999983, + "Options": "['a ) 24', 'b ) 48', 'c ) 64', 'd ) 80', 'e ) 512']", + "Correct": "e", + "Explanation": "volume = 64 = side ^ 3 i . e . side of cube = 4 new cube has dimensions 8 , 8 , and 8 as all sides are twice of teh side of first cube volume = 8 * 8 * 8 = 512 square feet answer : option e" + }, + { + "Answer": 678.5840131753953, + "Options": "a ) 678.6 m 3 , b ) 36 m 3 , c ) 40 m 3 , d ) 44 m 3 , e ) none", + "Correct": "a", + "Explanation": "\"solution volume = \u03c0 r 2 h \u2039 = \u203a ( 22 / 7 \u00d7 3 \u00d7 3 \u00d7 24 ) m 3 \u2039 = \u203a 678.6 m 3 . answer a\"" + }, + { + "Answer": 20, + "Options": "a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22", + "Correct": "d", + "Explanation": "\"the volume the box is : length * width * depth = 5 * 4 * 3 = 60 cubic feet . 60 cubic feet / 3 cubic feet per hour = 20 hours . it will take 20 hours to fill the box . the answer is d .\"" + }, + { + "Answer": 1764, + "Options": "a ) 54 , b ) 64 , c ) 81 , d ) 108 , e ) 1764", + "Correct": "e", + "Explanation": "\"volume of larger cube = 343 = 7 ^ 3 side of larger cube = 7 volume of smaller cube = 1 - - > side of smaller cube = 1 surface area of larger cube = 6 * 7 ^ 2 = 294 surface area of 27 smaller cubes = 343 * 6 * 1 = 2058 difference = 2058 - 294 = 1764 answer : e\"" + }, + { + "Answer": 72, + "Options": "a ) 18 \u00b0 , b ) 36 \u00b0 , c ) 54 \u00b0 , d ) 72 \u00b0 , e ) 90 \u00b0", + "Correct": "d", + "Explanation": "\"the percent of the budget for transportation is 100 - ( 60 + 9 + 5 + 4 + 2 ) = 20 % 100 % of the circle is 360 degrees . then ( 20 % / 100 % ) * 360 = 72 degrees the answer is d .\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 17 , c ) 18 , d ) 19 , e ) 14", + "Correct": "a", + "Explanation": "\"let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 432 3 b 2 = 432 b 2 = 144 b = 12 m . answer : option a\"" + }, + { + "Answer": 1440, + "Options": "['a ) $ 980', 'b ) $ 1060', 'c ) $ 1220', 'd ) $ 1440', 'e ) $ 1650']", + "Correct": "d", + "Explanation": "the total surface area is 2 ( 2 * 3 + 3 * 6 + 2 * 6 ) = 72 square feet the total cost is 72 * $ 20 = $ 1440 the answer is d ." + }, + { + "Answer": 7248, + "Options": "['a ) s . 4529', 'b ) s . 4586', 'c ) s . 7248', 'd ) s . 4530', 'e ) s . 4528']", + "Correct": "c", + "Explanation": "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 8 = rs . 7248 answer : c" + }, + { + "Answer": 9, + "Options": "a ) 6 / \u03c0 , b ) 9 / \u03c0 , c ) 6 , d ) 9 , e ) 12", + "Correct": "d", + "Explanation": "\"given area of the base of a hemisphere is 3 = pi * r ^ 2 thus r = sqrt ( 3 / pi ) . surface area of whole sphere = 4 * pi * r ^ 2 . = 4 * pi * 3 / pi = 12 . since the hemisphere is half of a sphere the surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . but the total surface area = 6 + area of the base of a hemisphere . = 6 + 3 = 9 . answer is d ! !\"" + }, + { + "Answer": 84, + "Options": "a ) 144 , b ) 131 , c ) 115 , d ) 84 , e ) 45", + "Correct": "d", + "Explanation": "\"there are 8 business exec and in each handshake 2 business execs are involved . hence 8 c 2 = 28 also , each of 8 exec will shake hand with every 7 other chairmen for total of 56 handshake . total = 28 + 56 = 84 ans : d\"" + }, + { + "Answer": 10, + "Options": "['a ) 4', 'b ) 6', 'c ) 8', 'd ) 9', 'e ) 10']", + "Correct": "e", + "Explanation": "if the width is w , then length and height would be w / 2 . so , w * w / 2 * w / 2 = 128 = > w ^ 3 = ( 2 ^ 3 ) * 64 = ( 2 ^ 3 ) * ( 4 ^ 3 ) = > w = 2 * 4 = 8 in . along the width of the cuboid , 8 cubes do n ' t touch the tin foil . so the actual width will be non - touching cubes + touching cubes = 8 + 2 = e = 10 ans e ." + }, + { + "Answer": 199.99999999999991, + "Options": "a ) 300 , b ) 150 , c ) 180 , d ) 109 , e ) 200", + "Correct": "e", + "Explanation": "\"lets suppose length = l , breadth = b , depth = d front face area = l * w = 1 / 2 w * d ( l = 1 / 2 d or d = 2 l ) top face area = w * d side face area = w * d = 1.5 d * l ( w = 1.5 l ) volume = l * w * d = 3000 l * 1.5 l * 2 l = 3000 l = 10 side face area = l * d = l * 2 l = 10 * 2 * 10 = 200 e is the answer\"" + }, + { + "Answer": 16, + "Options": "a ) 14 , b ) 16 , c ) 19 , d ) 21 , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : let the integer be x . then , x + x 2 = 272 x 2 + x - 272 = 0 ( x + 17 ) ( x \u2013 16 ) = 0 x = 16 answer : b\"" + }, + { + "Answer": 30, + "Options": "a ) 27 , b ) 28 , c ) 29 , d ) 30 , e ) 31", + "Correct": "d", + "Explanation": "chess board has 64 squares . so we can place 32 rectangular blocks , but 2 are cut off from the corner . hence 32 - 2 = 30 blocks answer : d" + }, + { + "Answer": 11.780972450961723, + "Options": "a ) 11.72 , b ) 11.52 , c ) 11.97 , d ) 10.91 , e ) 11.79", + "Correct": "e", + "Explanation": "\"let the side of the square be a cm . parameter of the rectangle = 2 ( 9 + 6 ) = 30 cm parameter of the square = 30 cm i . e . 4 a = 30 a = 7.5 diameter of the semicircle = 7.5 cm circimference of the semicircle = 1 / 2 ( \u00e2 \u02c6 \u008f ) ( 7.5 ) = 1 / 2 ( 22 / 7 ) ( 7.5 ) = 165 / 14 = 11.79 cm to two decimal places answer : e\"" + }, + { + "Answer": 7, + "Options": "['a ) 9', 'b ) 7', 'c ) - 9', 'd ) 11', 'e ) 6']", + "Correct": "b", + "Explanation": "a = l x w w = l - 2 l = w + 2 a = ( w + 2 ) x w a = w ^ 2 + 2 x w 63 = w ^ 2 + 2 w 0 = w ^ 2 + 2 w - 63 0 = ( w + 9 ) ( w - 7 ) w = - 9 and w = 7 , width can not be negative so w = 7 answer is b" + }, + { + "Answer": 220, + "Options": "a ) 160 , b ) 220 , c ) 360 , d ) 440 , e ) 560", + "Correct": "b", + "Explanation": "\"the number of jumbo tiles = x . the number of regular tiles = 2 x . assume the ratio of the dimensions of a regular tile is a : a - - > area = a ^ 2 . the dimensions of a jumbo tile is 3 a : 3 a - - > area = 9 a ^ 2 . the area of regular tiles = 2 x * a ^ 2 = 40 . the area of jumbo tiles = x * 9 a ^ 2 = 4.5 ( 2 x * a ^ 2 ) = 4.5 * 40 = 180 . total area = 40 + 180 = 220 . answer : b .\"" + }, + { + "Answer": 80, + "Options": "a ) 33 , b ) 45 , c ) 66 , d ) 80 , e ) 21", + "Correct": "d", + "Explanation": "\"r = 4 h = 5 \u03c0 * 4 * 4 * 5 = 80 \u03c0 cc answer : d\"" + }, + { + "Answer": 1518.7199999999993, + "Options": "a ) s . 1518.8 , b ) s . 1327 , c ) s . 1328 , d ) s . 1397 , e ) s . 1927", + "Correct": "a", + "Explanation": "\"area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 2.8 * 2 ) 2 * 2.8 = > 759.4 759.4 * 2 = rs . 1518.8 answer : a\"" + }, + { + "Answer": 143.36, + "Options": "['a ) 50', 'b ) 80', 'c ) 100', 'd ) 143.36', 'e ) 250']", + "Correct": "d", + "Explanation": "let old diameter be 4 , so radius is 2 old area = 4 \u03c0 new diameter is 6.24 , so radius is 3.12 new area = 9.7344 \u03c0 increase in area is 5.7344 \u03c0 % increase in area = 5.7344 / 4 * 100 so , % increase is 143.36 % answer will be ( d )" + }, + { + "Answer": 0.6, + "Options": "a ) 4 / 5 , b ) 5 / 4 , c ) 3 / 2 , d ) 5 / 7 , e ) 3 / 5", + "Correct": "e", + "Explanation": "\"we are basically given that the triangles are similar . in two similar triangles , the ratio of their areas is the square of the ratio of their sides and also , the square of the ratio of their corresponding heights . therefore , area / area = height ^ 2 / height ^ 2 = 9 / 25 - - > height / height = 3 / 5 . answer : e .\"" + }, + { + "Answer": 56.79999999999998, + "Options": "['a ) 75.00 %', 'b ) 56.80 %', 'c ) 110 %', 'd ) 150 %', 'e ) 180 %']", + "Correct": "b", + "Explanation": "let length of each side of square a be 10 area of a = 10 ^ 2 = 100 since , length of each side of square a is increased by 100 percent to make square b length of each side of square b = 2 * 10 = 20 area of b = 20 ^ 2 = 400 since , length of the side of square b is increased by 40 percent to make square c length of each side of square c = 1.4 * 20 = 28 area of c = 28 ^ 2 = 784 difference in areas of c and cummulative areas of a and b = 784 - ( 400 + 100 ) = 284 percent is the area of square c greater than the sum of the areas of squares a and b = ( 284 / 500 ) * 100 % = 56.80 % answer b" + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 2 , c ) 4 , d ) 8 , e ) 16", + "Correct": "a", + "Explanation": "\"as per the question - - width is negligible now , let l be the length of the fence = 2 pir l = 1 / 3 ( pir ^ 2 ) pir ^ 2 = 6 pir r = 6 answer : a\"" + }, + { + "Answer": 0.002, + "Options": "['a ) 0.005', 'b ) 0.002', 'c ) 0.001', 'd ) 0.0005', 'e ) 0.0002']", + "Correct": "b", + "Explanation": "it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 2 then x = 2 / 1000 = 0.002 . the answer is b" + }, + { + "Answer": 16, + "Options": "['a ) $ 1', 'b ) $ 2', 'c ) $ 4', 'd ) $ 8', 'e ) $ 16']", + "Correct": "e", + "Explanation": "let x be the radius of b and 2 h be the height of b . therefore , radius of v = 2 x and height = h vol of b = 3.14 * x ^ 2 * 2 h vol of a = 3.14 * 4 x ^ 2 * h cost to fill half of b = $ 4 - - > cost to fill full b = $ 8 - - > 3.14 * x ^ 2 * 2 h = 8 - - > 3.14 * x ^ 2 * h = 4 - - > 4 * ( 3.14 * x ^ 2 * h ) = $ 16 ans e" + }, + { + "Answer": 59, + "Options": "['a ) 34', 'b ) 59', 'c ) 68', 'd ) 88', 'e ) 92']", + "Correct": "b", + "Explanation": "given that length and area , so we can find the breadth . length x breadth = area 20 x breadth = 390 breadth = 19.5 feet area to be fenced = 2 b + l = 2 ( 19.5 ) + 20 = 59 feet answer : b" + }, + { + "Answer": 7, + "Options": "['a ) 2', 'b ) 3', 'c ) 5', 'd ) 7', 'e ) 11']", + "Correct": "d", + "Explanation": "1008 = 2 ^ 4 x 3 ^ 2 x 7 . therefore the smallest integer to multiplied to 1008 to make it a perfect square is 7 . answer d ." + }, + { + "Answer": 6, + "Options": "a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 12", + "Correct": "c", + "Explanation": "\"we can find the radius of all the three cases of cylinders . the only crux to find the answer faster is that : voulme is pi * r ^ 2 * h . the volume is a function of r ^ 2 . so r has to be the highest to find the largest volume . so r = 6 for the surface 8 * 12 face . volume = 216 pi answer c\"" + }, + { + "Answer": 70, + "Options": "a ) 70 , b ) 80 , c ) 85 , d ) 90 , e ) 95", + "Correct": "a", + "Explanation": "\"in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 \u00b0 ) . given : x + ( x + 40 ) = 180 - - > x = 70 . answer : a .\"" + }, + { + "Answer": 104, + "Options": "['a ) 100', 'b ) 104', 'c ) 108', 'd ) 112', 'e ) none of these']", + "Correct": "b", + "Explanation": "one side = 2 corners ( 1 nd 1 each ) plus 25 . . . 1 25 1 25 25 1 25 1 der 4 ans = 25 * 4 + 4 = 104 answer : b" + }, + { + "Answer": 5200, + "Options": "a ) 2288 , b ) 2779 , c ) 2779 , d ) 5200 , e ) 2781", + "Correct": "d", + "Explanation": "\"area = ( l + b \u00e2 \u20ac \u201c d ) d ( 80 + 60 \u00e2 \u20ac \u201c 10 ) 10 = > 1300 m 2 1300 * 4 = rs . 5200 answer : d\"" + }, + { + "Answer": 30, + "Options": "a ) 30 cm 2 , b ) 85 cm 2 , c ) 65 cm 2 , d ) 45 cm 2 , e ) 35 cm 2", + "Correct": "a", + "Explanation": "\"area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 24 / 2 = 30 cm 2 answer : a\"" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 4 , c ) 10 , d ) 12 , e ) 14", + "Correct": "a", + "Explanation": "p \u2217 3 \u2217 10 ^ 2 = s ^ 2 so , s = \u221a p \u2217 3 \u2217 10 ^ 2 so , if p = 3 we get a perfect square number ! ! hence answer will be ( a ) 3" + }, + { + "Answer": 400, + "Options": "a ) 400 , b ) 600 , c ) 750 , d ) 2400 , e ) 3200", + "Correct": "a", + "Explanation": "\"answer a ) 10800 yards need 1200 lbs 1 yard will need 1200 / 10800 = 1 / 9 lbs 3600 yards will need 1 / 9 * 3600 yards = 400 lbs\"" + }, + { + "Answer": 64, + "Options": "a ) 48 , b ) 56 , c ) 64 , d ) 76 , e ) 192", + "Correct": "c", + "Explanation": "\"say length of garden is l meters . then ( l * 24 ) = 16 * 12 [ given area is same . area = l * b ] therefore l works out to 8 meters . perimeter of garden = 2 * ( 8 + 24 ) = 64 meter . answer is c\"" + }, + { + "Answer": 5120, + "Options": "a ) 6420 , b ) 8960 , c ) 5120 , d ) 4830 , e ) none", + "Correct": "c", + "Explanation": "\"sol . clearly , l = ( 48 - 16 ) m = 32 m , b = ( 36 - 16 ) m = 20 m , h = 8 m . \u2234 volume of the box = ( 32 x 20 x 8 ) m 3 = 5120 m 3 answer c\"" + }, + { + "Answer": 45, + "Options": "a ) 76 , b ) 88 , c ) 66 , d ) 55 , e ) 45", + "Correct": "e", + "Explanation": "\"area of a triangle = r * s where r is the in radius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 36 / 2 = 45 cm 2 answer : e\"" + }, + { + "Answer": 363, + "Options": "['a ) 432 sq m', 'b ) 363 sq m', 'c ) 452 sq m', 'd ) 428 sq m', 'e ) 525 sq m']", + "Correct": "b", + "Explanation": "2 ( 3 x + x ) = 88 l = 33 b = 11 lb = 33 * 11 = 363 answer : b" + }, + { + "Answer": 49, + "Options": "a ) 7 , b ) 14 , c ) 42 , d ) 49 , e ) 98", + "Correct": "d", + "Explanation": "let r be the radius of the smaller sign . then the diameter of the smaller sign is 2 r , the diameter of the larger sign is 14 r , and the radius of the larger sign is 7 r . the area a of the smaller sign is a = pir ^ 2 . the area of the larger sign is pi ( 7 r ) ^ 2 = 49 pir ^ 2 = 49 a . since the area is 49 times larger , we need 49 times more paint for the larger sign . the answer is d ." + }, + { + "Answer": 300, + "Options": "a ) 176 , b ) 190 , c ) 150 , d ) 278 , e ) 300", + "Correct": "e", + "Explanation": "\"1 / 2 * 30 * 20 = 300 answer : e\"" + }, + { + "Answer": 120, + "Options": "a ) 56 , b ) 88 , c ) 112 , d ) 116 , e ) 120", + "Correct": "e", + "Explanation": "\"ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 8 + 8 = 16 length of 2 nd diagonal = 7.5 + 7.5 = 15 area = 1 / 2 * 16 * 15 = 120 e is the answer\"" + }, + { + "Answer": 864, + "Options": "a ) 760 , b ) 284 , c ) 288 , d ) 864 , e ) 820", + "Correct": "d", + "Explanation": "\"area of a parallelogram = base * height = 36 * 24 = 864 cm 2 answer : d\"" + }, + { + "Answer": 79.5, + "Options": "['a ) 79.5', 'b ) 89.3', 'c ) 85.5', 'd ) 75.4', 'e ) 72.5']", + "Correct": "a", + "Explanation": "if we take a square with side length x and draw a diagonal , we get two isosceles right triangles . if we focus on one such right triangle , we see that the legs have length x . square 28 - inch flat - screen television the diagonal ( hypotenuse ) = 28 so , we can apply the pythagorean theorem to get x \u00b2 + x \u00b2 = 28 \u00b2 simplify : 2 x \u00b2 = 28 \u00b2 divide both sides by 2 to get : x \u00b2 = 28 \u00b2 / 2 since the area of the square = x \u00b2 , we can see that the area of this square is 28 \u00b2 / 2 square 25 - inch flat - screen television the diagonal ( hypotenuse ) = 25 so , we can apply the pythagorean theorem to get x \u00b2 + x \u00b2 = 25 \u00b2 simplify : 2 x \u00b2 = 25 \u00b2 divide both sides by 2 to get : x \u00b2 = 25 \u00b2 / 2 since the area of the square = x \u00b2 , we can see that the area of this square is 25 \u00b2 / 2 difference in areas = 28 \u00b2 / 2 - 25 \u00b2 / 2 = ( 28 \u00b2 - 25 \u00b2 ) / 2 = ( 784 - 625 ) / 2 = 159 / 2 = 79.5 a" + }, + { + "Answer": 1350, + "Options": "a ) 2999 , b ) 1350 , c ) 2677 , d ) 2898 , e ) 2787", + "Correct": "b", + "Explanation": "\"area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 2.5 * 2 ) 2 * 2.5 = > 675 675 * 2 = rs . 1350 answerb\"" + }, + { + "Answer": 17, + "Options": "a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21", + "Correct": "a", + "Explanation": "let a and b be the two sides of the triangle such that a is longer than b . the statement ` ` the hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle ' ' may be fomulated by h = a + 2 or a = h - 2 the statement ` ` the shorter side of the triangle is 7 centimeters less than the longer side ' ' may be formulated . b = a - 7 or b = ( h - 2 ) - 7 = h - 9 we now use pythagora ' s theorem to write a third equation h 2 = a 2 + b 2 substitute a by h - 2 and b by h - 9 in the above equation to obtain an equation in one variable only . h 2 = ( h - 2 ) 2 + ( h - 9 ) 2 simplify and rewrite the above equation in standard form . h 2 - 22 h + 85 = 0 solve for h . h = 5 and h = 17 . only the solution h = 17 gives a and b positive and it is the length of the hypotenuse of the triangle . answer a" + }, + { + "Answer": 70, + "Options": "a ) 70 feet , b ) 52 feet , c ) 32 feet , d ) 12 feet , e ) 55 feet", + "Correct": "a", + "Explanation": "\"explanation : we are given with length and area , so we can find the breadth . as length * breadth = area = > 30 * breadth = 600 = > breadth = 20 feet area to be fenced = 2 b + l = 2 * 20 + 30 = 70 feet answer : option a\"" + }, + { + "Answer": 6, + "Options": "['a ) x ^ 2', 'b ) x ^ 3', 'c ) x ^ 6', 'd ) 6 x ^ 2', 'e ) 6 x ^ 3']", + "Correct": "d", + "Explanation": "the question basically asks you to calculate the surface area of the cube . volume of the cube = x ^ 3 this means each side of the cube = x hence area of each side = x ^ 2 total surfaces in a cube = 6 total surface area = 6 * x 2 correct option : d" + }, + { + "Answer": 156, + "Options": "a ) 43 , b ) 156 , c ) 68 , d ) 87 , e ) 92", + "Correct": "b", + "Explanation": "\"sol . monthly rent per square feet = 1300 / ( 10 * 10 ) = 13 & annual rent per square feet = 12 * 13 = 156 answer : b\"" + }, + { + "Answer": 61.69911184307752, + "Options": "['a ) 54', 'b ) 62', 'c ) 25', 'd ) 34', 'e ) 60']", + "Correct": "b", + "Explanation": "perimeter of a circle = 2 pi * r perimeter of a semicircle = pi * r + 2 r aprox perimiter = 3.14 * 12 + 2 * 12 = 61.68 approximately 62 answer b" + }, + { + "Answer": 96, + "Options": "a ) 96 cm 2 , b ) 104 cm 2 , c ) 78 cm 2 , d ) 86 cm 2 , e ) 76 cm 2", + "Correct": "a", + "Explanation": "\"area of a parallelogram = base * height = 12 * 8 = 96 cm 2 answer : a\"" + }, + { + "Answer": 130, + "Options": "a ) 176 , b ) 130 , c ) 150 , d ) 179 , e ) 172", + "Correct": "b", + "Explanation": "\"1 / 2 * 13 * 20 = 130 answer : b\"" + }, + { + "Answer": 1900, + "Options": "['a ) 2,000', 'b ) 1,800', 'c ) 1,900', 'd ) 1,700', 'e ) none of these']", + "Correct": "c", + "Explanation": "total area of road = area of road which parallel to length + area of road which parallel to breadth \u2013 overlapped road = 70 \u00d7 5 + 30 \u00d7 5 \u2013 5 \u00d7 5 = 350 + 150 \u2013 25 = 500 \u2013 25 = 475 m 2 \u2234 cost of gravelling the road = 475 \u00d7 4 = 1900 answer c" + }, + { + "Answer": 144, + "Options": "['a ) 56', 'b ) 80', 'c ) 100', 'd ) 120', 'e ) 144']", + "Correct": "e", + "Explanation": "r = 6 c 5 * ( 5 - 1 ) ! ( select 5 out of 6 and arrange them in circular manner ) = 6 * 4 ! = 6 * 24 = 144 answer - e" + }, + { + "Answer": 153.93804002589985, + "Options": "['a ) 154 cm 2', 'b ) 308 m 2', 'c ) 150 m 2', 'd ) 407 m 2', 'e ) none of these']", + "Correct": "a", + "Explanation": "area of the shaded portion = 1 \u2044 4 \u00d7 \u03c0 \u00d7 ( 14 ) 2 = 154 m 2 answer a" + }, + { + "Answer": 16, + "Options": "['a ) 1', 'b ) 2', 'c ) 4', 'd ) 8', 'e ) 16']", + "Correct": "e", + "Explanation": "as per the question - - width is negligible now , let l be the length of the fence = 2 pir l = 1 / 8 ( pir ^ 2 ) pir ^ 2 = 16 pir r = 16 answer : e" + }, + { + "Answer": 25.132741228718345, + "Options": "a ) 77.14 cm , b ) 25.14 cm , c ) 84.92 cm , d ) 94.94 cm , e ) 23.57 cm", + "Correct": "b", + "Explanation": "\"let the side of the square be a cm . parameter of the rectangle = 2 ( 18 + 14 ) = 64 cm parameter of the square = 64 cm i . e . 4 a = 64 a = 16 diameter of the semicircle = 16 cm circimference of the semicircle = 1 / 2 ( \u220f ) ( 16 ) = 1 / 2 ( 22 / 7 ) ( 16 ) = 352 / 14 = 25.14 cm to two decimal places answer : b\"" + }, + { + "Answer": 60, + "Options": "['a ) 450 m 3', 'b ) 100 m 2', 'c ) 60 m 3', 'd ) 400 m 3', 'e ) 500 m 3']", + "Correct": "c", + "Explanation": "lb = 20 ; lh = 15 ; fh = 12 ( lbh ) 2 = 20 * 15 * 12 = > lbh = 60 m 3 answer : c" + }, + { + "Answer": 462, + "Options": "a ) 462 cm 2 , b ) 478 cm 2 , c ) 490 cm 2 , d ) 268 cm 2 , e ) 668 cm 2", + "Correct": "a", + "Explanation": "\"area of a parallelogram = base * height = 22 * 21 = 462 cm 2 answer : a\"" + }, + { + "Answer": 12, + "Options": "a ) 8 m , b ) 10 m , c ) 12 m , d ) 15 m , e ) 17 m", + "Correct": "c", + "Explanation": "\"let the length of the hall be x m breadth of the hall = 1 x / 2 m area of the hall = length * breadth 288 = x * 1 x / 2 x \u00b2 = 576 x = 24 difference between the length and breadth of the hall = x - 1 x / 2 = x / 2 = 24 / 2 = 12 m answer : c\"" + }, + { + "Answer": 15, + "Options": "['a ) 7.5 cm rise', 'b ) 10 cm rise', 'c ) 15 cm rise', 'd ) 30 cm rise', 'e ) none of these']", + "Correct": "c", + "Explanation": "explanation : volume of cube = a 3 = a * a * a 60 cm * 30 cm * h = 30 cm * 30 cm * 30 cm h = 15 cm answer is c" + }, + { + "Answer": 196, + "Options": "a ) 196 cm 2 , b ) 187 cm 2 , c ) 178 cm 2 , d ) 189 cm 2 , e ) 176 cm 2", + "Correct": "a", + "Explanation": "\"the triangle with sides 30 cm , 28 cm and 14 cm is right angled , where the hypotenuse is 30 cm . area of the triangle = 1 / 2 * 28 * 14 = 196 cm 2 answer : a\"" + }, + { + "Answer": 4.71238898038469, + "Options": "a ) 4.51 , b ) 4.71 , c ) 4.32 , d ) 4.21 , e ) 4.68", + "Correct": "b", + "Explanation": "\"let the side of the square be a cm . parameter of the rectangle = 2 ( 4 + 2 ) = 12 cm parameter of the square = 12 cm i . e . 4 a = 12 a = 3 diameter of the semicircle = 3 cm circimference of the semicircle = 1 / 2 ( \u00e2 \u02c6 \u008f ) ( 3 ) = 1 / 2 ( 22 / 7 ) ( 3 ) = 66 / 14 = 4.71 cm to two decimal places answer : b\"" + }, + { + "Answer": 130, + "Options": "a ) 120 cm 2 , b ) 112 cm 2 , c ) 776 cm 2 , d ) 130 cm 2 , e ) 886 cm 2", + "Correct": "d", + "Explanation": "\"the triangle with sides 28 cm , 26 cm and 10 cm is right angled , where the hypotenuse is 28 cm . area of the triangle = 1 / 2 * 26 * 10 = 130 cm 2 answer : d\"" + }, + { + "Answer": 11, + "Options": "a ) 8 , b ) 9 , c ) 7 , d ) 11 , e ) 2", + "Correct": "d", + "Explanation": "\"2 x * x = 242 = > x = 11 answer : d\"" + }, + { + "Answer": 36, + "Options": "a ) 50 , b ) 40 , c ) 25 , d ) 36 , e ) 45", + "Correct": "d", + "Explanation": "\"area of tile = 25 * 65 = 1625 area of floor = 150 * 390 = 58500 no of tiles = 58500 / 1625 = 36 so , the no of tile = 36 answer : d\"" + }, + { + "Answer": 9, + "Options": "a ) 88 m 2 , b ) 9 m 2 , c ) 66 m 2 , d ) 77 m 2 , e ) 31 m 2", + "Correct": "b", + "Explanation": "\"1 / 2 * 3 * 6 = 9 m 2 answer : b\"" + }, + { + "Answer": 4, + "Options": "a ) 0 , b ) 5 , c ) 8 , d ) 9 , e ) 4", + "Correct": "e", + "Explanation": "\"explanation : let the number be x and on dividing x by 5 , we get k as quotient and 3 as remainder . x = 5 k + 3 x ^ 2 = ( 5 k + 3 ) ^ 2 = ( 25 k ^ 2 + 30 k + 9 ) = 5 ( 5 k ^ 2 + 6 k + 1 ) + 4 on dividing x 2 by 5 , we get 4 as remainder . e )\"" + }, + { + "Answer": 69, + "Options": "a ) 52.65 , b ) 69 , c ) 50.75 , d ) 42.75 , e ) 52.75", + "Correct": "b", + "Explanation": "\"a = 100 a 2 = 10000 a = 130 a 2 = 16900 - - - - - - - - - - - - - - - - 10000 - - - - - - - - - 6900 100 - - - - - - - ? = > 69 % answer : b\"" + }, + { + "Answer": 49, + "Options": "a ) 7 : 1 , b ) 14 : 1 , c ) 21 : 1 , d ) 42 : 1 , e ) 49 : 1", + "Correct": "e", + "Explanation": "\"let x be the length of the small cube ' s side . the total surface area of the small cube is 6 x ^ 2 . the total surface area of the large cube is 6 ( 7 x ) ^ 2 = 294 x ^ 2 . the ratio of surface areas is 49 : 1 . the answer is e .\"" + }, + { + "Answer": 64, + "Options": "['a ) 128 m', 'b ) 64 m', 'c ) 64 m ^ 2', 'd ) 128 m ^ 2', 'e ) none']", + "Correct": "b", + "Explanation": "b * h / 2 = 128 / 2 = 64 m . ans : ( b )" + }, + { + "Answer": 35.99114857512855, + "Options": "['a ) 36', 'b ) 25', 'c ) 15', 'd ) 28', 'e ) 37']", + "Correct": "a", + "Explanation": "perimeter of a circle = 2 pi * r perimeter of a semicircle = pi * r + 2 r aprox perimiter = 3.14 * 7 + 2 * 7 = 35.98 approximately 36 answer a" + }, + { + "Answer": 142.40786495134319, + "Options": "a ) 100 , b ) 141.7 , c ) 150 , d ) 180 , e ) none", + "Correct": "b", + "Explanation": "\"solution other side = \u221a ( 17 ) 2 - ( 13 ) 2 = \u221a 289 - 169 = \u221a 120 = 10.9 m . \u2234 area = ( 13 x 10.9 ) m 2 = 141.7 m 2 . answer b\"" + }, + { + "Answer": 50, + "Options": "a ) 76 , b ) 88 , c ) 66 , d ) 55 , e ) 50", + "Correct": "e", + "Explanation": "\"area of a triangle = r * s where r is the in radius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 40 / 2 = 50 cm 2 answer : e\"" + }, + { + "Answer": 125, + "Options": "['a ) 46', 'b ) 81', 'c ) 126', 'd ) 252', 'e ) none of these']", + "Correct": "c", + "Explanation": "solution clearly , we have : l = 9 and l + 2 b = 37 or b = 14 . \u2234 area = ( l \u00d7 b ) = ( 9 \u00d7 14 ) sq . ft . = 126 sq . ft . answer c" + }, + { + "Answer": 42, + "Options": "a ) 42 , b ) 56 , c ) 88 , d ) 112 , e ) 116", + "Correct": "a", + "Explanation": "\"ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 6 + 6 = 12 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 12 * 7 = 42 a is the answer\"" + }, + { + "Answer": 35, + "Options": "['a ) 30', 'b ) 31', 'c ) 32', 'd ) 34', 'e ) 35']", + "Correct": "e", + "Explanation": "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 28 / 2 = 35 cm 2 answer : option e" + }, + { + "Answer": 36, + "Options": "['a ) 4', 'b ) 6', 'c ) 12', 'd ) 24', 'e ) 36']", + "Correct": "e", + "Explanation": "( average ) = ( perimeter ) / 3 ; 12 = ( perimeter ) / 3 ; ( perimeter ) = 36 . answer : e ." + }, + { + "Answer": 102, + "Options": "['a ) 64', 'b ) 72', 'c ) 86', 'd ) 98', 'e ) 102']", + "Correct": "e", + "Explanation": "use the options . the options which after getting added to 23 shows a cube of a number could be right . here 64 + 23 = 87 72 + 23 = 95 86 + 23 = 109 98 + 23 = 121 102 + 23 = 125 - - - ( 5 * 5 * 5 ) so we have 102 as the answer ! e" + }, + { + "Answer": 16, + "Options": "a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 13", + "Correct": "b", + "Explanation": "\"4 ^ 2 + 3 ^ 2 + 8 ^ 2 + 1 ^ 2 = 90 - - > 1 + 3 + 8 + 4 = 16 . b\"" + }, + { + "Answer": 24, + "Options": "['a ) 24', 'b ) 28', 'c ) 36', 'd ) 48', 'e ) none of these']", + "Correct": "a", + "Explanation": "solution required perimeter = ( ab + bc + cp + pq + qr + ra ) = ab + bc + ( cp + qr ) + ( pq + ra ) = ab + bc + ab + bc = 2 ( ab + bc ) = [ 2 ( 8 + 4 ) ] cm = 24 cm . answer a" + }, + { + "Answer": 147, + "Options": "a ) 432 , b ) 212 , c ) 252 , d ) 992 , e ) 147", + "Correct": "e", + "Explanation": "\"2 ( 3 x + x ) = 56 l = 21 b = 7 lb = 21 * 7 = 147 answer : e\"" + }, + { + "Answer": 588, + "Options": "a ) 432 sq m , b ) 356 sq m , c ) 452 sq m , d ) 588 sq m , e ) 525 sq m", + "Correct": "d", + "Explanation": "\"2 ( 3 x + x ) = 112 l = 42 b = 14 lb = 42 * 14 = 588 answer : d\"" + }, + { + "Answer": 0.8, + "Options": "a ) 0.9 % , b ) 0.8 % , c ) 0.3 % , d ) 0.2 % , e ) 0.5 %", + "Correct": "b", + "Explanation": "\"explanation : let x and y be the sides of the rectangle then correct area = = error % = answer : b ) 0.8 %\"" + }, + { + "Answer": 14, + "Options": "a ) 16 , b ) 14 , c ) 25 , d ) 87 , e ) 171", + "Correct": "b", + "Explanation": "\"explanation : let the integer be x . then , x + x 2 = 210 x 2 + x - 210 = 0 ( x + 15 ) ( x \u2013 14 ) = 0 x = 14 answer : b\"" + }, + { + "Answer": 232, + "Options": "a ) 144 , b ) 131 , c ) 232 , d ) 90 , e ) 45", + "Correct": "c", + "Explanation": "\"there are 16 business exec and in each handshake 2 business execs are involved . hence 16 c 2 = 120 also , each of 16 exec will shake hand with every 7 other chairmen for total of 112 handshake . total = 120 + 112 = 232 ans : c\"" + }, + { + "Answer": 10, + "Options": "a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25", + "Correct": "b", + "Explanation": "\"l * w = 200 : area , l is the length and w is the width . 2 l + 2 w = 60 : perimeter l = 30 - w : solve for l ( 30 - w ) * w = 200 : substitute in the area equation w = 10 and l = 20 : correct answer b\"" + }, + { + "Answer": 3, + "Options": "a ) 3.1 feet , b ) 3.2 feet , c ) 3.3 feet , d ) 3.0 feet , e ) 3.5 feet", + "Correct": "d", + "Explanation": "\"we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 2 = 36 36 / 12 = 3.0 feet answer : d\"" + }, + { + "Answer": 4000, + "Options": "['a ) 400 square meters', 'b ) 4000 square meters', 'c ) 20 square meters', 'd ) 2000 square meters', 'e ) 1000 square meters']", + "Correct": "b", + "Explanation": "solution if the ratio of the length to the width is 5 : 2 , then the measure l of the length and and the measure w of the with can be written as l = 5 x and w = 2 x we now use the perimeter to write 280 = 2 ( 2 l + 2 w ) = 2 ( 5 x + 2 x ) = 14 x solve for x 280 = 14 x x = 280 / 14 = 20 the area a of the rectangle is given by a = l \u00d7 w = 5 x \u00d7 2 x = 10 x ^ 2 = 10 \u00d7 20 ^ 2 = 4000 square meters answer is b" + }, + { + "Answer": 118.8, + "Options": "a ) 52.6 , b ) 52.9 , c ) 52.8 , d ) 118.8 , e ) 52.2", + "Correct": "d", + "Explanation": "\"42 / 360 * 22 / 7 * 18 * 18 = 118.8 m 2 answer : d\"" + }, + { + "Answer": 31.999999999999996, + "Options": "a ) 13 , b ) 16 , c ) 18 , d ) 29 , e ) 32", + "Correct": "e", + "Explanation": "\"lets suppose length = l , breadth = b , depth = d front face area = l * w = 1 / 2 w * d ( l = 1 / 2 d or d = 2 l ) top face area = w * d side face area = w * d = 1.5 d * l ( w = 1.5 l ) volume = l * w * d = 192 l * 1.5 l * 2 l = 192 l = 4 side face area = l * d = l * 2 l = 4 * 2 * 4 = 32 e is the answer\"" + }, + { + "Answer": 200, + "Options": "a ) 140 , b ) 150 , c ) 160 , d ) 170 , e ) 200", + "Correct": "e", + "Explanation": "\"given that the area of the square = 2500 sq . units = > side of square = \u221a 2500 = 50 units the radius of the circle = side of the square = 50 units length of the rectangle = 2 / 5 * 50 = 20 units given that breadth = 10 units area of the rectangle = lb = 20 * 10 = 200 sq . units answer : option e\"" + }, + { + "Answer": 47.12388980384689, + "Options": "a ) 47.14 , b ) 45.15 , c ) 43.23 , d ) 41.44 , e ) 41.51", + "Correct": "a", + "Explanation": "\"let the side of the square be a cm . parameter of the rectangle = 2 ( 40 + 20 ) = 120 cm parameter of the square = 120 cm i . e . 4 a = 120 a = 30 diameter of the semicircle = 30 cm circimference of the semicircle = 1 / 2 ( \u00e2 \u02c6 \u008f ) ( 30 ) = 1 / 2 ( 22 / 7 ) ( 30 ) = 660 / 14 = 47.14 cm to two decimal places answer : a\"" + }, + { + "Answer": 6070.778380479544, + "Options": "a ) 2399 , b ) 3888 , c ) 2999 , d ) 5808 , e ) 6072", + "Correct": "e", + "Explanation": "\"explanation : area = ( 13.86 x 10000 ) sq . m = 138600 sq . m circumference = cost of fencing = rs . ( 1320 x 4.60 ) = rs . 6072 . answer : e ) 6072\"" + }, + { + "Answer": 10, + "Options": "a ) 10 , b ) 36 , c ) 38 , d ) 40 , e ) 42", + "Correct": "a", + "Explanation": "\"let length and breadth of photograph be l and b respectively . perimeter is given by 2 * ( l + b ) - - - - - ( 1 ) according to the question : ( l + 2 ) ( b + 2 ) = m - - - - ( 2 ) and ( l + 6 ) ( b + 6 ) = m + 52 - - - - - - - - - > ( l + 6 ) ( b + 6 ) - 52 = m - - - - - - ( 3 ) equating ( 2 ) and ( 3 ) ( l + 2 ) ( b + 2 ) = ( l + 6 ) ( b + 6 ) - 52 lb + 2 l + 2 b + 4 = lb + 6 l + 6 b + 36 - 52 simplify 4 l + 4 b = 20 - - - - - - > 2 ( l + b ) = 10 ( check eq ( 1 ) ) answer is a\"" + }, + { + "Answer": 45, + "Options": "a ) 90 \u00b0 , b ) 75 \u00b0 , c ) 60 \u00b0 , d ) 45 \u00b0 , e ) 30 \u00b0", + "Correct": "d", + "Explanation": "let smaller be x , larger becomes x + 90 . . . total of all angles = 360 so 4 x + 180 = 360 and x = 45 answer : d" + }, + { + "Answer": 7427.406478511646, + "Options": "a ) 4457 , b ) 4567 , c ) 4235 , d ) 4547 , e ) 7429", + "Correct": "e", + "Explanation": "\"explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . \u03c0 r 2 = 175600 \u21d4 ( r ) 2 = ( 175600 x ( 7 / 22 ) ) \u21d4 r = 236.37 m . circumference = 2 \u03c0 r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 5 ) = rs . 7429 . answer : option e\"" + }, + { + "Answer": 1875, + "Options": "['a ) 100', 'b ) 250', 'c ) 1875', 'd ) 1200', 'e ) 5625']", + "Correct": "c", + "Explanation": "6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 20 * 25 * 1 / 2 = 250 feet ^ 3 of water must be removed , which equals to 250 * 7.5 = 1875 gallons . answer : c ." + }, + { + "Answer": 16, + "Options": "['a ) 16', 'b ) 24', 'c ) 32', 'd ) 48', 'e ) none of these']", + "Correct": "a", + "Explanation": "area left after laying black tiles = [ ( 20 \u2013 4 ) \u00d7 ( 10 \u2013 4 ) ] sq . ft . = 96 sq . ft . area under white tiles = ( 1 \u2044 3 \u00d7 96 ) sq . ft = 32 sq . ft . area under blue tiles = ( 96 \u2013 32 ) sq . ft = 64 sq . ft . number of blue tiles = 64 / 2 \u00d7 2 = 16 . answer a" + }, + { + "Answer": 220, + "Options": "a ) 126 , b ) 156 , c ) 190 , d ) 321 , e ) 220", + "Correct": "e", + "Explanation": "\"sol . let width = x , length = ( 10 + x ) perimeter = 2 ( x + ( 10 + x ) ) = 2 ( 2 x = 10 ) & 2 ( 2 x + 10 ) * 6.5 = 1430 x = 50 required perimeter = 2 ( 50 + 60 ) = 220 e\"" + }, + { + "Answer": 598, + "Options": "['a ) 598 sq . units', 'b ) 556 sq . units', 'c ) 589 sq . units', 'd ) 958 sq . units', 'e ) 985 sq . units']", + "Correct": "a", + "Explanation": "given that the area of the square = 4761 sq . units = > side of square = \u00e2 \u02c6 \u0161 4761 = 69 units the radius of the circle = side of the square = 69 units length of the rectangle = 2 / 3 * 69 = 46 units given that breadth = 13 units area of the rectangle = lb = 46 * 13 = 598 sq . units answer : a" + }, + { + "Answer": 75, + "Options": "['a ) 40 %', 'b ) 50 %', 'c ) 75 %', 'd ) 80 %', 'e ) 90 %']", + "Correct": "c", + "Explanation": "let the volume of sphere pp be 64 parts . therefore volume of sphere qq = 64 \u2212 3764 % = 64 \u2212 3764 % of 6464 = 64 \u2212 37 = 27 = 64 \u2212 37 = 27 parts . the volume of rr = 27 \u2212 1927 \u00d7 27 = 27 \u2212 1927 \u00d7 27 = 27 \u2212 19 = 8 = 27 \u2212 19 = 8 parts . volume ratio : = p : q : r = 64 : 27 : 8 = p : q : r = 64 : 27 : 8 radius ratio : = p : q : r = 4 : 3 : 2 = p : q : r = 4 : 3 : 2 the surface area will be 16 : 9 : 516 : 9 : 5 surface area of rr is less than the surface area of sphere pp 16 k \u2212 4 k = 12 k 16 k \u2212 4 k = 12 k now , = 12 k 16 k \u00d7 100 = 12 k 16 k \u00d7 100 = 75 % = 75 % thus surface area of sphere rr is less than the surface area of sphere p by 75 % c" + }, + { + "Answer": 99, + "Options": "a ) 144 , b ) 131 , c ) 99 , d ) 90 , e ) 45", + "Correct": "c", + "Explanation": "there are 9 business exec and in each handshake 2 business execs are involved . hence 9 c 2 = 36 also , each of 9 exec will shake hand with every 7 other chairmen for total of 63 handshake . total = 36 + 63 = 99 ans : c" + }, + { + "Answer": 135, + "Options": "['a ) 145', 'b ) 135', 'c ) 75', 'd ) 140', 'e ) none of these']", + "Correct": "b", + "Explanation": "let breadth = x , length = 3 x . area of rectangle = length * breadth = 3 x ^ 2 = 6075 x ^ 2 = 2025 , x = \u221a 2025 = 45 m length = 135 m answer b" + }, + { + "Answer": 196, + "Options": "a ) 127 , b ) 196 , c ) 116 , d ) 140 , e ) 234", + "Correct": "b", + "Explanation": "b 196 the only numbers that can be turned upside down and still read as a number are 0 , 1 , 6 , 8 and 9 . the numbers 0 , 1 and 8 remain 0 , 1 and 8 when turned over , but 6 becomes 9 and 9 becomes 6 . therefore the possible numbers on the bus were 9 , 16 , 81 , 100 , 169 or 196 . however , the number 196 is the only number which becomes a perfect square when turned over because 961 is the perfect square of 31 . therefore 196 is the correct answer ." + }, + { + "Answer": 100, + "Options": "['a ) 250 meter', 'b ) 100 meter', 'c ) 50 \u221a 2 meter', 'd ) 50 meter', 'e ) 35 meter']", + "Correct": "b", + "Explanation": "area = 1 / 2 hectare = 10000 / 2 m 2 = 5000 m 2 again area = 1 / 2 x ( diagonal ) 2 so 1 / 2 x ( diagonal ) 2 = 5000 m 2 diagonal 2 = 10000 diagonal = 100 answer : b" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "\"imo it should be c that is 4 reason : formed an equation . . . bat = b ball = c 2 b + 4 c = 220 1 b + 6 c = 190 solving both we get b that is bat = 70 and c that is ball = 20 new equation 270 to be divided in equal 3 b + 3 c = 270 3 * 70 + 3 * 20 = 270 210 + 60 = 270\"" + }, + { + "Answer": 75, + "Options": "['a ) 300', 'b ) 150', 'c ) 75', 'd ) 40', 'e ) 20']", + "Correct": "c", + "Explanation": "area of rhombus = 0.5 x 15 x 20 = 150 cm \u00e2 \u00b2 area of triangle = 150 / 2 = 75 cm \u00e2 \u00b2 answer : c" + }, + { + "Answer": 16, + "Options": "['a ) 20', 'b ) 16', 'c ) 12', 'd ) 8', 'e ) 4']", + "Correct": "b", + "Explanation": "let x be the side length of square a . then the area of square a is x ^ 2 . the area of square b is ( 4 x ) ^ 2 = 16 x ^ 2 . the answer is b ." + }, + { + "Answer": 11236, + "Options": "['a ) 11236', 'b ) 11025', 'c ) 14400', 'd ) 12696', 'e ) can not be determined']", + "Correct": "a", + "Explanation": "explanatory answer the shape of the area used for growing cabbages has remained a square in both the years . let the side of the square area used for growing cabbages this year be x ft . therefore , the area of the ground used for cultivation this year = x 2 sq . ft . let the side of the square area used for growing cabbages last year be y ft . therefore , the area of the ground used for cultivation last year = y 2 sq . ft . as the number of cabbages grown has increased by 211 , the area would have increased by 211 sq ft because each cabbage takes 1 sq ft space . hence , x 2 - y 2 = 211 ( x + y ) ( x - y ) = 211 . 211 is a prime number and hence it will have only two factors . i . e . , 211 and 1 . therefore , 211 can be expressed as product of 2 numbers in only way = 211 * 1 i . e . , ( x + y ) ( x - y ) = 211 * 1 so , ( x + y ) should be 211 and ( x - y ) should be 1 . solving the two equations we get x = 106 and y = 105 . therefore , number of cabbages produced this year = x 2 = 1062 = 11236 . alternative approach : use answer choices the area in both the years are squares of two numbers . that rules out choice d . 12696 is not the square of any number . check choice a : if this year ' s produce is 11236 , last year ' s produce would have been 11236 - 211 = 11025 11025 is the square of 105 . so , 11236 is the answer . choice a is the correct answer ." + }, + { + "Answer": 4, + "Options": "['a ) 5', 'b ) 4', 'c ) 3', 'd ) 2', 'e ) 1']", + "Correct": "b", + "Explanation": "the equation is ; side + area - perimeter = s + a - p = s + s ^ 2 - 4 s = s ( 1 + s - 4 ) . by plugging in the answers we can test the answers quickly ; then , 4 is the only possible answer . answer : b" + }, + { + "Answer": 33893.63668085003, + "Options": "a ) 29960 sq m , b ) 33880 sq m , c ) 43120 sq m , d ) 27680 sq m , e ) 12786 sq m", + "Correct": "b", + "Explanation": "\"let the radii of the smaller and the larger circles be s m and l m respectively . 2 \u220f s = 264 and 2 \u220f l = 704 s = 264 / 2 \u220f and l = 704 / 2 \u220f difference between the areas = \u220f l ^ 2 - \u220f s ^ 2 = \u220f { 132 ^ 2 / \u220f ^ 2 - 352 ^ 2 / \u220f ^ 2 } = 132 ^ 2 / \u220f - 352 ^ 2 / \u220f = ( 132 - 352 ) ( 132 + 352 ) / \u220f = ( 220 ) ( 484 ) / ( 22 / 7 ) = 33880 sq m answer : b\"" + }, + { + "Answer": 60, + "Options": "['a ) 45', 'b ) 54', 'c ) 67', 'd ) 60', 'e ) 69']", + "Correct": "d", + "Explanation": "ans . ( d ) sol . length of original rectangle = 150 / 10 = 15 ( 10 * ( 15 + x ) ) / ( 10 * 15 ) = 4 / 3 x = 5 perimeter of new rectangle = 2 ( 10 + 20 ) = 60" + }, + { + "Answer": 96, + "Options": "a ) 96 , b ) 56.25 , c ) 50.75 , d ) 42.75 , e ) 52.75", + "Correct": "a", + "Explanation": "\"a = 100 a 2 = 10000 a = 140 a 2 = 19600 - - - - - - - - - - - - - - - - 10000 - - - - - - - - - 9600 100 - - - - - - - ? = > 96 % answer : a\"" + }, + { + "Answer": 10, + "Options": "a ) 10 units , b ) 20 units , c ) 30 units , d ) 40 units , e ) 15 units", + "Correct": "a", + "Explanation": "\"base of isoceles triangle is 40 - 15 - 15 = 10 units . answer : a\"" + }, + { + "Answer": 50, + "Options": "['a ) 40', 'b ) 45', 'c ) 50', 'd ) 55', 'e ) 60']", + "Correct": "c", + "Explanation": "let l be the number of lower seat tickets . let u be the number of upper seat tickets . l + u = 80 and u = 80 - l . 30 l + 20 u = 2100 . 30 l + 20 ( 80 - l ) = 2100 10 l + 1600 = 2100 . 10 l = 500 . l = 50 . the answer is c ." + }, + { + "Answer": 164, + "Options": "['a ) 46', 'b ) 64', 'c ) 164', 'd ) 146', 'e ) 56']", + "Correct": "c", + "Explanation": "the problem asks for a combination , since order does n ' t matter . now , selecting r items from a set of n gives the combination formula : ncr = n ! / r ! ( n - r ) ! n = 12 r = 3 so , total groups is 12 c 3 = 12 ! / ( 3 ! ( 12 - 3 ) ! ) = 220 , and n = 12 - 4 = 8 r = 3 for groups without a triangle is 8 c 3 = 8 ! / ( 3 ! ( 8 - 3 ) ! ) = 56 , so , groups with at least 1 triangle = 220 - 56 = 164 answer : c" + }, + { + "Answer": 244.9489742783178, + "Options": "a ) 244.85 , b ) 224.95 , c ) 244.85 , d ) 224.95 , e ) 244.95", + "Correct": "e", + "Explanation": "\"area of the rhombus = 1 / 2 * p * \u221a 4 ( a ) 2 - ( p ) 2 a = 25 ; p = 10 a = 1 / 2 * 10 * \u221a 4 ( 25 ) 2 - ( 10 ) 2 = 1 / 2 * 10 * \u221a 2500 - 100 = 1 / 2 * 10 * \u221a 2400 a = 244.95 answer : e\"" + }, + { + "Answer": 5760, + "Options": "a ) 4830 , b ) 5120 , c ) 6420 , d ) 7500 , e ) 5760", + "Correct": "e", + "Explanation": "\"l = ( 52 - 16 ) m = 36 m , b = ( 36 - 16 ) m = 20 m , h = 8 m . volume of the box = ( 36 x 20 x 8 ) m 3 = 5760 m 3 . answer : option e\"" + }, + { + "Answer": 14, + "Options": "a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 14", + "Correct": "e", + "Explanation": "\"let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 588 3 b 2 = 588 b 2 = 196 b = 14 m . answer : option e\"" + }, + { + "Answer": 90, + "Options": "['a ) 50 sq units', 'b ) 60 sq units', 'c ) 70 sq units', 'd ) 80 sq units', 'e ) 90 sq units']", + "Correct": "e", + "Explanation": "sum of length and breadth will be 21 units . 42 / 2 = 21 area will be max when lxb = 11 x 10 = 110 sq units area will be min when lxb = 20 x 1 = 20 sq units . . the difference between the largest and smallest possible ares of the rectangles that the students could have come up with = 110 - 20 = 90 sq units answer : e" + }, + { + "Answer": 157.5, + "Options": "a ) 277 , b ) 266 , c ) 150 , d ) 288 , e ) 157.5", + "Correct": "e", + "Explanation": "\"1 / 2 * 15 * 21 = 157.5 answer : e\"" + }, + { + "Answer": 30, + "Options": "a ) 25 , b ) 23 , c ) 32 , d ) 30 , e ) 18", + "Correct": "d", + "Explanation": "\"area of carol ' s rectangle = 24 * 5 = 120 let width of jordan ' s rectangle = w since , the areas are equal 4 w = 120 = > w = 30 answer d\"" + }, + { + "Answer": 704, + "Options": "['a ) 32', 'b ) 36', 'c ) 704', 'd ) 46', 'e ) 104']", + "Correct": "c", + "Explanation": "rug ' s area = 180 which is ( x ) x ( 8 + x ) = 180 so x = 10 rug maintains a uniform distance of 8 feet so room has dimension 10 + 16 and 18 + 16 i . e . 26 and 34 area of room 26 x 34 = 884 area covered is 180 so uncovered area is 884 - 180 = 704 ( answer c )" + }, + { + "Answer": 4, + "Options": "a ) 0 % , b ) 20 % increase , c ) 20 % decrease , d ) 4 % decrease , e ) insufficient data", + "Correct": "d", + "Explanation": "\"( 12 / 10 ) * ( 8 / 10 ) = 96 / 100 of original area 96 / 100 is a 4 % decrease from 100 / 100 - > d\"" + }, + { + "Answer": 9, + "Options": "a ) 6 / \u03c0 , b ) 9 / \u03c0 , c ) 6 , d ) 9 , e ) 12", + "Correct": "d", + "Explanation": "\"given area of the base of a hemisphere is 3 = pi * r ^ 2 thus r = sqrt ( 3 / pi ) . surface area of whole sphere = 4 * pi * r ^ 2 . = 4 * pi * 3 / pi = 12 . since the hemisphere is half of a sphere the surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . but the total surface area = 6 + area of the base of a hemisphere . = 6 + 3 = 9 . answer is d ! !\"" + }, + { + "Answer": 11, + "Options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14", + "Correct": "b", + "Explanation": "\"explanation : let the number be x . then , x 2 + x = 132 = > x 2 + x - 132 = 0 = > ( x + 12 ) ( x - 11 ) = 0 = > x = 11 answer : option b\"" + }, + { + "Answer": 450, + "Options": "['a ) 9', 'b ) 50', 'c ) 300', 'd ) 450', 'e ) 550']", + "Correct": "d", + "Explanation": "solution 3600 = 23 * 52 * 32 * 2 . to make it a perfect cube , it must be divided by 52 * 32 * 2 i . e . , 450 . answer d" + }, + { + "Answer": 50, + "Options": "['a ) 30', 'b ) 40', 'c ) 50', 'd ) 60', 'e ) 70']", + "Correct": "c", + "Explanation": "area of rectangle of max size inside circle will be a square with diagonal equal to 10 cms . then side of square = root ( 100 / 2 ) = root 50 area of square = root 50 * root 50 = 50 sq cms . answer : c" + }, + { + "Answer": 800, + "Options": "a ) 287 , b ) 269 , c ) 750 , d ) 200 , e ) 800", + "Correct": "e", + "Explanation": "\"d 2 / 2 = ( 40 * 40 ) / 2 = 800 answer : e\"" + }, + { + "Answer": 140, + "Options": "a ) 140 cm , b ) 767 cm , c ) 88 cm , d ) 666 cm , e ) 776 cm", + "Correct": "a", + "Explanation": "\"area of each slab = 98 / 50 m 2 = 1.96 m 2 length of each slab \u221a 1.96 = 1.4 m = 140 cm\"" + }, + { + "Answer": 2.5, + "Options": "a ) 5 / 2 , b ) 2 \u221a 5 , c ) 5 , d ) 4 \u221a 2 , e ) none of these", + "Correct": "a", + "Explanation": "\"area of sector , a = x / 360 * pi * r ^ 2 circumference of the sector = 10 = > x / 360 * 2 * pi * r + 2 r = 20 = > 2 a / r + 2 r = 10 or 2 a + 2 r ^ 2 = 10 r = > a = r 5 - r ^ 2 = r 5 - r ^ 2 we will now max using derivations i . e 5 - 2 r = 0 r = 5 / 2 a\"" + }, + { + "Answer": 32, + "Options": "a ) $ 1.60 , b ) $ 32.00 , c ) $ 96.00 , d ) $ 108.00 , e ) $ 196.00", + "Correct": "b", + "Explanation": "\"total surface area = 6 a ^ 2 = 6 * 10 * 10 = 600 each quart covers 20 sqr ft thus total number of quarts = 600 / 60 = 10 cost will be 10 * 3.2 = $ 32 ans : b\"" + }, + { + "Answer": 43.982297150257104, + "Options": "['a ) 14', 'b ) 28', 'c ) 42', 'd ) 44', 'e ) 56']", + "Correct": "d", + "Explanation": "side of the square = 28 / 4 = 7 diameter of the circle = 7 x 2 = 14 perimeter of the circle = \u00ef \u20ac xd = ( 22 / 7 ) x 14 = 44 cm answer : d" + }, + { + "Answer": 4, + "Options": "a ) 5 , b ) 7 , c ) 4 , d ) 8 , e ) 6", + "Correct": "c", + "Explanation": "since the side of the square is x + 2 , its perimeter = 4 ( x + 2 ) = 4 x + 8 since the side of the equilateral triangle is 2 x , its perimeter = 3 * 2 x = 6 x also , the perimeters of both are equal . ( i . e . ) 4 x + 8 = 6 x ( i . e . ) 2 x = 8 \u00e8 x = 4 . answer : c" + }, + { + "Answer": 71.99999999999999, + "Options": "['a ) 32', 'b ) 78', 'c ) 84', 'd ) 90', 'e ) 72']", + "Correct": "e", + "Explanation": "lets suppose length = l , breadth = b , depth = d front face area = l * w = 1 / 2 w * d ( l = 1 / 2 d or d = 2 l ) top face area = w * d side face area = w * d = 1.5 d * l ( w = 1.5 l ) volume = l * w * d = 648 l * 1.5 l * 2 l = 648 l = 6 side face area = l * d = l * 2 l = 6 * 2 * 6 = 72 e is the answer" + }, + { + "Answer": 380.132711084365, + "Options": "a ) 124 cm \u00b2 , b ) 144 cm \u00b2 , c ) 380 cm \u00b2 , d ) 284 cm \u00b2 , e ) 394 cm \u00b2", + "Correct": "c", + "Explanation": "\"area of circle = \u03c0 r \u00b2 = 22 / 7 \u00d7 11 \u00d7 11 cm \u00b2 = 154 cm \u00b2 answer : c\"" + }, + { + "Answer": 15, + "Options": "a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19", + "Correct": "a", + "Explanation": "\"perimeter = 2 ( w + l ) = 5 w 3 w = 2 l w = 2 l / 3 wl = 150 2 l ^ 2 / 3 = 150 l ^ 2 = 225 l = 15 cm the answer is a .\"" + }, + { + "Answer": 170, + "Options": "a ) 176 , b ) 186 , c ) 150 , d ) 170 , e ) 172", + "Correct": "d", + "Explanation": "\"1 / 2 * 17 * 20 = 170 answer : d\"" + }, + { + "Answer": 450, + "Options": "['a ) 425', 'b ) 430', 'c ) 440', 'd ) 450', 'e ) 460']", + "Correct": "d", + "Explanation": "l = 378 cm and b = 525 cm maximum length of a square tile = hcf of ( 378,525 ) = 21 cm number of tiles = ( 378 \u00d7 525 ) / ( 21 \u00d7 21 ) = ( 18 \u00d7 25 ) = 450 answer is d ." + }, + { + "Answer": 192, + "Options": "['a ) a ) 160 degree', 'b ) b ) 168 degree', 'c ) c ) 191 degree', 'd ) d ) 272 degree', 'e ) e ) 192 degree']", + "Correct": "e", + "Explanation": "let the common ratio be x . . so b = 2 x and g = 3 x and total = 5 x 1 / 3 of m = 2 x / 3 and 2 / 3 of f = 2 x . . total preferring that carrer = 2 x / 3 + 2 x = 8 x / 3 . . now 5 x = 360 , so x = 360 / 5 = 72 . . so x * 8 / 3 = 72 * 8 / 3 = 192 ans 192 e" + }, + { + "Answer": 1.9999999999999996, + "Options": "['a ) 2', 'b ) 3', 'c ) 4', 'd ) 16', 'e ) 41']", + "Correct": "a", + "Explanation": "d ^ 2 / ( 1 / 2 ) * d ^ 2 = 2 answer : a" + }, + { + "Answer": 41, + "Options": "a ) 34 , b ) 41 , c ) 68 , d ) 88 , e ) none", + "Correct": "b", + "Explanation": "\"explanation we have : l = 20 ft and lb = 210 sq . ft . so , b = 10.5 ft . length of fencing = ( l + 2 b ) = ( 20 + 21 ) ft = 41 ft . answer b\"" + }, + { + "Answer": 6, + "Options": "a ) 4 cm , b ) 6 cm , c ) 8 cm , d ) 10 cm , e ) 9 cm", + "Correct": "b", + "Explanation": "\"explanation : curved surface area of sphere = 4 / \u03c0 r 2 surface area of cylinder = 2 \u03c0 rh = > 4 / \u03c0 r 2 = 2 \u03c0 rh = > r 2 = 6 \u2217 12 / 2 = > r 2 = 36 = > r = 6 note : diameter of cylinder is 12 so radius is taken as 6 . option b\"" + }, + { + "Answer": 784.3155595568603, + "Options": "['a ) 1225 sq cm', 'b ) 441 sq cm', 'c ) 784 sq cm', 'd ) can \u2019 t say', 'e ) none of these']", + "Correct": "c", + "Explanation": "let the side of square = a cm and radius of circle = r cm given , 4 a = r also area of square = pi * r ^ 2 = 39424 , r ^ 2 = 12544 or r = 112 so a = r / 4 = 112 / 4 = 28 hence area of square = a ^ 2 = 28 ^ 2 = 784 cm ^ 2 answer : c" + }, + { + "Answer": 3.5000000000000004, + "Options": "a ) 3.5 percent increase , b ) 9.5 percent increase , c ) 1.5 percent increase , d ) 3.9 percent increase , e ) 3.5 percent increase", + "Correct": "e", + "Explanation": "\"let l and b be 100 each 100 * 100 = 10000 l increase by 15 % = 115 b decrease by 10 % = 90 115 * 90 = 10350 3.5 percent increase answer : e\"" + }, + { + "Answer": 10, + "Options": "a ) 10 metres , b ) 5 metres , c ) 7.5 metres , d ) data inadequate , e ) none of these", + "Correct": "a", + "Explanation": "\"l \u00d7 b = 20 \u00d7 b \u2234 l = 20 m and l \u2013 b = 10 \u2234 b = 20 \u2013 10 = 10 m answer a\"" + }, + { + "Answer": 659.7344572538566, + "Options": "a ) 330 , b ) 770 , c ) 660 , d ) 100 , e ) 600", + "Correct": "c", + "Explanation": "\"\u03c0 * 21 * 10 = 660 answer : c\"" + }, + { + "Answer": 48, + "Options": "a ) 38 . , b ) 40 . , c ) 42 . , d ) 48 . , e ) 46 .", + "Correct": "d", + "Explanation": "\"let the width = x x * 4 x = 1024 x ^ 2 = 256 x = 16 length = 4 * 16 = 64 difference = 64 - 16 = 48 d is the answer\"" + }, + { + "Answer": 72, + "Options": "a ) 144 , b ) 36 , c ) 72 , d ) 56 , e ) 112", + "Correct": "c", + "Explanation": "\"length of side 1 = 8 + 1 = 9 length of side 2 = 7 + 1 = 8 area of rectangle = 9 * 8 = 72 c is the answer\"" + }, + { + "Answer": 3, + "Options": "a ) 16 , b ) 8 , c ) 3 , d ) 2 , e ) 1", + "Correct": "c", + "Explanation": "\"x be radius of circle x y be radius of circle y given : pi * x ^ 2 = pi * y ^ 2 also , 2 * pi * x = 12 * pi x = 6 thus y = 6 y / 2 = 3 ans : c\"" + }, + { + "Answer": 0.28, + "Options": "a ) 0.11 % , b ) 0.7 % , c ) 0.4 % , d ) 0.6 % , e ) 0.28 %", + "Correct": "e", + "Explanation": "\"let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 12 / 11 ) x ( 23 / 25 ) y = ( 358 / 357 ) ( xy ) error in measurement = ( 358 / 357 ) xy - xy = ( 1 / 357 ) xy error percentage = [ ( 1 / 357 ) xy ( 1 / xy ) 100 ] % = ( 7 / 25 ) % = 0.28 % . answer is e .\"" + }, + { + "Answer": 1.3333333333333335, + "Options": "['a ) 1.33', 'b ) 1.25', 'c ) 8.0', 'd ) 12.5', 'e ) 80.0']", + "Correct": "a", + "Explanation": "density is mass divided by volume . so density of the given substance will be mass / volume = 800 kg / 1 m ^ 3 = 300 kg / m ^ 3 or 1 g / 1.33 cm ^ 3 = 0.3 g / cm ^ 3 . next , ask yourself if 300,000 g is equivalent to 1 , 000,000 cubic centimeters then 1 g is equivalent to how many cubic centimeters ? - - > 1 g - 1 , 000,000 / 300,000 = 10 / 3 = 1.33 cubic centimeters . answer is a" + }, + { + "Answer": 1, + "Options": "['a ) it will have no effect', 'b ) 1 % increase', 'c ) 1 % decrease', 'd ) 2 % increase', 'e ) 2 % decrease']", + "Correct": "c", + "Explanation": "let initial length = l , and breadth = b area = l * b new length = l * 110 % = [ l * 110 / 100 ] = 11 l / 10 , new breadth = 9 b / 10 new area = 11 l / 10 * 9 b / 10 = 99 / 100 lb decrease in area = [ lb - 99 / 100 lb ] = lb / 100 = % decrease = [ lb / 100 * 1 / lb * 100 ] = 1 % answer c" + }, + { + "Answer": 21.991148575128552, + "Options": "a ) 22 cm , b ) 47.14 cm , c ) 84.92 cm , d ) 94.94 cm , e ) 23.57 cm", + "Correct": "a", + "Explanation": "\"let the side of the square be a cm . parameter of the rectangle = 2 ( 16 + 12 ) = 56 cm parameter of the square = 56 cm i . e . 4 a = 56 a = 14 diameter of the semicircle = 14 cm circimference of the semicircle = 1 / 2 ( \u220f ) ( 14 ) = 1 / 2 ( 22 / 7 ) ( 14 ) = 308 / 14 = 22 cm answer : a\"" + }, + { + "Answer": 36, + "Options": "a ) 0 % , b ) 20 % increase , c ) 36 % decrease , d ) 1 % decrease , e ) insufficient data", + "Correct": "c", + "Explanation": "\"( 16 / 10 ) * ( 4 / 10 ) = 64 / 100 of original area 64 / 100 is a 36 % decrease from 100 / 100 - > c\"" + }, + { + "Answer": 14, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "c", + "Explanation": "\"let x be the width of the garden . 3 x ^ 2 = 588 x ^ 2 = 196 x = 14 the answer is c .\"" + }, + { + "Answer": 300, + "Options": "['a ) $ 5,330', 'b ) $ 3,360', 'c ) $ 1,350', 'd ) $ 300', 'e ) $ 150']", + "Correct": "d", + "Explanation": "basically the question an error . 1 acre = 43,560 square feet and if it is then the answer is 300 ( d )" + }, + { + "Answer": 60, + "Options": "['a ) 120', 'b ) 80', 'c ) 60', 'd ) 40', 'e ) none of these']", + "Correct": "c", + "Explanation": "let the length of the rectangular hall be \u2018 x \u2019 m , then the breadth of the rectangular hall = 2 x \u2044 3 m . area of hall = 2 x \u2044 3 \u00d7 x = 2 x 2 \u2044 3 or , 2 x 2 \u2044 3 = 2400 or x = 60 m answer c" + }, + { + "Answer": 1590, + "Options": "a ) 1590 , b ) 2535 , c ) 2530 , d ) 2515 , e ) 2520", + "Correct": "a", + "Explanation": "\"length = breadth + 23 . therefore , 4 \u00d7 breadth + 2 \u00d7 23 = 166 m \u21d2 breadth = 30 m length = 30 + 23 = 53 m area = 53 \u00d7 30 = 1590 m 2 answer is a .\"" + }, + { + "Answer": 12, + "Options": "['a ) 12', 'b ) 75', 'c ) 97', 'd ) 15', 'e ) 91']", + "Correct": "a", + "Explanation": "1 / 3 * \u03c0 * 3 * 3 * 4 = 12 \u03c0 answer : a" + }, + { + "Answer": 9, + "Options": "['a ) 16 p ^ 2', 'b ) 4 p', 'c ) 9 p ^ 2', 'd ) p / 16', 'e ) p ^ 2 / 16']", + "Correct": "c", + "Explanation": "each side is 3 p a = ( 3 p ) ^ 2 = 9 p ^ 2 answer c" + }, + { + "Answer": 120, + "Options": "a ) 140 sq . units , b ) 120 sq . units , c ) 187 sq . units , d ) 607 sq . units , e ) 815 sq . units", + "Correct": "b", + "Explanation": "\"given that the area of the square = 900 sq . units = > side of square = \u221a 900 = 30 units the radius of the circle = side of the square = 30 units length of the rectangle = 2 / 5 * 30 = 12 units given that breadth = 10 units area of the rectangle = lb = 12 * 10 = 120 sq . units answer : b\"" + }, + { + "Answer": 1200, + "Options": "a ) 1350 , b ) 1200 , c ) 9676 , d ) 1679 , e ) 2691", + "Correct": "b", + "Explanation": "\"area = ( l + b + 2 d ) 2 d = ( 60 + 55 + 2.5 * 2 ) 2 * 2.5 = > 600 600 * 2 = rs . 1200 answer : b\"" + }, + { + "Answer": 100, + "Options": "a ) 140 , b ) 99 , c ) 100 , d ) 72 , e ) 12", + "Correct": "c", + "Explanation": "\"given that the area of the square = 625 sq . units = > side of square = \u221a 625 = 25 units the radius of the circle = side of the square = 25 units length of the rectangle = 2 / 5 * 25 = 10 units given that breadth = 10 units area of the rectangle = lb = 10 * 10 = 100 sq . units answer : c\"" + }, + { + "Answer": 52, + "Options": "a ) 48 , b ) 40 , c ) 52 , d ) 54 , e ) 58", + "Correct": "c", + "Explanation": "\"isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side , the longer side with side 16 will be divided into 3 parts = 10 , 3 and 3 ( making one square and two right triangles ) for the right triangle , height will be = ( 5 ^ 2 - 3 ^ 2 ) ^ 1 / 2 = 4 and the area of trapezoid = 1 / 2 ( b 1 + b 2 ) h = 1 / 2 * 26 * 4 = 52 c is the answer\"" + }, + { + "Answer": 16, + "Options": "['a ) 32', 'b ) 8', 'c ) 16', 'd ) 24', 'e ) 0']", + "Correct": "c", + "Explanation": "16 = 2 ^ 3 each cube will have 2 ^ 3 cubes painted 1 side . answer : c" + }, + { + "Answer": 37500, + "Options": "a ) 37500 , b ) 38000 , c ) 38500 , d ) 39000 , e ) 39500", + "Correct": "a", + "Explanation": "\"given that breadth of the rectangular field is 60 % of its length . \u21d2 b = 60 l 100 = 3 l 5 perimeter of the field = 800 m \u21d2 2 ( l + b ) = 800 \u21d2 2 ( l + 3 l 5 ) = 800 \u21d2 l + 3 l 5 = 400 \u21d2 8 l 5 = 400 \u21d2 l 5 = 50 \u21d2 l = 5 \u00d7 50 = 250 m b = 3 l 5 = 3 \u00d7 2505 = 3 \u00d7 50 = 150 m area = lb = 250 \u00d7 150 = 37500 m 2 answer is a .\"" + }, + { + "Answer": 60, + "Options": "['a ) 48 m', 'b ) 52 m', 'c ) 54 m', 'd ) 60 m', 'e ) none of these']", + "Correct": "d", + "Explanation": "let length of new rectangle be x m then x \u00d7 10 = 150 \u00d7 4 / 3 = 200 or , x = 20 m hence new perimeter = 2 ( 10 + 20 ) = 60 m answer : d" + }, + { + "Answer": 2, + "Options": "a ) 4 , b ) 8 , c ) 2 , d ) 16 , e ) 18", + "Correct": "c", + "Explanation": "\"let length of rectangle = l 4 ^ 2 = l * 8 = > l = 16 / 8 = 2 answer c\"" + }, + { + "Answer": 56, + "Options": "a ) 22 , b ) 35 , c ) 56 , d ) 54 , e ) 23", + "Correct": "c", + "Explanation": "\"area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 3.5 * 32 / 2 = 56 cm 2 answer : c\"" + }, + { + "Answer": 2.5, + "Options": "a ) 16 , b ) 8 , c ) 4 , d ) 2.5 , e ) 1", + "Correct": "d", + "Explanation": "\"x be radius of circle x y be radius of circle y given : pi * x ^ 2 = pi * y ^ 2 also , 2 * pi * x = 10 * pi x = 5 thus y = 5 y / 2 = 2.5 ans : d\"" + }, + { + "Answer": 15, + "Options": "a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 15", + "Correct": "e", + "Explanation": "\"2 x * x = 450 = > x = 15 answer : e\"" + }, + { + "Answer": 0.6944444444444444, + "Options": "a ) 9 % less , b ) 0.7 % less , c ) equal to each other , d ) 1 % more , e ) 9 % more", + "Correct": "b", + "Explanation": "\"wish the question specified that we are talking about corresponding height . base of a = 13 / 12 * base of b height of a = 11 / 12 * height of b area of a = ( 1 / 2 ) * base of a * height of a = 13 / 12 * 11 / 12 * area of b = 143 / 144 * area of b area of a is 0.7 % less than the area of b . answer ( b )\"" + }, + { + "Answer": 405, + "Options": "a ) 875 , b ) 405 , c ) 1425 , d ) 2025 , e ) 2500", + "Correct": "b", + "Explanation": "\"there ' s a direct formula for this . number of diagonals in a regular polygon = [ n * ( n - 3 ) ] / 2 , n = number of sides of the regular polygon . here , n = 30 . plugging it in , we get 405 diagonals ! answer ( b ) .\"" + }, + { + "Answer": 16, + "Options": "a ) 54 , b ) 32 , c ) 75 , d ) 28 , e ) 16", + "Correct": "e", + "Explanation": "\"a / 8 = 4 * 4 = > a = 4 * 4 * 8 x * 2 x = 4 * 4 * 8 x = 8 = > 2 x = 16 answer : e\"" + }, + { + "Answer": 0.5714285714285714, + "Options": "a ) 4 / 5 , b ) 5 / 4 , c ) 3 / 2 , d ) 4 / 7 , e ) 2 / 3", + "Correct": "d", + "Explanation": "\"we are basically given that the triangles are similar . in two similar triangles , the ratio of their areas is the square of the ratio of their sides and also , the square of the ratio of their corresponding heights . therefore , area / area = height ^ 2 / height ^ 2 = 16 / 49 - - > height / height = 4 / 7 . answer : d .\"" + }, + { + "Answer": 15, + "Options": "a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25", + "Correct": "c", + "Explanation": "\"the base of the isosceles triangle is 55 - 20 - 20 = 15 units the answer is c .\"" + }, + { + "Answer": 3120, + "Options": "['a ) 3,200', 'b ) 3,150', 'c ) 3,448', 'd ) 3,120', 'e ) 2,980']", + "Correct": "d", + "Explanation": "the answer is d ) 3,120 . a 1 x 1 x 1 cube has an area of 1 . the 15 x 16 x 13 box has an area of 3,120 . if you divide 3,120 by 1 , you get 3,120 . therefore the answer is d ." + }, + { + "Answer": 148, + "Options": "['a ) 228', 'b ) 148', 'c ) 992', 'd ) 772', 'e ) 222']", + "Correct": "b", + "Explanation": "2 ( 4 * 5 + 5 * 6 + 4 * 6 ) = 148 answer : b" + }, + { + "Answer": 156.00000000000006, + "Options": "a ) 150 % , b ) 160 % , c ) 156 % , d ) 158 % , e ) 162 %", + "Correct": "c", + "Explanation": "\"the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 60 % increase a surface = 6 * ( ( 1.6 a ) ^ 2 ) = 6 * 2.56 * a ^ 2 the increase in the surface area = ( 6 * 2.56 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 2.56 - 1 ) ) / ( 6 * a ^ 2 ) = 2.56 - 1 = 1.56 = 156 % answer : c\"" + }, + { + "Answer": 625, + "Options": "['a ) 125 cm 3', 'b ) 625 cm 3', 'c ) 15525 cm 3', 'd ) 1225 cm 3', 'e ) none']", + "Correct": "b", + "Explanation": "solution the new solid formed is a cuboid of length 25 cm , breadth 5 cm and height 5 cm \u2234 volume = ( 25 x 5 x 5 ) cm 3 \u2039 = \u203a 625 cm 3 answer b" + }, + { + "Answer": 70.37037037037037, + "Options": "['a ) 54.9 %', 'b ) 58.7 %', 'c ) 62.5 %', 'd ) 66.3 %', 'e ) 70.4 %']", + "Correct": "e", + "Explanation": "there are a total of 6 * 6 * 6 = 216 cubes . all the exterior cubes will have at least one face painted red . the interior is formed by 4 * 4 * 4 = 64 cubes . the number of cubes with at least one side painted red is 216 - 64 = 152 cubes the probability that a cube has at least one side painted red is 152 / 216 which is about 70.4 % the answer is e ." + }, + { + "Answer": 8, + "Options": "['a ) 4', 'b ) 8', 'c ) 16', 'd ) 24', 'e ) 2']", + "Correct": "b", + "Explanation": "there are 64 small cubes , hence one side side of the big cube is 3 \u221a 64 = 4 cm number of small cubes having three faces coloured = no . of corners = 8 answer : b" + }, + { + "Answer": 25, + "Options": "a ) 25 % , b ) 50 % , c ) 100 % , d ) 200 % , e ) 400 %", + "Correct": "a", + "Explanation": "let the original square have sides of length l and the new square have sides of length 2 l . the resulting areas are l ^ 2 for the original square and 4 l ^ 2 for the new square ( as the length of the side is square to get the area ) . the original square ' s area is l ^ 2 / 4 l ^ 2 or 25 % of the new square ' s area . choice a" + }, + { + "Answer": 132, + "Options": "a ) 124 m 2 , b ) 132 m 2 , c ) 148 m 2 , d ) 152 m 2 , e ) none of these", + "Correct": "b", + "Explanation": "\"area of the outer rectangle = 21 \u00e3 \u2014 16 = 336 m 2 area of the inner rectangle = 17 \u00e3 \u2014 12 = 204 m 2 required area = ( 336 \u00e2 \u20ac \u201c 204 ) = 132 m 2 answer b\"" + }, + { + "Answer": 14.000000000000002, + "Options": "['a ) 14 percent increase', 'b ) 5 percent increase', 'c ) 24 percent increase', 'd ) 13 percent increase', 'e ) 11 percent increase']", + "Correct": "a", + "Explanation": "let l and b be 100 each 100 * 100 = 10000 l increase by 20 % = 120 b decrease by 5 % = 95 120 * 95 = 11400 14 percent increase answer : a" + }, + { + "Answer": 5, + "Options": "['a ) 3', 'b ) 4', 'c ) 5', 'd ) 6', 'e ) 7']", + "Correct": "c", + "Explanation": "explanation : let the lengths of the sides be a , b and c . given , triagle ' s perimeter < 14 = > a + b + c < 14 - - - - - - - - - - ( i ) from triangle inequality theorem , c < a + b = > 2 c < a + b + c . - - - - - - - - - - ( ii ) from ( i ) and ( ii ) , 2 c < a + b + c < 14 . = > c < 7 - - - - - - - - - - ( iii ) = > by similarity , we can say that length of any side must be less than 7 . keeping these in mind , we can find the following possibilities : - ( 2 , 3,4 ) ( 2 , 4,5 ) ( 2 , 5,6 ) ( 3 , 4,5 ) ( 3 , 4,6 ) = > total 5 possibilities . answer : c" + }, + { + "Answer": 10800, + "Options": "a ) rs . 962 , b ) rs . 672 , c ) rs . 546 , d ) rs . 10800 , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : surface area of a cube = 6 x 30 ^ 2 = 5400 sq . ft quantity of paint required = ( 5400 / 20 ) = 270 kg cost of painting = 40 x 270 = rs . 10800 answer : d\"" + }, + { + "Answer": 9, + "Options": "a ) 9 square inches , b ) 10 square inches , c ) 15 square inches , d ) 25 square inches , e ) 350 square inches", + "Correct": "a", + "Explanation": "\"in the first case each can buy one pizza of $ 10 and one pizza of $ 20 . in square inches that would be ( 6 * 6 = 36 ) for the small pizza and ( 9 * 9 = 81 ) for the large pizza . in total sq inches that would be ( 36 + 81 ) * 2 = 234 sq inches . in the second case if they pool their money together they can buy 3 large pizzas . in terms of square inches that would be 3 * 81 = 243 sq inches . hence , the difference is 9 square inches more ( 243 - 234 ) . the correct answer is a\"" + }, + { + "Answer": 10, + "Options": "a ) 12 h , b ) 10 h , c ) 8 h , d ) 6 h , e ) none of these", + "Correct": "b", + "Explanation": "explanation area of field = 1600 km 2 . then , each side of field = \u221a 1600 = 40 km distance covered by the horse = perimeter of square field = 40 \u00d7 4 = 160 km \u2234 time taken by horse = distances / peed = 160 / 16 = 10 h answer b" + }, + { + "Answer": 40, + "Options": "a ) 50 , b ) 54 , c ) 47 , d ) 40 , e ) 45", + "Correct": "d", + "Explanation": "\"area of tile = 60 * 56 = 3360 area of floor = 560 * 240 = 134400 no of tiles = 134400 / 3360 = 40 so , the no of tile = 40 answer : d\"" + }, + { + "Answer": 33.94112549695428, + "Options": "['a ) 31.84 cm', 'b ) 33.84 cm', 'c ) 35.84 cm', 'd ) 38.84 cm', 'e ) 38.92 cm']", + "Correct": "b", + "Explanation": "diagonal of a square = 12 cm area of square = 1 / 2 ( d ) \u00b2 = 1 / 2 ( 12 ) \u00b2 = 1 / 2 \u00d7 12 \u00d7 12 = 72 side of a square = \u221a area = \u221a 72 = \u221a ( 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 3 ) = 2 \u00d7 3 \u221a 2 = 6 \u00d7 1.41 = 8.46 cm perimeter of square = 4 \u00d7 8.46 = 33.84 cm answer option : b" + }, + { + "Answer": 12.053571428571429, + "Options": "a ) 6 cm , b ) 12.05 cm , c ) 11.25 cm , d ) 15.12 cm , e ) 20.62 cm", + "Correct": "b", + "Explanation": "\"increase in volume = volume of the cube = 15 * 15 * 15 cm ^ 3 rise in water level = volume / area = 15 * 15 * 15 / 20 * 14 = 12.05 cm answer is b\"" + }, + { + "Answer": 1470, + "Options": "a ) 120 cm 2 , b ) 1470 cm 2 , c ) 216 cm 2 , d ) 197 cm 2 , e ) 275 cm 2", + "Correct": "b", + "Explanation": "\"the triangle with sides 91 cm , 84 cm and 35 cm is right angled , where the hypotenuse is 91 cm . area of the triangle = 1 / 2 * 84 * 35 = 1470 cm 2 answer : b\"" + }, + { + "Answer": 8, + "Options": "['a ) 2 \u221a 2', 'b ) 2 \u221a 5', 'c ) 5', 'd ) 4 \u221a 2', 'e ) 8']", + "Correct": "e", + "Explanation": "area of sector , a = x / 360 * pi * r ^ 2 circumference of the sector = 32 = > x / 360 * 2 * pi * r + 2 r = 32 = > 2 a / r + 2 r = 32 = > a = r 16 - r ^ 2 = r 16 - r ^ 2 we will now max using derivations max value of a will found at a = 0 i . e 16 - 2 r = 0 r = 8 e" + }, + { + "Answer": 24, + "Options": "['a ) 24', 'b ) 27', 'c ) 25', 'd ) 26', 'e ) 29']", + "Correct": "a", + "Explanation": "if the length of the square is s , then s 2 = 36 so s = 6 . the perimeter is therefore 4 s = 24 . correct answer a" + }, + { + "Answer": 9, + "Options": "['a ) 3 : 1', 'b ) 8 : 1', 'c ) 9 : 1', 'd ) 12 : 1', 'e ) 9 : 1']", + "Correct": "c", + "Explanation": "a 1 : a 2 = 3 : 1 6 a 12 : 6 a 22 = 9 : 1 answer : c" + }, + { + "Answer": 15, + "Options": "a ) 40 , b ) 70 , c ) 20 , d ) 80 , e ) 60", + "Correct": "c", + "Explanation": "\"l * w = 300 : area , l is the length and w is the width . 2 l + 2 w = 70 : perimeter l = 35 - w : solve for l ( 35 - w ) * w = 300 : substitute in the area equation w = 15 and l = 20 : solve for w and find l using l = 35 - w . correct answer c\"" + }, + { + "Answer": 169, + "Options": "['a ) 121', 'b ) 144', 'c ) 169', 'd ) 196', 'e ) 225']", + "Correct": "c", + "Explanation": "we know that the perimeter of square = 4 \u00e3 \u2014 side side = 13 cm therefore , perimeter = 4 \u00e3 \u2014 13 cm = 52 cm now , area of the square = ( side \u00e3 \u2014 side ) sq . units = 13 \u00e3 \u2014 13 cm \u00e2 \u00b2 = 169 cm \u00e2 \u00b2 answer : c" + }, + { + "Answer": 30, + "Options": "['a ) 15', 'b ) 30', 'c ) 18', 'd ) 12', 'e ) 25']", + "Correct": "b", + "Explanation": "sol . height of the triangle = [ ( 13 ) 2 - ( 12 ) 2 ] ( 1 / 2 ) cm = ( 25 ) ( 1 / 2 ) cm = 5 cm . its area = ( 1 / 2 ) * base * height = ( ( 1 / 2 ) * 12 * 5 ) cm ^ 2 = 30 cm ^ 2 . ans : b" + }, + { + "Answer": 90, + "Options": "a ) 72 , b ) 180 , c ) 70 , d ) 90 , e ) 140", + "Correct": "d", + "Explanation": "\"length of side 1 = 9 + 1 = 10 length of side 2 = 8 + 1 = 9 area of rectangle = 10 * 9 = 90 d is the answer\"" + }, + { + "Answer": 0.11785113019775793, + "Options": "['a ) 3.11545466', 'b ) 0.76678113', 'c ) 0.11785113', 'd ) 2.11785113', 'e ) 0.11786667']", + "Correct": "c", + "Explanation": "the answer is sqr ( 2 ) / 12 = 0.11785113 the following can be derived using the pythagorean theorem : the height of a face is 3.5 / 2 . the area of any face is 3.5 / 4 . the distance from any corner to the center of a joining face is 1 / 3.5 . the height of the tetrahedron is ( 2 / 3 ) . 5 the area is 1 / 3 * base * height = ( 1 / 3 ) * 3.5 / 4 * ( 2 / 3 ) . 5 = 21 / 2 / 12 . the above cube has sides of length 1 / sqr ( 2 ) . the area formed by the diagonals along four of the faces as shown in the diagram is a tetrahedrom . left over are four pyramids . the base of each pyramid is half of the side of the cube and the height is the height of the cube . thus the area of each pyramid is : 1 / 2 * ( 1 / sqr ( 2 ) ) 2 * 1 / sqr ( 2 ) * 1 / 3 = ( 12 * sqr ( 2 ) ) - 1 the total area of the cube is ( 1 / sqr ( 2 ) ) 3 = ( 2 * sqr ( 2 ) ) - 1 the area of the tetrahedrom is thus ( 2 * sqr ( 2 ) ) - 1 - 4 * ( 12 * sqr ( 2 ) ) - 1 = 3 / ( 6 * sqr ( 2 ) ) - 2 / ( 6 * sqr ( 2 ) ) = 1 / ( 6 * sqr ( 2 ) ) = sqr ( 2 ) / 12 correct answer c" + }, + { + "Answer": 75, + "Options": "a ) 30 square inches , b ) 75 square inches , c ) 68 square inches , d ) 89 square inches , e ) 92 square inches", + "Correct": "b", + "Explanation": "\"if the width is 5 in and the length is 3 times the width , then the length is 3 * 5 = 15 in the area is given by 5 * 15 = 75 square inches correct answer b\"" + }, + { + "Answer": 3, + "Options": "['a ) 2', 'b ) 4', 'c ) 3', 'd ) 5', 'e ) 6']", + "Correct": "c", + "Explanation": "let the width = w total area of the pool and deck = ( 2 w + 20 ) ( 2 w + 22 ) we can test the answer choices along with unit digit method a ) 2 feet . . . . . . . . . . . 24 * 26 has unit digit 8 . . . . . . . . . . eliminate b ) 2.5 feet . . . . . . . . . 25 * 33 has unit digit 5 . . . . . . . . . . eliminate c ) 3 feet . . . . . . . . . . . . 26 * 28 has unit digit 4 . . . . . . . . . . . hold d ) 4 feet . . . . . . . . . . . . 28 * 30 has unit digit 0 . . . . . . . . . . . eliminate e ) 5 feet . . . . . . . . . . . . 30 * 32 has unit digit 0 . . . . . . . . . . . eliminate answer : c w = 3" + }, + { + "Answer": 61.69911184307752, + "Options": "a ) 58 , b ) 62 , c ) 66 , d ) 70 , e ) 74", + "Correct": "b", + "Explanation": "\"the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 12 + 2 * 12 which is about 62 . the answer is b .\"" + }, + { + "Answer": 10, + "Options": "a ) 5 , b ) 10 , c ) 12 , d ) 15 , e ) 20", + "Correct": "b", + "Explanation": "as abce is an isosceles trapezoid and ec is twice times ab , we can consider the given trapezoid as half of a regular hexagon ( as length of diagonal in regular hexagon is always double the side ) . thus , sides ab = ae = bc . = > ae = 10 . answer : b" + }, + { + "Answer": 60, + "Options": "['a ) 30 pi m ^ 2', 'b ) 40 pi m ^ 2', 'c ) 60 pi m ^ 2', 'd ) 80 pi m ^ 2', 'e ) 100 pi m ^ 2']", + "Correct": "c", + "Explanation": "l = 10 m h = 8 m r = root ( i ^ 2 - h ^ 2 ) = root ( 10 ^ 2 - 8 ^ 2 ) = 6 m curved surface area = pi ri = 60 pi m ^ 2 answer c" + }, + { + "Answer": 1.5, + "Options": "a ) 3 : 6 , b ) 1.5 : 1 , c ) 3 : 1.5 , d ) 2 : 1 , e ) 3 : 2", + "Correct": "b", + "Explanation": "\"d = 1.5 d d = d a \u221a 2 = 1.5 d a \u221a 2 = d a = 1.5 d / \u221a 2 a = d / \u221a 2 = > 1.5 : 1 answer : b\"" + }, + { + "Answer": 12, + "Options": "a ) 1 , b ) 2 , c ) 4 , d ) 8 , e ) 12", + "Correct": "e", + "Explanation": "\"as per the question - - width is negligible now , let l be the length of the fence = 2 pir l = 1 / 6 ( pir ^ 2 ) pir ^ 2 = 12 pir r = 12 answer : e\"" + }, + { + "Answer": 4.020725758589058, + "Options": "a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 9", + "Correct": "a", + "Explanation": "\"if sides are 7 , vol = 7 ^ 3 = 343 60 % = 205.8 , 85 % = 291.55 so vol above water , between 137.2 and 51.45 - - > too big if side are 4 , vol = 64 60 % = 38.4 , 85 % = 54.4 vol above water between 25.6 and 9.6 so 4 should be the answer . check option c , if sides are 5 , vol = 125 60 % = 75 , . 85 % = 106.25 vol above water between 18.75 - 50 ( sides are 4 cubic centimeters ) a\"" + }, + { + "Answer": 30, + "Options": "a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35", + "Correct": "d", + "Explanation": "\"the base of the isosceles triangle is 70 - 20 - 20 = 30 units the answer is d .\"" + }, + { + "Answer": 213.33333333333331, + "Options": "['a ) a ) 160 degree', 'b ) b ) 168 degree', 'c ) c ) 191 degree', 'd ) d ) 192 degree', 'e ) e ) 213 degree']", + "Correct": "e", + "Explanation": "here is my approach = > males = > 2 x and females = 7 x = > total = 9 x now 9 x = > 360 therefore 16 x / 3 = > 213 degree . p . s = > 16 x / 3 is nothing but total number of students with the given preference answer e" + }, + { + "Answer": 7, + "Options": "['a ) 5', 'b ) 6', 'c ) 7', 'd ) 8', 'e ) 9']", + "Correct": "c", + "Explanation": "7 is the smallest number which divides 2800 and gives a perfect square . as 2800 = 2 * 2 * 2 * 2 * 5 * 5 * 7 and 7 is not in a pair which gives 400 ( a perfect square of 20 ) on dividing 2800 . answer : c" + }, + { + "Answer": 5, + "Options": "['a ) 5', 'b ) 13', 'c ) 14', 'd ) 11', 'e ) 15']", + "Correct": "a", + "Explanation": "abc and ade are similar triangles . so ( side of abc / side of ade ) ^ 2 = 25 / 169 side of abc / side of ade = 5 / 13 so the length of bc = 5 answer - a" + }, + { + "Answer": 42.81481481481482, + "Options": "a ) 22.8 , b ) 33.8 , c ) 42.8 , d ) 63.8 , e ) 56.8", + "Correct": "c", + "Explanation": "\"since the mirror is 42 inches in all sides , it must be a square . area of a square is a = a ^ 2 ; 34 ^ 2 = 1156 . area of rectangle is double of that 2 * 1156 = 2312 . now a = lw and we need find w so a / l = w ; 2312 / 54 = 42.8 answer ! answer is c\"" + }, + { + "Answer": 14.500000000000002, + "Options": "['a ) 210.25', 'b ) 75.69', 'c ) 14.5', 'd ) 145', 'e ) 150']", + "Correct": "c", + "Explanation": "let the number be x given , 3 / 5 x ^ 2 = 126.5 x ^ 2 = 126.15 * 5 / 3 x ^ 2 = 42.05 * 5 = 210.25 x = 14.5 answer c ." + }, + { + "Answer": 80, + "Options": "a ) 80 feet , b ) 70 feet , c ) 60 feet , d ) 50 feet , e ) 20 feet", + "Correct": "a", + "Explanation": "\"explanation : we are given with length and area , so we can find the breadth . as length * breadth = area = > 20 * breadth = 600 = > breadth = 30 feet area to be fenced = 2 b + l = 2 * 30 + 20 = 80 feet answer : option a\"" + }, + { + "Answer": 25, + "Options": "a ) 28 cm 2 , b ) 27 cm 2 , c ) 29 cm 2 , d ) 25 cm 2 , e ) 35 cm 2", + "Correct": "d", + "Explanation": "\"area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 20 / 2 = 25 cm 2 answer : d\"" + }, + { + "Answer": 30, + "Options": "['a ) 28', 'b ) 29', 'c ) 30', 'd ) 31', 'e ) 32']", + "Correct": "c", + "Explanation": "try filling the numbers into the answer y x y = find the closest to 900 . answer c" + }, + { + "Answer": 324, + "Options": "['a ) 100', 'b ) 169', 'c ) 324', 'd ) 196', 'e ) 225']", + "Correct": "c", + "Explanation": "one point ( - 6 - 4 ) , intersection ( 3,2 ) so the distance from the first point - 6 - 3 = - 9 is the midpoint of the square - - > whole side 18 , 18 * 18 = 324 c" + }, + { + "Answer": 0.06000000000000001, + "Options": "['a ) 0.6', 'b ) 0.06', 'c ) 0.9', 'd ) 0.2', 'e ) 0.61']", + "Correct": "b", + "Explanation": "answer : b ) . 06" + }, + { + "Answer": 1624, + "Options": "a ) 3944 , b ) 1624 , c ) 2999 , d ) 2667 , e ) 2121", + "Correct": "b", + "Explanation": "\"let the side of the square plot be a ft . a 2 = 49 = > a = 7 length of the fence = perimeter of the plot = 4 a = 28 ft . cost of building the fence = 28 * 58 = rs . 1624 . answer : b\"" + }, + { + "Answer": 10, + "Options": "a ) 8 , b ) 9 , c ) 7 , d ) 10 , e ) 5", + "Correct": "d", + "Explanation": "\"2 x * x = 200 = > x = 10 answer : d\"" + }, + { + "Answer": 10, + "Options": "['a ) 12 h', 'b ) 10 h', 'c ) 8 h', 'd ) 6 h', 'e ) none of these']", + "Correct": "b", + "Explanation": "explanation area of field = 900 km 2 . then , each side of field = \u221a 900 = 30 km distance covered by the horse = perimeter of square field = 30 \u00d7 4 = 120 km \u2234 time taken by horse = distances / peed = 120 / 12 = 10 h answer b" + }, + { + "Answer": 6, + "Options": "['a ) 2', 'b ) 8', 'c ) 7', 'd ) 6', 'e ) 9']", + "Correct": "d", + "Explanation": "33 + 43 + 53 = a 3 = > a = 6 answer : d" + }, + { + "Answer": 0.064, + "Options": "a ) 0.008 , b ) 0.08 , c ) 0.064 , d ) 0.64 , e ) 6.4", + "Correct": "c", + "Explanation": "\"the volume of oil pumped to the tank = the volume of oil taken away from stationary cylinder . pi * 64 * 10 = pi * h * 100 * 100 ( h is distance that the oil level dropped ) h = 640 / 10,000 = 64 / 1000 = 0.064 ft the answer is c .\"" + }, + { + "Answer": 28.274333882308138, + "Options": "a ) 28.28 cm , b ) 25.45 cm , c ) 26.45 cm , d ) 20.18 cm , e ) 32.14 cm", + "Correct": "a", + "Explanation": "\"let the side of the square be a cm . parameter of the rectangle = 2 ( 20 + 16 ) = 72 cm parameter of the square = 72 cm i . e . 4 a = 72 a = 18 diameter of the semicircle = 18 cm circimference of the semicircle = 1 / 2 ( \u220f ) ( 18 ) = 1 / 2 ( 22 / 7 ) ( 18 ) = 396 / 14 = 28.28 cm to two decimal places answer : a\"" + }, + { + "Answer": 50, + "Options": "['a ) 25 are', 'b ) 30 are', 'c ) 50 are', 'd ) 60 are', 'e ) 45 are']", + "Correct": "c", + "Explanation": "speed of man = [ 3 * 5 / 18 ] m / sec . = 5 / 6 m / sec . , distance travel in 2 minute = { 5 / 6 * 2 * 60 } m . = 100 m . diagonal of square field = 100 m area of field = 1 / 2 * diagonal ^ 2 = [ 1 / 2 * 100 * 100 ] sq . m = 5000 sq . m = 5000 / 100 = 50 are ( 1 are = 100 sq . m ) answer c" + }, + { + "Answer": 50, + "Options": "['a ) 50 square inches', 'b ) 75 square inches', 'c ) 68 square inches', 'd ) 89 square inches', 'e ) 92 square inches']", + "Correct": "a", + "Explanation": "if the width is 5 in and the length is 2 times the width , then the length is 2 * 5 = 10 in the area is given by 5 * 10 = 50 square inches correct answer a" + }, + { + "Answer": 30, + "Options": "a ) 30 , b ) 15 , c ) 12 , d ) 23 , e ) 17", + "Correct": "a", + "Explanation": "5880 = 2 * 2 * 7 * 7 * 5 * 6 , so we need one 5 and one 6 to make it a square of a number . so 5 * 6 = 30 ans : a" + }, + { + "Answer": 4.04, + "Options": "['a ) 4 %', 'b ) 4.04 %', 'c ) 4.23 %', 'd ) 4.56 %', 'e ) 5 %']", + "Correct": "b", + "Explanation": "100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 102 x 102 ) cm 2 . ( a 2 - a 1 ) = [ ( 102 ) 2 - ( 100 ) 2 ] = ( 102 + 100 ) x ( 102 - 100 ) = 404 cm 2 . percentage error = 404 x 100 % = 4.04 % 100 x 100 b" + }, + { + "Answer": 60, + "Options": "a ) 60 feet , b ) 50 feet , c ) 40 feet , d ) 30 feet , e ) 5 feet", + "Correct": "a", + "Explanation": "\"explanation : we are given with length and area , so we can find the breadth . as length * breadth = area = > 20 * breadth = 400 = > breadth = 20 feet area to be fenced = 2 b + l = 2 * 20 + 20 = 60 feet answer : option a\"" + }, + { + "Answer": 11.25, + "Options": "['a ) 11.25 cm .', 'b ) 12.25 cm', 'c ) 13.25 cm', 'd ) 14.25 cm', 'e ) none of these']", + "Correct": "a", + "Explanation": "sol . increase in volume = volume of the cube = ( 15 * 15 * 15 ) cm \u00b3 . \u2234 rise in water level = [ volume / area ] = [ 15 * 15 * 15 / 20 * 15 ] cm = 11.25 cm . answer a" + }, + { + "Answer": 328.19506394825623, + "Options": "a ) 326.2 , b ) 324.2 , c ) 328.2 , d ) 338.2 , e ) 328.9", + "Correct": "c", + "Explanation": "\"area of the rhombus = 1 / 2 * p * \u221a 4 ( a ) 2 - ( p ) 2 a = 28 ; p = 12 a = 1 / 2 * 12 * \u221a 4 ( 28 ) 2 - ( 12 ) 2 = 1 / 2 * 12 * \u221a 3136 - 144 = 1 / 2 * 12 * \u221a 2992 a = 328.2 answer : c\"" + }, + { + "Answer": 2304, + "Options": "['a ) 1896', 'b ) 1912', 'c ) 2108', 'd ) 2304', 'e ) 2524']", + "Correct": "d", + "Explanation": "2 hl + 2 hw = 2 lw h = lw / ( l + w ) volume = lwh = ( lw ) ^ 2 / ( l + w ) = 2304 the answer is d ." + }, + { + "Answer": 10, + "Options": "a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25", + "Correct": "b", + "Explanation": "\"the base of the isosceles triangle is 50 - 20 - 20 = 10 units the answer is b .\"" + }, + { + "Answer": 75, + "Options": "a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 75", + "Correct": "e", + "Explanation": "\"let l be the length and w be the width . l = ( 7 / 5 ) w perimeter : 2 l + 2 w = 360 , 2 ( 7 / 5 ) w + 2 w = 360 solve the above equation to find : w = 75 m and l = 105 m . correct answer e ) 75\"" + }, + { + "Answer": 10, + "Options": "a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 10", + "Correct": "e", + "Explanation": "\"if the width is w , then length and height would be w / 2 . so , w * w / 2 * w / 2 = 128 = > w ^ 3 = ( 2 ^ 3 ) * 64 = ( 2 ^ 3 ) * ( 4 ^ 3 ) = > w = 2 * 4 m = 8 in . along the width of the cuboid , 8 cubes do n ' t touch the tin foil . so the actual width will be non - touching cubes + touching cubes = 8 + 2 = 10 ans e .\"" + }, + { + "Answer": 25, + "Options": "a ) a ) 72 , b ) b ) 828 , c ) c ) 25 , d ) d ) 34 , e ) e ) 35", + "Correct": "c", + "Explanation": "\"explanation : area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 20 / 2 = 25 cm 2 answer : option c\"" + }, + { + "Answer": 7.22, + "Options": "['a ) 7.22 m ^ 2', 'b ) 3.86 m ^ 2', 'c ) 8.96 m ^ 2', 'd ) 2.68 m ^ 2', 'e ) 7.89 m ^ 2']", + "Correct": "a", + "Explanation": "area of the square = 1 / 2 ( diagonal ) ^ 2 = ( 1 / 2 * 3.8 * 3.8 ) m ^ 2 = 7.22 m ^ 2 answer ( a )" + }, + { + "Answer": 121, + "Options": "['a ) 121', 'b ) 132', 'c ) 144', 'd ) 156', 'e ) 169']", + "Correct": "a", + "Explanation": "to find the area of a square , knowing the length of one side is sufficient . from the coordinates given , we can see that one side equals 11 . the area is 11 * 11 = 121 . the answer is a ." + }, + { + "Answer": 15, + "Options": "a ) 8 m , b ) 10 m , c ) 12 m , d ) 15 m , e ) 17 m", + "Correct": "d", + "Explanation": "\"let the length of the hall be x m breadth of the hall = 1 x / 2 m area of the hall = length * breadth 450 = x * 1 x / 2 x \u00b2 = 900 x = 30 difference between the length and breadth of the hall = x - 1 x / 2 = x / 2 = 30 / 2 = 15 m answer : d\"" + }, + { + "Answer": 56, + "Options": "a ) 56 , b ) 88 , c ) 112 , d ) 116 , e ) 120", + "Correct": "a", + "Explanation": "\"area of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 8 + 8 = 16 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 16 * 7 = 56 a is the answer\"" + }, + { + "Answer": 22, + "Options": "['a ) 22 square inches', 'b ) 20 square inches', 'c ) 24 square inches', 'd ) 28 square inches', 'e ) 30 square inches']", + "Correct": "a", + "Explanation": "total = a + b + c - ( sum of exactly 2 - group overlaps ) - 2 * ( all three ) + neither 80 % * 175 = 208 - 24 - 2 * ( all three ) + 0 2 * ( all three ) = 208 - 24 - 140 all three = 22 answer : a" + }, + { + "Answer": 13, + "Options": "['a ) 10', 'b ) 11', 'c ) 12', 'd ) 13', 'e ) 14']", + "Correct": "d", + "Explanation": "let x be the width of the garden . 3 x ^ 2 = 507 x ^ 2 = 169 x = 13 the answer is d ." + }, + { + "Answer": 17.647058823529417, + "Options": "['a ) 10 %', 'b ) 20 %', 'c ) 17.6 %', 'd ) 30 %', 'e ) 35 %']", + "Correct": "c", + "Explanation": "sol . required change = ( 15 * 100 ) / ( 100 - 15 ) = 17.6 % c" + }, + { + "Answer": 9, + "Options": "['a ) 9 v \u00e2 \u20ac \u2122', 'b ) 4 v \u00e2 \u20ac \u2122', 'c ) v \u00e2 \u20ac \u2122 / 2', 'd ) v \u00e2 \u20ac \u2122 / 4', 'e ) v \u00e2 \u20ac \u2122']", + "Correct": "a", + "Explanation": "when h = 4 v = v ' so v ' = k . 16 hence k = v ' / 16 now when h = 12 v = ( v ' / 16 ) . 12 ^ 2 v = v ' . 144 / 16 v = 9 v ' ans : a" + }, + { + "Answer": 144, + "Options": "['a ) 56', 'b ) 80', 'c ) 100', 'd ) 120', 'e ) 144']", + "Correct": "e", + "Explanation": "q = 6 c 5 * ( 5 - 1 ) ! ( select 5 out of 6 and arrange them in circular manner ) = 6 * 4 ! = 6 * 24 = 144 answer - e" + }, + { + "Answer": 8, + "Options": "a ) 15 , b ) 26 , c ) 8 , d ) 91 , e ) none of these", + "Correct": "c", + "Explanation": "\"let the number be x . then , x + x 2 = 72 ( x + 9 ) ( x - 8 ) = 0 x = 8 answer : c\"" + }, + { + "Answer": 21.000000000000018, + "Options": "a ) 25 % , b ) 28 % , c ) 21 % , d ) 30 % , e ) 32 %", + "Correct": "c", + "Explanation": "\"the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 10 % increase a surface = 6 * ( ( 1.1 a ) ^ 2 ) = 6 * 1.21 * a ^ 2 the increase in the surface area = ( 6 * 1.21 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 1.21 - 1 ) ) / ( 6 * a ^ 2 ) = 1.21 - 1 = 0.21 = 21 % answer : c\"" + }, + { + "Answer": 11, + "Options": "['a ) 11', 'b ) 12', 'c ) 13', 'd ) 14', 'e ) none']", + "Correct": "a", + "Explanation": "pretend width = 1 , then length = 6 ( 1 + 5 ) 2 \u00d7 1 + 2 \u00d7 7 = 2 + 14 = 16 . notice that 16 is far from a perimeter of 34 try much bigger number . how about if we . . . pretend width = 4 , then length = 9 ( 4 + 5 ) 2 \u00d7 4 + 2 \u00d7 9 = 6 + 18 = 24 . we are getting closer to a perimeter of 34 pretend width = 5 , then length = 10 ( 5 + 5 ) 2 \u00d7 5 + 2 \u00d7 10 = 10 + 30 = 30 . pretend width = 7 , then length = 12 ( 7 + 5 ) 2 \u00d7 7 + 2 \u00d7 12 = 14 + 24 = 38 . this is higher than a perimeter of 34 . so width should be higher than 5 and smaller than 7 . may be a width of 6 will work . pretend width = 6 , then length = 11 ( 6 + 5 ) 2 \u00d7 6 + 2 \u00d7 11 = 12 + 22 = 34 . use of algebra : let width = x let length = x + 5 p = 2 \u00d7 l + 2 \u00d7 w 34 = 2 \u00d7 ( x + 5 ) + 2 \u00d7 x 34 = 2 x + 10 + 2 x 34 = 4 x + 10 34 - 10 = 4 x + 10 - 10 24 = 4 x 24 / 4 = 4 x / 4 6 = x therefore , width = 6 and length = x + 5 = 6 + 5 = 11 answer a" + }, + { + "Answer": 60, + "Options": "['a ) 87', 'b ) 16', 'c ) 17', 'd ) 60', 'e ) 18']", + "Correct": "d", + "Explanation": "\u03c0 r 2 = 30 h = 6 1 / 3 * 30 * 6 = 60 answer : d" + }, + { + "Answer": 200, + "Options": "['a ) 350 sq . units', 'b ) 250 sq . units', 'c ) 300 sq . units', 'd ) 200 sq . units', 'e ) 100 sq . units']", + "Correct": "d", + "Explanation": "given that the area of the square = 6400 sq . units = > side of square = \u221a 6400 = 80 units the radius of the circle = side of the square = 35 units length of the rectangle = 1 / 4 * 80 = 20 units given that breadth = 10 units area of the rectangle = lb = 20 * 10 = 200 sq . units answer : d" + }, + { + "Answer": 200, + "Options": "a ) 289 cm , b ) 200 cm , c ) 829 cm , d ) 288 cm , e ) 289 cm", + "Correct": "b", + "Explanation": "\"area of the square = s * s = 5 ( 50 * 10 ) = > s = 50 = 50 cm perimeter of the square = 4 * 50 = 200 cm . answer : b\"" + }, + { + "Answer": 60, + "Options": "['a ) 33', 'b ) 60', 'c ) 88', 'd ) 27', 'e ) 26']", + "Correct": "b", + "Explanation": "explanation : length of the diagonal = 52 * ( 15 / 60 ) = 13 m sum of length and breadth = 68 * ( 15 / 60 ) = 17 m \\ inline { \\ color { black } \\ sqrt { l ^ { 2 } + b ^ { 2 } } = 13 \\ ; or \\ ; l + b = 17 } area = lb = 1 / 2 [ ( 2 lb ) ] = 1 / 2 [ ( l + b ) \u00b2 - ( l \u00b2 + b \u00b2 ) ] = 1 / 2 [ 17 \u00b2 - 169 ] = 1 / 2 * 120 = 60 sq meter answer : b ) 60" + }, + { + "Answer": 36.56637061435917, + "Options": "['a ) 28.32', 'b ) 36.57', 'c ) 44.57', 'd ) 48.93', 'e ) 54.24']", + "Correct": "b", + "Explanation": "circumference of the semicircle = \u00ef \u20ac xd / 2 = ( 22 / 7 ) x 4 = 12.57 perimeter of the square plot = 3 x 8 = 24 perimeter of the shape = 36.57 cm answer : b" + }, + { + "Answer": 10000, + "Options": "a ) 10,000 , b ) 11,025 , c ) 14,400 , d ) 12,696 , e ) can not be determined", + "Correct": "a", + "Explanation": "\"let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 199 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 199 ( x + y ) ( x - y ) = 199 199 is a prime number and thus it will be ( 100 + 99 ) * ( 100 - 99 ) . thus x = 100 and y = 99 x ^ 2 = 100 ^ 2 = 10,000 the answer is a .\"" + }, + { + "Answer": 84, + "Options": "a ) 34 , b ) 40 , c ) 68 , d ) 84 , e ) none", + "Correct": "d", + "Explanation": "\"explanation we have : l = 30 ft and lb = 810 sq . ft . so , b = 27 ft . length of fencing = ( l + 2 b ) = ( 30 + 54 ) ft = 84 ft . answer d\"" + }, + { + "Answer": 2088, + "Options": "a ) 3944 , b ) 2287 , c ) 2977 , d ) 2088 , e ) 1298", + "Correct": "d", + "Explanation": "\"let the side of the square plot be a ft . a 2 = 81 = > a = 9 length of the fence = perimeter of the plot = 4 a = 36 ft . cost of building the fence = 36 * 58 = rs . 2088 . answer : d\"" + }, + { + "Answer": 308.1239698259094, + "Options": "['a ) 306', 'b ) 307', 'c ) 308', 'd ) 309', 'e ) 310']", + "Correct": "c", + "Explanation": "side of the square = sqrt ( 12 ) = 11 perimeter of the square = 44 2 * pie * r = 44 r = 44 / 2 * pie area of the circle = pie * r ^ 2 = 308 answer : c" + }, + { + "Answer": 4.5, + "Options": "a ) 3.5 % , b ) 2.4 % , c ) 3 % , d ) 4.5 % , e ) 2.6 %", + "Correct": "d", + "Explanation": "\"say both sides of the rectangle are equal to 100 ( so consider that we have a square ) . in this case the area is 100 * 100 = 10,000 . now , the area obtained with wrong measurements would be 110 * 95 = 10,450 , which is 4.5 % greater than the actual area . answer : d .\"" + }, + { + "Answer": 10, + "Options": "a ) 2.5 , b ) 5 , c ) 10 , d ) 15 , e ) 20", + "Correct": "c", + "Explanation": "\"longest chord of a circle is the diameter of the circle diameter = 2 * radius if diameter of the circle is given as 20 = 2 * 10 so radius of the circle = 10 correct answer - c\"" + }, + { + "Answer": 14.365000000000002, + "Options": "['a ) 16.665', 'b ) 16.565', 'c ) 15.465', 'd ) 14.365', 'e ) 14.378']", + "Correct": "d", + "Explanation": "explanation : smaller triangle and original triangle will be similar to each other . ratio of area = ( ratio of side ) 2 area of smaller triangle = area of original triangle * ( 65 / 100 ) 2 = 14.365 . answer : d" + }, + { + "Answer": 100, + "Options": "a ) 50 % , b ) 87 % , c ) 100 % , d ) 187 % , e ) 200 %", + "Correct": "c", + "Explanation": "\"let ' s just look at the dimensions ( no calculation needed ) . with dimension 11 the same , the other dimension 19 is twice 9.5 then the area will be double which means 100 % greater . the answer is c .\"" + }, + { + "Answer": 5.555555555555555, + "Options": "['a ) 5.6 %', 'b ) 8.4 %', 'c ) 11.2 %', 'd ) 14.8 %', 'e ) 17.5 %']", + "Correct": "a", + "Explanation": "the area of each half is 100 + 4 ( 400 ) + 100 = 1800 the area that is not painted is 100 . the fraction that is not painted is 100 / 1800 = 1 / 18 = 5.6 % the answer is a ." + }, + { + "Answer": 104, + "Options": "['a ) 48', 'b ) 56', 'c ) 60', 'd ) 76', 'e ) 104']", + "Correct": "e", + "Explanation": "say length of garden is l meters . then ( l * 4 ) = 16 * 12 [ given area is same . area = l * b ] therefore l works out to 48 meters . perimeter of garden = 2 * ( 48 + 4 ) = 104 meter . answer is e" + }, + { + "Answer": 54, + "Options": "['a ) 34 cm \u00b2', 'b ) 38 cm \u00b2', 'c ) 54 cm \u00b2', 'd ) 56 cm \u00b2', 'e ) 64 cm \u00b2']", + "Correct": "c", + "Explanation": "ab \u00b2 = ac \u00b2 - bc \u00b2 = 15 \u00b2 - 12 \u00b2 = 225 - 144 = 81 therefore , ab = 9 therefore , area of the triangle = \u00b9 / \u2082 \u00d7 base \u00d7 height = \u00b9 / \u2082 \u00d7 12 \u00d7 9 = 54 cm \u00b2 answer : c" + }, + { + "Answer": 20.25, + "Options": "a ) 25.25 sq cm , b ) 20.25 sq cm , c ) 30.25 sq cm , d ) 36.25 sq cm , e ) 40.25 sq cm", + "Correct": "b", + "Explanation": "\"though there might be some technicalities concerning the termnearest ( as 4.5 is equidistant from both 4 and 5 ) the answer still should be : 4.5 ^ 2 = 20.25 . answer : b\"" + }, + { + "Answer": 3.5, + "Options": "['a ) 16', 'b ) 8', 'c ) 4', 'd ) 3.5', 'e ) 1']", + "Correct": "d", + "Explanation": "x be radius of circle x y be radius of circle y given : pi * x ^ 2 = pi * y ^ 2 also , 2 * pi * x = 14 * pi x = 7 thus y = 7 y / 2 = 3.5 ans : d" + }, + { + "Answer": 125, + "Options": "['a ) 135', 'b ) 155', 'c ) 125', 'd ) 145', 'e ) 115']", + "Correct": "c", + "Explanation": "lateral surface = 4 a ( power ) 2 = 100 sq . units a ( power ) 2 = 25 a = 5 . cube volume = a ( power ) 3 = > 125 m ( power ) 3 answer is c ." + }, + { + "Answer": 12, + "Options": "['a ) 11', 'b ) 12', 'c ) 13', 'd ) 15', 'e ) 18']", + "Correct": "b", + "Explanation": "if we take person a 1 in the set then it will cover a 36 and a 2 for shaking hand . similarly if we take person a 4 in the set then it will cover a 5 and a 3 for shaking hand and so on , so minimum 12 persons are required . answer : b" + }, + { + "Answer": 17, + "Options": "a ) 16 , b ) 77 , c ) 25 , d ) 17 , e ) 171", + "Correct": "d", + "Explanation": "\"explanation : let the integer be x . then , x + x 2 = 306 x 2 + x - 306 = 0 ( x + 18 ) ( x \u2013 17 ) = 0 x = 17 answer : d\"" + }, + { + "Answer": 3600, + "Options": "a ) s . 3988 , b ) s . 3900 , c ) s . 3228 , d ) s . 3922 , e ) s . 3600", + "Correct": "e", + "Explanation": "\"area = ( l + b \u2013 d ) d ( 70 + 60 \u2013 10 ) 10 = > 1200 m 2 1200 * 3 = rs . 3600 answer : e\"" + }, + { + "Answer": 15, + "Options": "a ) 16 , b ) 17 , c ) 18 , d ) 15 , e ) 14", + "Correct": "d", + "Explanation": "\"let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 675 3 b 2 = 675 b 2 = 225 b = 15 m . answer : option d\"" + }, + { + "Answer": 1918, + "Options": "a ) s . 1350 , b ) s . 1327 , c ) s . 1328 , d ) s . 1397 , e ) s . 1918", + "Correct": "e", + "Explanation": "\"area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 3.5 * 2 ) 2 * 3.5 = > 959 959 * 2 = rs . 1918 answer : e\"" + }, + { + "Answer": 5775.414574918697, + "Options": "a ) 388.15 , b ) 2992 , c ) 4312.5 , d ) 2887.27 , e ) 5773.09", + "Correct": "e", + "Explanation": "\"let the radii of the smaller and the larger circles be s m and l m respectively . 2 \u220f s = 268 and 2 \u220f l = 380 s = 268 / 2 \u220f and l = 380 / 2 \u220f difference between the areas = \u220f l 2 - \u220f s 2 = \u220f { 1902 / \u220f 2 - 1342 / \u220f 2 } = 1902 / \u220f - 1342 / \u220f = ( 190 - 134 ) ( 190 + 134 ) / \u220f = ( 56 ) ( 324 ) / ( 22 / 7 ) = ( 18144 ) / ( 22 ) ( 7 ) = 5773.09 sq m . answer : e\"" + }, + { + "Answer": 360, + "Options": "a ) 43 , b ) 56 , c ) 68 , d ) 360 , e ) 92", + "Correct": "d", + "Explanation": "\"sol . monthly rent per square feet = 2400 / ( 10 * 8 ) = 30 & annual rent per square feet = 12 * 30 = 360 answer : d\"" + }, + { + "Answer": 1727.9999999999993, + "Options": "a ) 24 , b ) 1728 , c ) 64 , d ) 80 , e ) 100", + "Correct": "b", + "Explanation": "\"volume = 216 = side ^ 3 i . e . side of cube = 6 new cube has dimensions 12 , 12 , and 12 as all sides are twice of teh side of first cube volume = 12 * 12 * 12 = 1728 square feet answer : option b\"" + }, + { + "Answer": 0.8584073464102069, + "Options": "['a ) 0.76', 'b ) 0.86', 'c ) 0.96', 'd ) 1.16', 'e ) 1.26']", + "Correct": "b", + "Explanation": "let the radius of circle is ' r ' area of the circle which is at corner = ( 22 / 7 * r ^ 2 ) / 4 hence the area of all four circles are = 22 / 7 * r ^ 2 areaof circle which is made on center of suare is = 22 / 7 * r ^ 2 total area of all circles are = 2 * 22 / 7 * r ^ 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . ( 1 ) if we construct the diagram we get the relation 4 r = 2 sqrt 2 r = 1 / sqrt 2 put the value of r in eqn 1 and we get 2 * 22 / 7 * 1 / 2 = 22 / 7 = 3.14 area of suare = 2 ^ 2 = 4 area of remaining part = 4 - 3.14 = 0.86 answer : b" + }, + { + "Answer": 10, + "Options": "a ) 21 , b ) 10 , c ) 61 , d ) 72 , e ) 14", + "Correct": "b", + "Explanation": "\"31360 = 8 * 8 * 7 * 7 * 5 * 2 , so we need one 5 and one 2 to make it a square of a number . so 5 * 2 = 10 ans : b\"" + }, + { + "Answer": 3315, + "Options": "['a ) 375', 'b ) 2570', 'c ) 2800', 'd ) 3315', 'e ) none of these']", + "Correct": "d", + "Explanation": "explanation : since we require minimum number of square tiles , the size of the tile is given as the h . c . f . of two sides of the room . the h . c . f . of 1625 cm & 1275 cm . is 25 cm . hence , we get , required number = ( 1625 * 1275 ) / ( 25 * 25 ) = 3315 answer : d" + }, + { + "Answer": 65, + "Options": "['a ) 2', 'b ) 7', 'c ) 6', 'd ) 889', 'e ) 1']", + "Correct": "b", + "Explanation": "answer : b" + }, + { + "Answer": 69, + "Options": "['a ) 68 cm', 'b ) 69 cm', 'c ) 70 cm', 'd ) 71 cm', 'e ) none']", + "Correct": "b", + "Explanation": "solution : all three sides of an equilateral triangle are equal . thus , its perimeter will be 23 \u00d7 3 = 69 cm answer b" + }, + { + "Answer": 6.65, + "Options": "a ) 4.65 % increase , b ) 5.65 % increase , c ) 6.65 % increase , d ) 6.65 % decrease , e ) 7.65 % increase", + "Correct": "c", + "Explanation": "\"let l and b be 100 each 100 * 100 = 10000 l increase by 35 % = 135 b decrease by 21 % = 79 135 * 79 = 10665 6.65 % increase answer : c\"" + }, + { + "Answer": 1200, + "Options": "a ) 3348 , b ) 3898 , c ) 1200 , d ) 2881 , e ) 7881", + "Correct": "c", + "Explanation": "answer : c ) 1200" + }, + { + "Answer": 10, + "Options": "['a ) 12 b ^ 2', 'b ) 10 b ^ 2', 'c ) 6 b ^ 2', 'd ) 4 b ^ 2', 'e ) 2 b ^ 2']", + "Correct": "b", + "Explanation": "l = 2 b ; b = b ; h = b ; surface area = 2 * ( lb + bh + hl ) = 2 * ( 2 b ^ 2 + b ^ 2 + 2 b ^ 2 ) = 10 b ^ 2 answer : b" + }, + { + "Answer": 9261, + "Options": "['a ) 8000', 'b ) 9261', 'c ) 9999', 'd ) none of these', 'e ) can not be determined']", + "Correct": "b", + "Explanation": "solution clearly , 9261 is a perfect cube satisfying the given property . answer b" + }, + { + "Answer": 3, + "Options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4", + "Correct": "d", + "Explanation": "\"sol . let x = 6 q + 3 . then x 2 = ( 6 q + 3 ) 2 = 36 q 2 + 36 q + 9 = 6 ( 6 q 2 + 6 q + 1 ) + 3 . so , when x 2 is divided by 6 , remainder = 3 . answer d\"" + }, + { + "Answer": 1600, + "Options": "['a ) 2399', 'b ) 1600', 'c ) 2679', 'd ) 1697', 'e ) 1711']", + "Correct": "b", + "Explanation": "in a square , number of squares on the diagonal is equal to the tiles on a single row . if there are even number of square on a side , then total squares on the diagonal is 2 n - 1 , otherwise 2 n . as the total tiles on the diagonal are given as 81 , then number of tiles on a side = 2 n - 1 = 81 so n = 41 . so number of white tiles = 412 \u2212 81 = 1681 \u2212 81412 \u2212 81 = 1681 \u2212 81 = 1600 answer : b" + }, + { + "Answer": 110, + "Options": "a ) 120 , b ) 110 , c ) 130 , d ) 140 , e ) 150", + "Correct": "b", + "Explanation": "\"the triangle with sides 26 cm , 22 cm and 10 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 22 * 10 = 110 cm 2 answer : option b\"" + }, + { + "Answer": 25, + "Options": "a ) 5 : 1 , b ) 10 : 1 , c ) 25 : 1 , d ) 50 : 1 , e ) 150 : 1", + "Correct": "c", + "Explanation": "\"let x be the length of the small cube ' s side . the total surface area of the small cube is 6 x ^ 2 . the total surface area of the large cube is 6 ( 5 x ) ^ 2 = 150 x ^ 2 . the ratio of surface areas is 25 : 1 . the answer is c .\"" + }, + { + "Answer": 60, + "Options": "['a ) 50', 'b ) 60', 'c ) 70', 'd ) 80', 'e ) 90']", + "Correct": "b", + "Explanation": "let l be the length and w be the width . l = ( 7 / 5 ) w perimeter : 2 l + 2 w = 288 , 2 ( 7 / 5 ) w + 2 w = 288 solve the above equation to find : w = 60 m and l = 84 m . correct answer b ) 60" + }, + { + "Answer": 19, + "Options": "a ) 18 square meters , b ) 19 square meters , c ) 24 square meters , d ) 28 square meters , e ) 30 square meters", + "Correct": "b", + "Explanation": "\"total = rug 1 + rug 2 + rug 3 - { overlap of exactly 2 rugs } - 2 * { overlap of exactly 3 rugs } 138 = 200 - 24 - 2 * { overlap of exactly 2 rugs } - - > { overlap of exactly 3 rugs } = 19 . answer : b .\"" + }, + { + "Answer": 6000, + "Options": "a ) 0.36 , b ) 3.6 , c ) 360 , d ) 6000 , e ) 36000", + "Correct": "d", + "Explanation": "1 degree * 1 / 100 = 1 anglet so 1 degree = 100 anglets = > 60 degrees = 6000 anglets answer - d" + }, + { + "Answer": 76, + "Options": "['a ) 64', 'b ) 68', 'c ) 72', 'd ) 76', 'e ) 80']", + "Correct": "d", + "Explanation": "by graphing the points , we can see that this figure is a trapezoid . a trapezoid is any quadrilateral that has one set of parallel sides , and the formula for the area of a trapezoid is : area = ( 1 / 2 ) \u00d7 ( base 1 + base 2 ) \u00d7 ( height ) , where the bases are the parallel sides . we can now determine the area of the quadrilateral : area = 1 / 2 \u00d7 ( 10 + 9 ) \u00d7 8 = 76 . the answer is d ." + }, + { + "Answer": 88.5, + "Options": "a ) 88.25 , b ) 87.5 , c ) 86.0 , d ) 88.0 , e ) 88.5", + "Correct": "e", + "Explanation": "\"100 * 100 = 10000 130 * 145 = 18850 - - - - - - - - - - - 8850 10000 - - - - 8850 100 - - - - - 88.50 answer e\"" + }, + { + "Answer": 8.999999999999998, + "Options": "['a ) 7 cm', 'b ) 8.5 cm', 'c ) 9 cm', 'd ) 9.5 cm', 'e ) none']", + "Correct": "c", + "Explanation": "sol . let the radius of the ball be r cm . volume of ball = volume of water displaced by it . \u2234 4 / 3 \u220f r \u00b3 = \u220f * 12 * 12 * 6.75 \u21d2 r \u00b3 = 9 * 9 * 9 \u21d2 r = 9 cm . answer c" + }, + { + "Answer": 44, + "Options": "a ) 44.00 % , b ) 45.25 % , c ) 48.75 % , d ) 50.00 % , e ) 40.00 %", + "Correct": "a", + "Explanation": "\"a = 100 a 2 = 10000 a = 120 a 2 = 14400 - - - - - - - - - - - - - - - - 10000 - - - - - - - - - 4400 100 - - - - - - - ? = > 44.00 % answer : a\"" + }, + { + "Answer": 13, + "Options": "a ) 13 metres , b ) 5 metres , c ) 7.5 metres , d ) data inadequate , e ) none of these", + "Correct": "a", + "Explanation": "\"l \u00d7 b = 23 \u00d7 b \u2234 l = 23 m and l \u2013 b = 10 \u2234 b = 23 \u2013 10 = 13 m answer a\"" + }, + { + "Answer": 32, + "Options": "['a ) 32 cm 2', 'b ) 16 cm 2', 'c ) 20 cm 2', 'd ) 64 cm 2', 'e ) none of these']", + "Correct": "a", + "Explanation": "solution : side of the first square is 4 cm . side of second square = 2 \u221a 2 cm . side of third square = 2 cm . and so on . i . e . 4 , 2 \u221a , 2 , \u221a 2 , 1 . . . . . . thus , area of these square will be , = 16 , 8 , 4 , 2 , 1 , 1 / 2 . . . . . . . hence , sum of the area of first , second , third square . . . . . . = 16 + 8 + 4 + 2 + 1 + . . . . . = [ 16 / { 1 - ( 1 / 2 ) } ] = 32 cm 2 . answer : option a" + }, + { + "Answer": 256, + "Options": "['a ) 236', 'b ) 256', 'c ) 456', 'd ) 656', 'e ) 756']", + "Correct": "b", + "Explanation": "area of the square = s * s = 2 ( 32 * 64 ) = > s = 64 cm perimeter of the square = 4 * 64 = 256 cm . answer : option b" + }, + { + "Answer": 234, + "Options": "a ) 216 \u00b0 , b ) 222 \u00b0 , c ) 228 \u00b0 , d ) 234 \u00b0 , e ) 240 \u00b0", + "Correct": "d", + "Explanation": "\"the percent of the budget for salaries is 100 - ( 15 + 9 + 5 + 4 + 2 ) = 65 % 100 % of the circle is 360 degrees . then ( 65 % / 100 % ) * 360 = 234 degrees the answer is d .\"" + }, + { + "Answer": 25, + "Options": "['a ) 5', 'b ) 10', 'c ) 15', 'd ) 20', 'e ) 25']", + "Correct": "e", + "Explanation": "l * w = 750 : area , l is the length and w is the width . 2 l + 2 w = 110 : perimeter l = 55 - w : solve for l ( 55 - w ) * w = 750 : substitute in the area equation w = 25 and l = 30 correct answer e" + }, + { + "Answer": 448, + "Options": "a ) 498 cm 2 , b ) 384 cm 2 , c ) 430 cm 2 , d ) 128 cm 2 , e ) 448 cm 2", + "Correct": "e", + "Explanation": "\"area of a parallelogram = base * height = 32 * 14 = 448 cm 2 answer : e\"" + }, + { + "Answer": 17, + "Options": "a ) 8 m , b ) 10 m , c ) 12 m , d ) 15 m , e ) 17 m", + "Correct": "e", + "Explanation": "\"let the length of the hall be x m breadth of the hall = 1 x / 2 m area of the hall = length * breadth 578 = x * 1 x / 2 x \u00b2 = 1156 x = 34 difference between the length and breadth of the hall = x - 1 x / 2 = x / 2 = 34 / 2 = 17 m answer : e\"" + }, + { + "Answer": 54, + "Options": "a ) 24 a 8 , b ) 24 a 4 , c ) 24 a 1 , d ) 54 a 2 , e ) 24 a 7", + "Correct": "d", + "Explanation": "\"6 a 2 = 6 * 3 a * 3 a = 54 a 2 answer : d\"" + }, + { + "Answer": 280, + "Options": "['a ) 150 cm', 'b ) 200 cm', 'c ) 162 cm', 'd ) 220 cm', 'e ) 280 cm']", + "Correct": "e", + "Explanation": "ratio of sides = 5 : 6 : 7 largest side = 720 * 7 / 18 = 280 cm answer is e" + }, + { + "Answer": 0.00205761316872428, + "Options": "['a ) 1 / 27', 'b ) 1 / 54', 'c ) 1 / 81', 'd ) 1 / 162', 'e ) 1 / 486']", + "Correct": "e", + "Explanation": "fraction of area unpainted after first shift of amit = 1 - ( 1 / 2 ) = 1 / 2 fraction of area unpainted after first shift of ian = ( 1 / 2 ) - ( 1 / 3 ) ( 1 / 2 ) = ( 2 / 3 ) ( 1 / 2 ) fraction of area unpainted after second shift of amit = ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) fraction of area unpainted after second shift of ian = ( 2 / 3 ) ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) fraction of area unpainted after third shift of amit = ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) fraction of area unpainted after third shift of ian = ( 2 / 3 ) ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) fraction of area unpainted after forth shift of amit = ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) fraction of area unpainted after forth shift of ian = ( 2 / 3 ) ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) fraction of area unpainted after fifth shift of amit = ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) fraction of area unpainted after fifth shift of ian = ( 2 / 3 ) ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) fraction of area unpainted after sixth shift of amit = ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) ( 2 / 3 ) ( 1 / 2 ) = 486 answer : option e" + }, + { + "Answer": 50, + "Options": "['a ) 34 %', 'b ) 45 %', 'c ) 50 %', 'd ) 60 %', 'e ) 67 %']", + "Correct": "c", + "Explanation": "let original length = x and original breadth = y . original area = xy . new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c" + }, + { + "Answer": 11, + "Options": "a ) 11 , b ) 17 , c ) 18 , d ) 101 , e ) 1322", + "Correct": "a", + "Explanation": "\"let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 363 3 b 2 = 363 b 2 = 121 = 11 ( b > 0 ) b = 11 m . answer : a\"" + }, + { + "Answer": 9, + "Options": "a ) 9 , b ) 15 , c ) 12 , d ) 11 , e ) 10", + "Correct": "a", + "Explanation": "\"area of tile = 50 * 40 = 2000 area of floor = 120 * 150 = 18000 no of tiles = 18000 / 2000 = 9 so , the no of tile = 9 answer : a\"" + }, + { + "Answer": 600, + "Options": "a ) $ 5,330 , b ) $ 3,360 , c ) $ 1,350 , d ) $ 600 , e ) $ 150", + "Correct": "d", + "Explanation": "basically the question an error . 1 acre = 43,560 square feet and if it is then the answer is 600 ( d )" + }, + { + "Answer": 452.3893421169302, + "Options": "a ) 26 , b ) 452 , c ) 450 , d ) 440 , e ) 28", + "Correct": "b", + "Explanation": "\"\u03c0 * 18 * 8 = 452 answer : b\"" + }, + { + "Answer": 2, + "Options": "['a ) 2', 'b ) 1', 'c ) 3', 'd ) 5', 'e ) 6']", + "Correct": "a", + "Explanation": "1152 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 required smallest number = 2 2 is the smallest number which should be multiplied with 1152 to make it a perfect square . answer : a" + }, + { + "Answer": 180, + "Options": "a ) 180 cm , b ) 220 cm , c ) 240 cm , d ) 270 cm , e ) 300 cm", + "Correct": "a", + "Explanation": "\"we have 30 for first triangle , when we join mid - points of first triangle we get the second equilateral triangle then the length of second one is 15 and continues . so we have 30,15 , 7.5 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 30 / 1 - ( 1 / 2 ) = 60 equilateral triangle perimeter is 3 a = 3 * 60 = 180 . so option a .\"" + }, + { + "Answer": 480, + "Options": "a ) 200 , b ) 384 , c ) 345 , d ) 480 , e ) 242", + "Correct": "d", + "Explanation": "\"area of a parallelogram = base * height = 32 * 15 = 480 cm 2 answer : option d\"" + }, + { + "Answer": 22, + "Options": "['a ) 22 .', 'b ) 25 .', 'c ) 30 .', 'd ) 32 .', 'e ) 34 .']", + "Correct": "a", + "Explanation": "given : one side is 6 cm and another side is 8 cm . so the 3 rd side will be > 3 and < 15 . thus the perimeter will be : 18 < perimeter < 30 . only option satisfying this condition is 22 . hence a ." + }, + { + "Answer": 450, + "Options": "a ) 189 cm 2 , b ) 150 cm 2 , c ) 127 cm 2 , d ) 450 cm 2 , e ) 187 cm 2", + "Correct": "d", + "Explanation": "\"1 / 2 * 50 ( 10 + 8 ) = 450 cm 2 answer : d\"" + }, + { + "Answer": 36, + "Options": "['a ) 35', 'b ) 36', 'c ) 37', 'd ) 38', 'e ) 39']", + "Correct": "b", + "Explanation": "the circumference of a circle is given by c = 2 pi r , where r is the radius of the circle . substitute c by 72 pi to obtain the equation 72 pi = 2 pi r simplify and solve for r to obtain r = 36 answer b" + }, + { + "Answer": 5.6, + "Options": "['a ) 5.6 cm', 'b ) 2.4 cm', 'c ) 4.8 cm', 'd ) 2.16 cm', 'e ) 3.2 cm']", + "Correct": "a", + "Explanation": "look at the diagram below : now , in case when qy is perpendicular to pr , two right triangles pqr and pqy are similar : qy : qp = qr : pr - - > qy : 7 = 8 : 10 - - > qy = 5.6 . answer : a ." + }, + { + "Answer": 32, + "Options": "a ) 73 , b ) 32 , c ) 34 , d ) 43 , e ) 42", + "Correct": "b", + "Explanation": "\"explanation : a / 8 = 8 * 8 = > a = 8 * 8 * 8 x * 2 x = 8 * 8 * 8 x = 16 = > 2 x = 32 answer : option b\"" + }, + { + "Answer": 11600, + "Options": "a ) 1288 , b ) 1299 , c ) 1000 , d ) 10000 , e ) 11600", + "Correct": "e", + "Explanation": "\"100 * 100 = 10000 145 * 80 = 11600 answer : e\"" + }, + { + "Answer": 82.5, + "Options": "a ) 52.6 , b ) 52.9 , c ) 52.8 , d ) 52.1 , e ) 82.5", + "Correct": "e", + "Explanation": "\"42 / 360 * 22 / 7 * 15 * 15 = 82.5 m 2 answer : e\"" + }, + { + "Answer": 10, + "Options": "['a ) 10', 'b ) 12', 'c ) 8', 'd ) 14', 'e ) 9']", + "Correct": "a", + "Explanation": "think of a can . if you took off the bottom and top and cut a slit down the length , it would flatten to a rectangle . the dimensions of the rectangle are the height of the can and the circumference of the circle . since you know both , use pythagoreans theorem or properties of 3 - 4 - 5 triangles to solve for the hypothenuse , 10 . ( correct answer : a )" + }, + { + "Answer": 330, + "Options": "a ) 358 , b ) 329 , c ) 350 , d ) 330 , e ) 317", + "Correct": "d", + "Explanation": "\"1 / 2 * 22 * 30 = 330 answer : d\"" + }, + { + "Answer": 201.06192982974676, + "Options": "a ) 124 cm \u00b2 , b ) 201 cm \u00b2 , c ) 210 cm \u00b2 , d ) 184 cm \u00b2 , e ) 194 cm \u00b2", + "Correct": "b", + "Explanation": "\"area of circle = \u03c0 r \u00b2 = 22 / 7 \u00d7 8 \u00d7 8 cm \u00b2 = 201 cm \u00b2 answer : b\"" + }, + { + "Answer": 140, + "Options": "['a ) 140 cm', 'b ) 240 cm 2', 'c ) 560 cm 2', 'd ) none of these', 'e ) can not be determined']", + "Correct": "a", + "Explanation": "solution when folded along breadth , we have : 2 ( l / 2 + b ) = 34 or l + 2 b = 34 when folded along length , we have : 2 ( l / 2 + b ) = 38 or 2 l + b = 38 solving ( i ) and ( ii ) , we get : l = 14 and b = 10 . \u2234 area of the paper = ( 1410 ) cm 2 = 140 cm 2 answer a" + }, + { + "Answer": 2250, + "Options": "a ) 100 , b ) 2250 , c ) 750 , d ) 1200 , e ) 5625", + "Correct": "b", + "Explanation": "\"6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 60 * 10 * 1 / 2 = 300 feet ^ 3 of water must be removed , which equals to 300 * 7.5 = 2250 gallons . answer : b\"" + }, + { + "Answer": 3808, + "Options": "a ) s . 3944 , b ) s . 3948 , c ) s . 3942 , d ) s . 3808 , e ) s . 3929", + "Correct": "d", + "Explanation": "\"let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 56 = rs . 3808 . answer : d\"" + }, + { + "Answer": 8, + "Options": "['a ) 12 % deficit', 'b ) 10 % excess', 'c ) 8 % excess', 'd ) 9 % excess', 'e ) none of these']", + "Correct": "c", + "Explanation": "since side 1 x side 2 = area therefore , error % in area = ( x + y + xy / 100 ) % = [ 20 - 10 + ( - 10 x 20 ) / 100 ] % or 8 % i . e . , 8 % excess answer : c" + }, + { + "Answer": 5.793103448275862, + "Options": "['a ) 148 / 29', 'b ) 168 / 29', 'c ) 168 / 26', 'd ) 158 / 29', 'e ) 198 / 29']", + "Correct": "b", + "Explanation": "by heron ' s formula , the area , a , of a triangle with sides a , b , c is given by a = square root [ s ( s \u2212 a ) ( s \u2212 b ) ( s \u2212 c ) ] , where s = \u00bd ( a + b + c ) is the semi - perimeter of the triangle . then s = \u00bd ( 10 + 17 + 21 ) = 24 , and a = 84 . a square inscribed in a 10 by 17 by 21 triangle , with perpendicular dropped onto the side of length 21 . now drop a perpendicular of length h onto the side of length 21 . we also have a = \u00bd \u00d7 base \u00d7 perpendicular height . hence a = 21 h / 2 = 84 , from which h = 8 . notice that the triangle above the square is similar to the whole triangle . ( this follows because its base , the top of the square , is parallel to the base of the whole triangle . ) let the square have side of length d . considering the ratio of altitude to base in each triangle , we have 8 / 21 = ( 8 \u2212 d ) / d = 8 / d \u2212 1 . therefore the length of the side of the square is 168 / 29 . answer : b" + }, + { + "Answer": 3.3379421944391545, + "Options": "['a ) 3.34', 'b ) 3.36', 'c ) 3.34', 'd ) 6.32', 'e ) 3.31']", + "Correct": "a", + "Explanation": "area of the path = area of the outer circle - area of the inner circle = \u220f { 4 / 2 + 25 / 100 } 2 - \u220f [ 4 / 2 ] 2 = \u220f [ 2.252 - 22 ] = \u220f ( 0.25 ) ( 4.25 ) { ( a 2 - b 2 = ( a - b ) ( a + b ) } = ( 3.14 ) ( 1 / 4 ) ( 17 / 4 ) = 53.38 / 16 = 3.34 sq m . answer : a" + }, + { + "Answer": 400, + "Options": "a ) 100 cm 2 , b ) 150 cm 2 , c ) 333 cm 2 , d ) 400 cm 2 , e ) 750 cm 2", + "Correct": "d", + "Explanation": "\"1 / 2 * 40 ( 11 + 9 ) = 400 cm 2 answer : d\"" + }, + { + "Answer": 4, + "Options": "a ) 3 , b ) 6 , c ) 4 , d ) 9 , e ) 1", + "Correct": "c", + "Explanation": "s = ( 1 + 2 + 5 ) / 2 = 4 answer : c" + }, + { + "Answer": 7.2, + "Options": "['a ) 7 cm', 'b ) 7.1 cm', 'c ) 7.2 cm', 'd ) 7.3 cm', 'e ) none of these']", + "Correct": "c", + "Explanation": "solution let the breadth be b . then , \u21d2 25 b = 18 \u00d7 10 \u21d2 b = ( 18 x 10 / 25 ) cm = 7.2 cm answer c" + }, + { + "Answer": 78.53981633974483, + "Options": "['a ) 75.5 sq inch', 'b ) 76.5 sq inch', 'c ) 77.5 sq inch', 'd ) 78.5 sq inch', 'e ) 79.5 sq inch']", + "Correct": "d", + "Explanation": "10 inch square means sides of sq are 10 inch then circle is within square so diameter would be 10 inch maximum and radius is 5 inch so area of the circle is = pi * r * r = 3.14 * 5 * 5 = 78.5 sq inch answer : d" + }, + { + "Answer": 11, + "Options": "['a ) 11', 'b ) 9', 'c ) 7', 'd ) 5', 'e ) 3']", + "Correct": "a", + "Explanation": "let the number of sides be n . the number of diagonals is given by nc 2 - n therefore , nc 2 - n = 44 , n > 0 n ( n - 1 ) / 2 - n = 44 n 2 - 3 n - 88 = 0 n 2 - 11 n + 8 n - 88 = 0 n ( n - 11 ) + 8 ( n - 11 ) = 0 n = - 8 or n = 11 . answer : a" + }, + { + "Answer": 100, + "Options": "a ) 50 % , b ) 87 % , c ) 100 % , d ) 187 % , e ) 200 %", + "Correct": "c", + "Explanation": "\"area of sheet a = 11 * 17 area of sheet b = 11 * 8.5 difference in area = 11 * 8.5 required % = ( 11 * 8.5 ) * 100 / ( 11 * 8.5 ) % = 100 % answer : c\"" + }, + { + "Answer": 1.975367389481267, + "Options": "['a ) 1.967', 'b ) 1.963', 'c ) 2.388', 'd ) 3.388', 'e ) 2.382']", + "Correct": "a", + "Explanation": "explanation : required area = ( area of an equilateral triangle of side 7 cm ) - ( 3 * area of sector with \u00e3 = 60 degrees and r = 3.5 cm ) \\ inline { \\ color { black } ( \\ frac { \\ sqrt { 3 } } { 4 } \\ times 7 \\ times 7 ) - ( 3 \\ times \\ frac { 22 } { 7 } \\ times 3.5 \\ times 3.5 \\ times \\ frac { 60 } { 360 } ) } sq cm = \\ inline { \\ color { black } ( \\ frac { \\ sqrt { 3 } } { 4 } \\ times 49 ) - ( 11 \\ times 0.5 \\ times 3.5 ) } sq cm = 1.967 sq cm answer : a ) 1.967" + }, + { + "Answer": 2, + "Options": "a ) 3 : 8 , b ) 3 : 6 , c ) 3 : 7 , d ) 2 : 1 , e ) 3 : 3", + "Correct": "d", + "Explanation": "\"d = 2 d d = d a \u221a 2 = 2 d a \u221a 2 = d a = 2 d / \u221a 2 a = d / \u221a 2 = > 2 : 1 answer : d\"" + }, + { + "Answer": 24, + "Options": "a ) 27 , b ) 36 , c ) 42 , d ) 24 , e ) 147", + "Correct": "d", + "Explanation": "\"112 ounces of a substance has a volume of 48 cubic inches 56 ounces of a substance has a volume of ( 48 / 112 ) * 56 = 24 cubic inches answer d\"" + }, + { + "Answer": 0.6, + "Options": "['a ) 1 / 4', 'b ) 3 / 8', 'c ) 1 / 2', 'd ) 3 / 5', 'e ) 2']", + "Correct": "d", + "Explanation": "one side surface area of a cube = x * x = x ^ 2 total 6 sides = 6 x ^ 2 as for the rectangular , height ( h ) and width ( w ) are same as cube , x . only length = 2 x . l x h = 2 x * x = 2 x ^ 2 - - - - > 4 sides = 2 x ^ 2 * 4 = 8 x ^ 2 w * h = x * x = x ^ 2 - - - - - - > 2 sides = x ^ 2 * 2 = 2 x ^ 2 total 6 sides = 8 x ^ 2 + 2 x ^ 2 = 10 x ^ 2 ratio of cube area to rectangular area g = 6 x ^ 2 / 10 x ^ 2 - - - - > 6 / 10 - - - - > 3 / 5 ( d )" + }, + { + "Answer": 30, + "Options": "a ) 28 , b ) 30 , c ) 32 , d ) 35 , e ) 37", + "Correct": "b", + "Explanation": "\"least number of cubes will be required when the cubes that could fit in are biggest . 8 is the biggest number that could divide all three , 24 , 40 and 16 . thus side of cube must be 8 , and total number of cubes = 24 / 8 * 40 / 8 * 16 / 8 = 30 ans b\"" + }, + { + "Answer": 120, + "Options": "a ) 110 , b ) 120 , c ) 130 , d ) 140 , e ) 150", + "Correct": "b", + "Explanation": "\"other side = [ ( 17 x 17 ) - ( 15 x 15 ) ] = ( 289 - 225 ) = 8 m area = 15 x 8 = 120 sq . m answer : b\"" + }, + { + "Answer": 6, + "Options": "['a ) \u2013 2 / pi', 'b ) 2', 'c ) 3', 'd ) 4', 'e ) 6']", + "Correct": "e", + "Explanation": "pi * r ^ 2 + 2 r - 2 * pi * r = 12 simplifying the equation : pi * r ( r - 2 ) + 2 r = 12 without much algebraic : we can test the answers quickly , then 6 is the only possible answer that will eliminate pi from equation . answer is e" + }, + { + "Answer": 81.99999999999999, + "Options": "['a ) 82 %', 'b ) 78 %', 'c ) 80 %', 'd ) 90 %', 'e ) none of these']", + "Correct": "a", + "Explanation": "since side 1 x side 2 = area therefore , net % change in area = ( x + y + xy / 100 ) % = [ 40 + 30 + ( 40 x 30 ) / 100 ] % or 82 % . therefore , area is increased by 82 % . answer : a" + }, + { + "Answer": 25, + "Options": "['a ) 15 m', 'b ) 22.5 m', 'c ) 25 m', 'd ) 30 m', 'e ) none']", + "Correct": "c", + "Explanation": "solution let the length = xmetres . then length = ( x + 5 ) metres . then , x ( x + 5 ) = 750 = x \u00b2 + 5 x - 750 = 0 ( x + 30 ) ( x - 25 ) = 0 x = 25 . answer c" + }, + { + "Answer": 102.83185307179586, + "Options": "a ) 50 , b ) 25 , c ) 86 , d ) 75 , e ) 102", + "Correct": "e", + "Explanation": "\"circumference of a circle = 2 pi * r perimeter of a semicircle = pi * r + 2 r aprox perimiter = 3.14 * 20 + 2 * 20 = 102.8 approximately 102 answer e\"" + }, + { + "Answer": 108, + "Options": "a ) 107 , b ) 108 , c ) 109 , d ) 110 , e ) 111", + "Correct": "b", + "Explanation": "\"number of cubes required = volume of box / volume of cube = 9 * 12 * 3 / 3 = 108 cubes answer : b\"" + }, + { + "Answer": 32, + "Options": "a ) w = 16 , b ) w = 32 , c ) 64 , d ) 128 , e ) 512", + "Correct": "b", + "Explanation": "\"weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )\"" + }, + { + "Answer": 200, + "Options": "['a ) 600', 'b ) 400', 'c ) 200', 'd ) 500', 'e ) 100']", + "Correct": "c", + "Explanation": "area of tile = 35 * 30 = 1050 area of floor = 1000 * 210 = 210000 no of tiles = 210000 / 1050 = 200 so , the no of tile = 200 answer : c" + }, + { + "Answer": 42, + "Options": "['a ) 24 cm', 'b ) 36 * 2 ^ 1 / 2 cm', 'c ) 36 cm', 'd ) 54 cm', 'e ) 42 cm']", + "Correct": "e", + "Explanation": "1 ) the radius of the incircle of a right triangle with legs a and b and hypotenuse c is r = ( a + b - c ) / 2 2 ) the radius of the circumcircle is half the length of the hypotenuse r = c / 2 3 ) thus the sum of the circumradius and the inradius is half the sum of the legs r + r = ( a + b ) / 2 from 2 nd rule c = 18 cm from 3 rd rule a + b = 2 * ( 9 + 3 ) = 24 cm hence perimeter a + b + c = 24 + 18 = 42 cm answer : e" + }, + { + "Answer": 8, + "Options": "['a ) 6', 'b ) 5', 'c ) 8', 'd ) 6', 'e ) 3']", + "Correct": "c", + "Explanation": "let the radii of the larger and the smaller circles be l cm and s cm respectively . let the side of the square be a cm . a 2 = 784 = ( 4 ) ( 196 ) = ( 22 ) . ( 142 ) a = ( 2 ) ( 14 ) = 28 a = 2 l , l = a / 2 = 14 l = ( 7 / 3 ) s therefore s = ( 3 / 7 ) ( l ) = 6 circumference of the smaller circle = 2 \u220f s = 12 \u220f cm . answer : c" + }, + { + "Answer": 600, + "Options": "['a ) 140 %', 'b ) 350 %', 'c ) 450 %', 'd ) 600 %', 'e ) 700 %']", + "Correct": "d", + "Explanation": "the area a of the large cube is 7 * 7 * 6 = 294 square cm . the area of the 343 small cubes is 7 * 7 * 7 * 6 = 7 a , an increase of 600 % . the answer is d ." + }, + { + "Answer": 12, + "Options": "a ) 4 , b ) 8 , c ) 12 , d ) 15 , e ) 20", + "Correct": "c", + "Explanation": "\"i understand this might not be required but i used the equation of a circle . since the origin is at 0 , x ^ 2 + y ^ 2 = 5 ^ 2 . x , y could be + / - ( 0,5 or 5,0 ) - 4 possibilities . x , y could be + / - ( 3,4 or 4,3 ) - 8 possibilities . ans : k = c\"" + }, + { + "Answer": 15.249999999999998, + "Options": "a ) 13 \u03c0 , b ) 15.25 \u03c0 , c ) 262 \u221a \u03c0 , d ) 52 \u03c0 , e ) 64 \u03c0", + "Correct": "b", + "Explanation": "\"the distance between the two points is sqrt ( 61 ) . radius = sqrt ( 61 ) / 2 area = pi * ( sqrt ( 61 ) / 2 ) ^ 2 b . 15.25 \u03c0\"" + }, + { + "Answer": 16, + "Options": "['a ) 1 : 4', 'b ) 1 : 16', 'c ) 4 : 1', 'd ) 16 : 1', 'e ) none']", + "Correct": "d", + "Explanation": "solution let the radil of a and b be r and r respectively . required ratio = 4 \u03c0 r 2 / 4 \u03c0 r 2 \u2039 = \u203a r 2 / r 2 \u2039 = \u203a ( r / r ) 2 \u2039 = \u203a ( 40 / 10 ) 2 \u2039 = \u203a 16 : 1 . answer d" + }, + { + "Answer": 1200, + "Options": "a ) 720 , b ) 900 , c ) 1200 , d ) 1800 , e ) none", + "Correct": "c", + "Explanation": "\"solution 2 ( 15 + 12 ) \u00d7 h = 2 ( 15 x 12 ) \u2039 = \u203a h = 180 / 27 m = 20 / 3 m volume = ( 15 \u00d7 12 \u00d7 20 / 3 ) m 3 \u2039 = \u203a 1200 m 3 . answer c\"" + }, + { + "Answer": 27, + "Options": "a ) 8 cc , b ) 27 cc , c ) 2 cc , d ) 4 cc , e ) 6 cc", + "Correct": "b", + "Explanation": "\"6 a 2 = 54 = 6 * 9 a = 3 = > a 3 = 27 cc answer : b\"" + }, + { + "Answer": 18.84955592153876, + "Options": "a ) 23.56 , b ) 23.59 , c ) 23.55 , d ) 18.86 , e ) 23.57", + "Correct": "d", + "Explanation": "\"let the side of the square be a cm . parameter of the rectangle = 2 ( 14 + 10 ) = 48 cm parameter of the square = 48 cm i . e . 4 a = 48 a = 12 diameter of the semicircle = 12 cm circimference of the semicircle = 1 / 2 ( \u00e2 \u02c6 \u008f ) ( 12 ) = 1 / 2 ( 22 / 7 ) ( 12 ) = 264 / 14 = 18.86 cm to two decimal places answer : d\"" + }, + { + "Answer": 4200, + "Options": "a ) s . 3988 , b ) s . 3900 , c ) s . 3228 , d ) s . 4200 , e ) s . 3928", + "Correct": "d", + "Explanation": "\"area = ( l + b \u2013 d ) d ( 90 + 60 \u2013 10 ) 10 = > 1400 m 2 1400 * 3 = rs . 4200 answer : d\"" + }, + { + "Answer": 200, + "Options": "['a ) 288', 'b ) 289', 'c ) 200', 'd ) 112', 'e ) 178']", + "Correct": "c", + "Explanation": "d 2 / 2 = ( 20 * 20 ) / 2 = 200 answer : c" + }, + { + "Answer": 0.4444444444444444, + "Options": "a ) 4 / 9 , b ) 2 / 3 , c ) 3 / 2 , d ) 9 / 2 , e ) 9 / 4", + "Correct": "a", + "Explanation": "\"the area of rectangle a is ab . c = 3 a / 2 and d = 3 b / 2 . the area of rectangle b is cd = 9 ab / 4 . the ratio of rectangle a ' s area to rectangle b ' s area is ab / ( 9 ab / 4 ) = 4 / 9 . the answer is a .\"" + }, + { + "Answer": 0.8677685950413223, + "Options": "a ) 9 / 25 , b ) 1 / 5 , c ) 16 / 121 , d ) 105 / 121 , e ) 6 / 25", + "Correct": "d", + "Explanation": "\"i guess it ' s mean that square b is placed within square aentirely . since , the perimeter of b is 16 , then its side is 16 / 4 = 4 and the area is 4 ^ 2 = 16 ; empty space between the squares is 121 - 16 = 105 square centimeters , so if a random point is in this area then it wo n ' t be within square b : p = favorable / total = 105 / 121 . answer : d .\"" + }, + { + "Answer": 5120, + "Options": "a ) 3220 , b ) 4830 , c ) 5120 , d ) 6420 , e ) none", + "Correct": "c", + "Explanation": "\"solution clearly , l = ( 48 - 16 ) m = 32 m \u2039 = \u203a b = ( 36 - 16 ) m = 20 m , \u2039 = \u203a h = 8 m . . volume of the box = ( 32 x 20 x 8 ) m 3 = 5120 m 3 . answer c\"" + }, + { + "Answer": 0.0003, + "Options": "a ) 0.005 , b ) 0.002 , c ) 0.001 , d ) 0.0003 , e ) 0.0002", + "Correct": "d", + "Explanation": "\"it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 0.3 then x = 0.3 / 1000 = 0.0003 . the answer is d\"" + }, + { + "Answer": 0.64, + "Options": "a ) 9 / 25 , b ) 1 / 5 , c ) 16 / 25 , d ) 3 / 5 , e ) 6 / 25", + "Correct": "c", + "Explanation": "\"i guess it ' s mean that square b is placed within square aentirely . since , the perimeter of b is 12 , then its side is 12 / 4 = 3 and the area is 3 ^ 2 = 9 empty space between the squares is 25 - 9 = 16 square centimeters , so if a random point is in this area then it wo n ' t be within square b : p = favorable / total = 16 / 25 . answer : c\"" + }, + { + "Answer": 1, + "Options": "['a ) 1', 'b ) 3', 'c ) 8', 'd ) 5', 'e ) 7']", + "Correct": "a", + "Explanation": "if the cube is cut in to 27 smaller cubes , then number of separations made = n = 3 ( since 3 \u00d7 3 \u00d7 3 = 27 ) . number of smaller cubes with no color = ( n \u2013 2 ) 3 = ( 3 \u2013 2 ) 3 = 13 = 1 answer : a" + }, + { + "Answer": 95.4, + "Options": "a ) 75.4 feet , b ) 98.4 feet , c ) 95.4 feet , d ) 85.4 feet , e ) 92.4 feet", + "Correct": "c", + "Explanation": "\"area of the field = 880 sq . feet . length of the adjacent sides are 25 feet and 880 / 25 = 35.2 feet . required length of the fencing = 25 + 35.2 + 35.2 = 95.4 feet answer : c\"" + }, + { + "Answer": 11.25, + "Options": "a ) 6 cm , b ) 8.25 cm , c ) 11.25 cm , d ) 15.12 cm , e ) 20.62 cm", + "Correct": "c", + "Explanation": "\"increase in volume = volume of the cube = 15 * 15 * 15 cm ^ 3 rise in water level = volume / area = 15 * 15 * 15 / 20 * 15 = 11.25 cm answer is c\"" + }, + { + "Answer": 11, + "Options": "a ) 10 metres , b ) 5 metres , c ) 11 metres , d ) data inadequate , e ) none of these", + "Correct": "c", + "Explanation": "\"l \u00d7 b = 21 \u00d7 b \u2234 l = 21 m and l \u2013 b = 10 \u2234 b = 21 \u2013 10 = 11 m answer c\"" + }, + { + "Answer": 20, + "Options": "['a ) 54', 'b ) 32', 'c ) 75', 'd ) 20', 'e ) 11']", + "Correct": "d", + "Explanation": "a / 8 = 5 * 5 = > a = 5 * 5 * 8 x * 2 x = 5 * 5 * 8 x = 10 = > 2 x = 20 answer : d" + }, + { + "Answer": 50, + "Options": "['a ) 30', 'b ) 40', 'c ) 50', 'd ) 60', 'e ) 70']", + "Correct": "c", + "Explanation": "length is halved . i . e . , length is decreased by 50 % breadth is tripled i . e . , breadth is increased by 200 % formula for change in area is : = ( - x + y - xy / 100 ) % = ( \u2212 50 + 200 \u2212 50 \u00d7 200 / 100 ) % = 50 % i . e . , area is increased by 50 % answer is c ." + }, + { + "Answer": 92, + "Options": "a ) 34 , b ) 92 , c ) 68 , d ) 88 , e ) none", + "Correct": "b", + "Explanation": "\"explanation we have : l = 20 ft and lb = 720 sq . ft . so , b = 36 ft . length of fencing = ( l + 2 b ) = ( 20 + 72 ) ft = 92 ft . answer b\"" + }, + { + "Answer": 63, + "Options": "a ) 63 , b ) 88 , c ) 112 , d ) 116 , e ) 120", + "Correct": "a", + "Explanation": "\"ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 9 + 9 = 18 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 18 * 7 = 63 a is the answer\"" + }, + { + "Answer": 19, + "Options": "['a ) 18 square meters', 'b ) 20 square meters', 'c ) 24 square meters', 'd ) 19 square meters', 'e ) 30 square meters']", + "Correct": "d", + "Explanation": "total = rug 1 + rug 2 + rug 3 - { overlap of exactly 2 rugs } - 2 * { overlap of exactly 3 rugs } 140 = 200 - 22 - 2 * { overlap of exactly 2 rugs } - - > { overlap of exactly 3 rugs } = 19 . answer : d ." + }, + { + "Answer": 136, + "Options": "a ) 136 cu cm , b ) 124 cu cm , c ) 164 cu cm , d ) 180 cu cm , e ) none", + "Correct": "a", + "Explanation": "\"sol . surface area = [ 2 ( 10 x 4 + 4 x 2 + 10 x 2 ) ] = ( 2 x 68 ) = 136 cu cm answer a\"" + }, + { + "Answer": 19.130000000000003, + "Options": "['a ) 17', 'b ) 19', 'c ) 21', 'd ) 23', 'e ) 25']", + "Correct": "b", + "Explanation": "area = l * w = ( l ) * ( l - 10 ) = 171 trial and error : 20 * 10 = 200 ( too high ) 19 * 9 = 171 the length is 19 meters . the answer is b ." + }, + { + "Answer": 41, + "Options": "['a ) 5 square meters', 'b ) 36 square meters', 'c ) 42 square meters', 'd ) 83.3 square meters', 'e ) 41 square meters']", + "Correct": "e", + "Explanation": "300 - 180 = 120 sq m of the wallpaper overlaps ( in either two layers or three layers ) if 36 sq m has two layers , 120 - 38 = 82 sq m of the wallpaper overlaps in three layers . 82 sq m makes two extra layers hence the area over which it makes two extra layers is 41 sq m . answer ( e ) ." + }, + { + "Answer": 18000, + "Options": "['a ) 18000', 'b ) 40000', 'c ) 31000', 'd ) 19000', 'e ) 16000']", + "Correct": "a", + "Explanation": "let breadth is x then length is 30 + x now the perimeter = 2 ( x + 30 + x ) = 540 solving this we get x = 120 now the area is 120 * 150 = 18000 answer : a" + }, + { + "Answer": 3495.2789939856775, + "Options": "['a ) a ) rs . 3944', 'b ) b ) rs . 3495.28', 'c ) c ) rs . 3988', 'd ) d ) rs . 3949', 'e ) e ) rs . 3923']", + "Correct": "b", + "Explanation": "let the side of the circular plot be a ft . pi * ( r ) ^ 2 = 289 = > r = 9.59 length of the fence = perimeter of the plot = 2 * pi * r = 60.26 ft . cost of building the fence = 60.26 * 58 = rs . 3495.28 answer : b" + }, + { + "Answer": 7, + "Options": "['a ) 2 \u221a 2', 'b ) 2 \u221a 5', 'c ) 5', 'd ) 7', 'e ) none of these']", + "Correct": "d", + "Explanation": "area of sector , a = x / 360 * pi * r ^ 2 circumference of the sector = 28 = > x / 360 * 2 * pi * r + 2 r = 28 = > 2 a / r + 2 r = 28 = > a = r 14 - r ^ 2 = r 14 - r ^ 2 we will now max using derivations max value of a will found at a = 0 i . e 14 - 2 r = 0 r = 7 d" + }, + { + "Answer": 5120, + "Options": "a ) 4120 m cube , b ) 4140 m cube , c ) 5140 m cube , d ) 5120 m cube , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : l = ( 48 - 16 ) m = 32 m , [ because 8 + 8 = 16 ] b = ( 36 - 16 ) m = 20 m , h = 8 m . volume of the box = ( 32 x 20 x 8 ) m cube = 5120 m cube . option d\"" + }, + { + "Answer": 4.04, + "Options": "['a ) 4.09', 'b ) 4.0', 'c ) 4.04', 'd ) 4.02', 'e ) 4.01']", + "Correct": "c", + "Explanation": "explanation : given error = 2 % while measuring the side of a square . if the correct value of the side of square is 100 , the measured value : = > 100 + 2 % * 100 = 100 + 2 = 102 the area of square with edge 100 = side * side = > 100 * 100 = > 10000 the area of square with side 102 = 102 * 102 = 10404 error in area calculation = 10404 - 1000 = 404 % error = ( 404 / 10000 ) * 100 = 4.04 % answer : c" + }, + { + "Answer": 1000, + "Options": "a ) 125 cm 3 , b ) 400 cm 3 , c ) 250 cm 3 , d ) 1000 cm 3 , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : edge of cude = 40 / 4 = 10 cm volume = a * a * a = 10 * 10 * 10 = 1000 cm cube option d\"" + }, + { + "Answer": 56.55751918948772, + "Options": "['a ) 45', 'b ) 51', 'c ) 57', 'd ) 63', 'e ) 69']", + "Correct": "c", + "Explanation": "the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 11 + 2 * 11 which is about 57 . the answer is c ." + }, + { + "Answer": 20, + "Options": "a ) 18 square inches , b ) 20 square inches , c ) 24 square inches , d ) 28 square inches , e ) 30 square inches", + "Correct": "b", + "Explanation": "\"total = a + b + c - ( sum of exactly 2 - group overlaps ) - 2 * ( all three ) + neither 80 % * 175 = 204 - 24 - 2 * ( all three ) + 0 2 * ( all three ) = 204 - 24 - 140 all three = 20 answer : b\"" + }, + { + "Answer": 6.000000000000001, + "Options": "a ) 4 , b ) 4 \u221a 2 , c ) 8 , d ) 6 , e ) can not be determined from the information provided", + "Correct": "d", + "Explanation": "\"ans d . . 6 . . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 9 or yz = 3 * \\ sqrt { 2 } . . therefore hyp = xy = 6\"" + }, + { + "Answer": 30, + "Options": "['a ) 15 m', 'b ) 22.5 m', 'c ) 25 m', 'd ) 30 m', 'e ) none of these']", + "Correct": "d", + "Explanation": "solution let breadth = x metres . then , length = ( x + 5 ) metres . then x ( x + 5 ) = 750 \u21d4 x 2 + 5 x \u2212 750 = 0 \u21d4 ( x + 30 ) ( x + 25 ) = 0 \u21d4 x = 25 . \u2234 length = ( x + 5 ) = 30 m . answer d" + }, + { + "Answer": 22, + "Options": "a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28", + "Correct": "b", + "Explanation": "\"let the original side of the square be x . ( x - 12 ) * ( x - 10 ) = 120 = 10 * 12 x = 22 the answer is b .\"" + }, + { + "Answer": 336, + "Options": "a ) 336 , b ) 384 , c ) 345 , d ) 244 , e ) 242", + "Correct": "a", + "Explanation": "\"area of a parallelogram = base * height = 14 * 24 = 336 cm 2 answer : option a\"" + }, + { + "Answer": 8, + "Options": "a ) 7 , b ) 10 , c ) 8 , d ) 12 , e ) 15", + "Correct": "c", + "Explanation": "think of a pringles can . if you took off the bottom and top and cut a slit down the length , it would flatten to a rectangle . the dimensions of the rectangle are the height of the can and the circumference of the circle . since you know both , one side and thehypothenuse use pythagoreans theorem or properties of 3 - 4 - 5 triangles to solve for the other side , 8 . correct answer c ." + }, + { + "Answer": 256, + "Options": "a ) 225 , b ) 777 , c ) 256 , d ) 288 , e ) 261", + "Correct": "c", + "Explanation": "\"16 * 16 = 256 sq m answer : c\"" + }, + { + "Answer": 21.000000000000018, + "Options": "a ) 21 % , b ) 30 % , c ) 25 % , d ) 40 % , e ) 50 %", + "Correct": "a", + "Explanation": "\"let original length = x meters original breadth = y meters original area = xy m ^ 2 new length = 110 x / 100 new breadth = 110 y / 100 = 11 y / 10 new area = 11 x / 10 * 11 y / 10 = 121 xy / 100 m ^ 2 increase percent = 21 xy / 100 * 1 / xy * 100 = 21 % answer is a\"" + }, + { + "Answer": 45, + "Options": "['a ) 33', 'b ) 45', 'c ) 66', 'd ) 77', 'e ) 21']", + "Correct": "b", + "Explanation": "r = 3 h = 5 \u03c0 * 3 * 3 * 5 = 45 \u03c0 cc answer : b" + }, + { + "Answer": 6, + "Options": "['a ) 4 cm ^ 2', 'b ) 6 cm ^ 2', 'c ) 5 cm ^ 2', 'd ) 7 cm ^ 2', 'e ) 8 cm ^ 2']", + "Correct": "b", + "Explanation": "the radius of the incircle in a equilateral triangle is a / 2 ( sqrt ) 3 where a = side of triangle = 6 cm so the diameter of the circle would be the diagonal of square so diagonal = 2 * a / 2 ( sqrt ) 3 = a / ( sqrt ) 3 so area of square = 1 / 2 * ( diagonal ) ^ 2 = 6 * 6 / 2 * 3 = 6 cm ^ 2 answer : b" + }, + { + "Answer": 12, + "Options": "['a ) 12 cm', 'b ) 10 cm', 'c ) 11 cm', 'd ) 15 cm', 'e ) 20 cm']", + "Correct": "a", + "Explanation": "area of square = 6 ^ 2 = 36 area of triangle = 36 1 / 2 bh = 36 h = 12 cm answer a" + }, + { + "Answer": 2002, + "Options": "a ) 3008 , b ) 2002 , c ) 1008 , d ) 2016 , e ) 3000", + "Correct": "b", + "Explanation": "\"note that trapezoids axy d and bxy c are congruent , so the area of axy d is always 4004 / 2 = 2002 . correct answer b\"" + }, + { + "Answer": 5, + "Options": "a ) 16 , b ) 5 , c ) 4 , d ) 2 , e ) 1", + "Correct": "b", + "Explanation": "\"x b \u00e9 radius of circle x \u00fd b \u00e9 radius of circle y given : pi * x ^ 2 = pi * \u00fd ^ 2 also , 2 * pi * x = 20 * pi x = 10 thus \u00fd = 10 y / 2 = 5 ans : b\"" + }, + { + "Answer": 8154, + "Options": "a ) 4000 , b ) 345 , c ) 5673 , d ) 6530 , e ) 8154", + "Correct": "e", + "Explanation": "\"area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 9 = rs . 8154 answer : option e\"" + }, + { + "Answer": 0.025, + "Options": "['a ) 2.5 ft', 'b ) 1 ft', 'c ) 0.5 ft', 'd ) 0.25 ft', 'e ) 0.025 ft']", + "Correct": "e", + "Explanation": "in order to fill up the tank , same volume is shifted from one tank to the other . pi r 1 ^ 2 h 1 = pi r 2 ^ 2 h 2 5 * 5 * 10 = 100 * 100 * h 2 h 2 = . 025 ft e is the answer" + }, + { + "Answer": 125, + "Options": "a ) 8 cc , b ) 9 cc , c ) 125 cc , d ) 4 cc , e ) 6 cc", + "Correct": "c", + "Explanation": "\"6 a 2 = 150 = 6 * 25 a = 5 = > a 3 = 125 cc answer : c\"" + }, + { + "Answer": 740, + "Options": "a ) 875 , b ) 740 , c ) 1425 , d ) 2025 , e ) 2500", + "Correct": "b", + "Explanation": "\"there ' s a direct formula for this . number of diagonals in a regular polygon = [ n * ( n - 3 ) ] / 2 , n = number of sides of the regular polygon . here , n = 40 . plugging it in , we get 740 diagonals ! answer ( b ) .\"" + }, + { + "Answer": 50, + "Options": "a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60", + "Correct": "c", + "Explanation": "\"the number of males is 160 - 90 = 70 . the number of males with advanced degrees is 70 - 40 = 30 . the number of females with advanced degrees is 80 - 30 = 50 . the answer is c .\"" + }, + { + "Answer": 216, + "Options": "a ) 216 a 2 , b ) 24 a 4 , c ) 24 a 1 , d ) 24 a 2 , e ) 24 a 7", + "Correct": "a", + "Explanation": "\"6 a 2 = 6 * 6 a * 6 a = 216 a 2 answer : a\"" + }, + { + "Answer": 42.85714285714287, + "Options": "a ) 42.8 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 35 %", + "Correct": "a", + "Explanation": "\"sol . required change = ( 30 * 100 ) / ( 100 - 30 ) = 42.8 % a\"" + }, + { + "Answer": 2, + "Options": "['a ) 1', 'b ) 2', 'c ) 3', 'd ) 4', 'e ) 5']", + "Correct": "b", + "Explanation": "find slopes first slope of l = ( a - 0 ) / ( 0 - ( - 2 ) ) = a / 2 slope of ll = ( 2 - 0 ) / ( 6 - 4 ) = 1 for l and ll to be parallel , their slopes must be equal a / 2 = 1 , a = 2 correct answer b" + }, + { + "Answer": 125, + "Options": "['a ) 125 cm 3', 'b ) 400 cm 3', 'c ) 1000 cm 3', 'd ) 8000 cm 3', 'e ) none']", + "Correct": "a", + "Explanation": "solution edge of the cube = ( 20 / 4 ) cm \u2039 = \u203a 5 cm . volume = ( 5 \u00d7 5 \u00d7 5 ) cm 3 \u2039 = \u203a 125 cm 3 . answer a" + }, + { + "Answer": 20, + "Options": "['a ) 20', 'b ) 27', 'c ) 26', 'd ) 188', 'e ) 11']", + "Correct": "a", + "Explanation": "explanation : let breadth = x meters . then , length = meters given that , = > x = 20 breadth = 20 answer : a ) 20 m" + }, + { + "Answer": 10, + "Options": "a ) 25 , b ) 23 , c ) 22 , d ) 20 , e ) 10", + "Correct": "e", + "Explanation": "\"area of carol ' s rectangle = 24 * 5 = 120 let width of jordan ' s rectangle = w since , the areas are equal 12 w = 120 = > w = 10 answer e\"" + }, + { + "Answer": 88, + "Options": "['a ) 80 feet', 'b ) 85 feet', 'c ) 83 feet', 'd ) 88 feet', 'e ) 90 feet']", + "Correct": "d", + "Explanation": "given that area of the field = 680 sq . feet = > lb = 680 sq . feet length ( l ) = 20 feet = > 20 \u00d7 b = 680 = > b = 680 / 20 = 34 feet required length of the fencing = l + 2 b = 20 + ( 2 \u00d7 34 ) = 88 feet answer is d ." + }, + { + "Answer": 300, + "Options": "a ) 300 % , b ) 400 % , c ) 500 % , d ) 200 % , e ) 600 %", + "Correct": "a", + "Explanation": "original area = a * b where a and b are sides after increase in side increase in area will be = ( ( ( 2 a * 2 b ) - ( a * b ) ) * 100 ) / ( a * b ) = 300 % answer : a" + }, + { + "Answer": 4.000000000000001, + "Options": "['a ) 3', 'b ) 4', 'c ) 5', 'd ) 6', 'e ) 7']", + "Correct": "b", + "Explanation": "there is a direct formula to calculate the are of a triangle based on coordinates of its vertices and one could use it to solve this problem . though if you make a diagram minimum simple calculations will be needed : answer : b ." + }, + { + "Answer": 2.8284271247461903, + "Options": "a ) 2.82 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "a", + "Explanation": "\"side of triangle is a then perimeter = a + a + a . sqrt 2 ( right angle and pythagorus ) = 2 a + a . sqrt 2 = 4 + 4 sqrt 2 or , a . ( 2 + sqrt 2 ) = 4 ( 1 + sqrt 2 ) a = 4 . ( 1 + sqrt 2 ) / 2 + sqrt 2 = 4 * 2.414 / 3.414 = then hypotenuse = 2.82 a\"" + }, + { + "Answer": 0.5454545454545454, + "Options": "['a ) 3 / 7', 'b ) 5 / 8', 'c ) 3 / 10', 'd ) 5 / 11', 'e ) 6 / 11']", + "Correct": "e", + "Explanation": "the longer wire will form a square with an area more than 4 if the wire is cut at a point within three meters of either end . the probability of this is 6 / 11 . the answer is e ." + }, + { + "Answer": 45, + "Options": "a ) 60 , b ) 45 , c ) 90 , d ) 180 , e ) 120", + "Correct": "b", + "Explanation": "let angle = x ; by question - - 180 - x = 3 ( 90 - x ) x = 45 answer : b" + }, + { + "Answer": 36, + "Options": "['a ) 18', 'b ) 6', 'c ) 27', 'd ) 48', 'e ) 36']", + "Correct": "e", + "Explanation": "volume of cube = lbh = 3 new cube l , b , h are increases of 3 l , 2 b , 2 h new volume of cube = 3 l * 2 b * 2 h = 12 lbh = 12 * 3 = 36 answer : e" + }, + { + "Answer": 9, + "Options": "['a ) 5', 'b ) 6', 'c ) 9', 'd ) 13', 'e ) 28']", + "Correct": "c", + "Explanation": "suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 126 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , number of tiles = ( r - 2 ) * ( c + 4 ) = 126 comparing both of them we get c * r = ( r - 2 ) * ( c + 4 ) = > 4 r - 2 c = 8 c = 2 r - 4 putting it in c * r = 126 ( 2 r - 4 ) * r = 126 2 r ^ 2 - 4 r - 126 = 0 r can not be negative so r = 9 and c = 14 so , answer will be c" + }, + { + "Answer": 24, + "Options": "a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 32", + "Correct": "a", + "Explanation": "\"a strip of 2 meters is covering the inner rectangular rug for all 4 sides . length of inner rug = 10 - ( 2 * 2 ) breadth of inner rug = 8 - ( 2 * 2 ) area of rug = 6 * 4 = 24 sq . mt \u00e2 nswer : a\"" + }, + { + "Answer": 7, + "Options": "a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 5", + "Correct": "c", + "Explanation": "\"2 x * x = 98 = > x = 7 answer : c\"" + }, + { + "Answer": 4800, + "Options": "a ) 4,800 , b ) 19,600 , c ) 20,000 , d ) 20,400 , e ) 20,800", + "Correct": "a", + "Explanation": "\"you can avoid a lot of work in this problem by recognizing that , with the info provided , the diagonal forms a triangle inside the rectangle with sides that have a 3 : 4 : 5 ratio . diagonal = 200 2 x + 2 y = 560 , or x + y = 280 a ^ 2 + b ^ 2 = c ^ 2 for each the sides of the triangle using the ratio 3 : 4 : 5 for sides , and knowing c = 100 , you can deduce the following a = 60 b = 80 60 x 80 = 4,800 a is the answer .\"" + }, + { + "Answer": 120, + "Options": "['a ) 127 cm ^ 2', 'b ) 125 cm ^ 2', 'c ) 120 cm ^ 2', 'd ) 102 cm ^ 2', 'e ) none of them']", + "Correct": "c", + "Explanation": "let length = x and breadth = y . then , 2 ( x + y ) = 46 or x + y = 23 and x ^ 2 + y ^ 2 = ( 17 ) ^ 2 = 289 . now , ( x + y ) ^ 2 = ( 23 ) ^ 2 < = > ( x ^ 2 + y ^ 2 ) + 2 xy = 529 < = > 289 + 2 xy = 529 = xy = 120 area = xy = 120 cm ^ 2 answer is c ." + }, + { + "Answer": 7, + "Options": "a ) 2.5 , b ) 5 , c ) 10 , d ) 7 , e ) 9", + "Correct": "d", + "Explanation": "\"longest chord of a circle is the diameter of the circle diameter = 2 * radius if diameter of the circle is given as 14 = 2 * 7 so radius of the circle = 7 correct answer - d\"" + }, + { + "Answer": 20, + "Options": "a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25", + "Correct": "d", + "Explanation": "\"l * w = 800 : area , l is the length and w is the width . 2 l + 2 w = 120 : perimeter l = 60 - w : solve for l ( 60 - w ) * w = 800 : substitute in the area equation w = 20 and l = 40 correct answer d\"" + }, + { + "Answer": 225, + "Options": "a ) 225 cm 2 , b ) 150 cm 2 , c ) 127 cm 2 , d ) 177 cm 2 , e ) 187 cm 2", + "Correct": "a", + "Explanation": "\"1 / 2 * 30 ( 9 + 6 ) = 225 cm 2 answer : a\"" + }, + { + "Answer": 16, + "Options": "['a ) no change', 'b ) 16 % increase', 'c ) 8 % decrease', 'd ) 16 % decrease', 'e ) none of thes']", + "Correct": "d", + "Explanation": "regd effect = \u2223 \u2223 40 \u2212 40 \u2212 40 \u00d7 40100 \u2223 \u2223 % = \u2212 16 % | 40 \u2212 40 \u2212 40 \u00d7 40100 | % = \u2212 16 % i . e . , the area will decrease by 16 % answer d" + }, + { + "Answer": 700, + "Options": "['a ) 868 sq . cm', 'b ) 600 sq . cm', 'c ) 700 sq . cm', 'd ) 900 sq . cm', 'e ) none of these']", + "Correct": "c", + "Explanation": "explanation : surface area = [ 2 ( 12 x 14 + 14 x 7 + 12 x 7 ) ] cm 2 = ( 2 x 350 ) cm 2 = 700 cm 2 . answer : c" + }, + { + "Answer": 5.5, + "Options": "['a ) 5.0', 'b ) 6.0', 'c ) 6.8', 'd ) 5.8', 'e ) 5.5']", + "Correct": "e", + "Explanation": "if we take a square with side length x and draw a diagonal , we get two isosceles right triangles . if we focus on one such right triangle , we see that the legs have length x . square 6 - inch flat - screen television the diagonal ( hypotenuse ) = 6 so , we can apply the pythagorean theorem to get x \u00b2 + x \u00b2 = 6 \u00b2 simplify : 2 x \u00b2 = 6 \u00b2 divide both sides by 2 to get : x \u00b2 = 6 \u00b2 / 2 since the area of the square = x \u00b2 , we can see that the area of this square is 6 \u00b2 / 2 square 5 - inch flat - screen television the diagonal ( hypotenuse ) = 5 so , we can apply the pythagorean theorem to get x \u00b2 + x \u00b2 = 5 \u00b2 simplify : 2 x \u00b2 = 5 \u00b2 divide both sides by 2 to get : x \u00b2 = 5 \u00b2 / 2 since the area of the square = x \u00b2 , we can see that the area of this square is 5 \u00b2 / 2 difference in areas = 6 \u00b2 / 2 - 5 \u00b2 / 2 = ( 6 \u00b2 - 5 \u00b2 ) / 2 = ( 36 - 25 ) / 2 = 11 / 2 = 5.5 e" + }, + { + "Answer": 120, + "Options": "a ) 120 , b ) 56 , c ) 68 , d ) 87 , e ) 92", + "Correct": "a", + "Explanation": "\"sol . monthly rent per square feet = 3600 / ( 18 * 20 ) = 10 & annual rent per square feet = 12 * 10 = 120 answer : a\"" + }, + { + "Answer": 4, + "Options": "['a ) 4 cm', 'b ) 8 cm', 'c ) 16 cm', 'd ) 24 cm', 'e ) none of the above']", + "Correct": "a", + "Explanation": "l x w x h = 64 l x w - 8 = h l = w solving the 3 equations we get area of base = 16 square cm and height = 8 cm , which means length = 4 cm and width = 4 cm correct answer : a" + }, + { + "Answer": 209, + "Options": "a ) 201 , b ) 159 , c ) 179 , d ) 189 , e ) 209", + "Correct": "e", + "Explanation": "\"if i calculate it using the formulae , # diagonals = n ( n - 3 ) / 2 each vertex sends of n - 3 diagonals n = 23 - 1 then 22 * ( 22 - 3 ) / 2 = 209 correct option : e\"" + }, + { + "Answer": 432, + "Options": "a ) 432 , b ) 288 , c ) 376 , d ) 397 , e ) 592", + "Correct": "a", + "Explanation": "\"2 ( 3 x + x ) = 96 l = 36 b = 12 lb = 36 * 12 = 432 answer : a\"" + }, + { + "Answer": 956.614963018092, + "Options": "['a ) 952 cm ^ 2', 'b ) 957 cm ^ 2', 'c ) 954 cm ^ 2', 'd ) 958 cm ^ 2', 'e ) none of them']", + "Correct": "b", + "Explanation": "volume = \u220f r 2 h = ( ( 22 / 7 ) x ( 7 / 2 ) x ( 7 / 2 ) x 40 ) = 1540 cm ^ 3 . . curved surface area = 2 \u220f rh = ( 2 x ( 22 / 7 ) x ( 7 / 2 ) x 40 ) = 880 cm ^ 2 . total surface area = 2 \u220f rh + 2 \u220f r 2 = 2 \u220f r ( h + r ) = ( 2 x ( 22 / 7 ) x ( 7 / 2 ) x ( 40 + 3.5 ) ) cm 2 = 957 cm ^ 2 answer is b" + }, + { + "Answer": 12, + "Options": "a ) 4 , b ) 6 , c ) 8 , d ) 12 , e ) 18", + "Correct": "d", + "Explanation": "we need to make 1152 x a perfect cube , hence we need to have the powers a multiple of 3 1152 = 2 ^ 7 * 3 ^ 2 the minimum value of x for which 1152 x is a perfect cube = 2 ^ 2 * 3 = 12 correct option : d" + }, + { + "Answer": 0.6666666666666666, + "Options": "['a ) 2 / 3', 'b ) 3 / 4', 'c ) 4 / 5', 'd ) 5 / 6', 'e ) 6 / 7']", + "Correct": "a", + "Explanation": "the longer wire will form a square with an area more than 1 if the wire is cut at a point within two meters of either end . the probability of this is 4 / 6 = 2 / 3 . the answer is a ." + }, + { + "Answer": 21.991148575128552, + "Options": "a ) 22.51 , b ) 22.0 , c ) 22.15 , d ) 22.17 , e ) 22.63", + "Correct": "b", + "Explanation": "\"let the side of the square be a cm . parameter of the rectangle = 2 ( 18 + 10 ) = 56 cm parameter of the square = 56 cm i . e . 4 a = 56 a = 14 diameter of the semicircle = 15 cm circimference of the semicircle = 1 / 2 ( \u00e2 \u02c6 \u008f ) ( 14 ) = 1 / 2 ( 22 / 7 ) ( 14 ) = 308 / 14 = 22 cm to two decimal places answer : b\"" + }, + { + "Answer": 16, + "Options": "a ) $ 1.60 , b ) $ 16.00 , c ) $ 96.00 , d ) $ 108.00 , e ) $ 196.00", + "Correct": "b", + "Explanation": "\"total surface area = 6 a ^ 2 = 6 * 10 * 10 = 600 each quart covers 20 sqr ft thus total number of quarts = 600 / 120 = 5 cost will be 5 * 3.2 = $ 16 ans : b\"" + }, + { + "Answer": 26.703537555513243, + "Options": "a ) 77.14 cm , b ) 47.14 cm , c ) 26.71 cm , d ) 94.94 cm , e ) 23.57 cm", + "Correct": "c", + "Explanation": "\"let the side of the square be a cm . parameter of the rectangle = 2 ( 20 + 14 ) = 68 cm parameter of the square = 68 cm i . e . 4 a = 68 a = 17 diameter of the semicircle = 17 cm circimference of the semicircle = 1 / 2 ( \u220f ) ( 17 ) = 1 / 2 ( 22 / 7 ) ( 17 ) = 374 / 14 = 26.71 cm to two decimal places answer : c\"" + }, + { + "Answer": 10, + "Options": "['a ) 8 m', 'b ) 10 m', 'c ) 12 m', 'd ) 15 m', 'e ) 17 m']", + "Correct": "b", + "Explanation": "let the length of the hall be x m breadth of the hall = 1 x / 2 m area of the hall = length * breadth 200 = x * 1 x / 2 x \u00b2 = 400 x = 20 difference between the length and breadth of the hall = x - 1 x / 2 = x / 2 = 20 / 2 = 10 m answer : b" + }, + { + "Answer": 51.54285714285714, + "Options": "a ) 49 m 2 , b ) 50 m 2 , c ) 51.5 m 2 , d ) 53 m 2 , e ) 59 m 2", + "Correct": "c", + "Explanation": "\"41 / 360 * 22 / 7 * 12 * 12 = 51.5 m 2 answer : c\"" + }, + { + "Answer": 3900, + "Options": "['a ) rs . 3919', 'b ) rs . 3910', 'c ) rs . 3997', 'd ) rs . 3900', 'e ) rs . 3902']", + "Correct": "d", + "Explanation": "area = ( l + b \u2013 d ) d ( 80 + 60 \u2013 10 ) 10 = > 1300 m 2 1300 * 3 = rs . 3900 answer : d" + }, + { + "Answer": 63.04958277186395, + "Options": "['a ) 68', 'b ) 54', 'c ) 63.04', 'd ) 62', 'e ) 60']", + "Correct": "c", + "Explanation": "area of triangle = \u00e2 \u02c6 \u0161 3 a 2 / 4 . = 1.732 * 25 / 4 = 10.825 m 2 . area of square = 2 * 2 = 4 m 2 . rest area after square = 10.825 - 4 = 6.825 m 2 . % rest area after square = 6.825 / 10.825 * 100 = 63.04 % answer c" + }, + { + "Answer": 18, + "Options": "['a ) 18', 'b ) 17', 'c ) 16', 'd ) 15', 'e ) 14']", + "Correct": "a", + "Explanation": "the total number of ways we can choose three dots is 6 c 3 = 20 . we can form two equilateral triangles from these six dots . there are 20 - 2 = 18 combinations which do not form an equilateral triangle . the answer is a ." + }, + { + "Answer": 0.049, + "Options": "a ) 0.07 , b ) 0.049 , c ) 0.7 , d ) 0.49 , e ) 4.9", + "Correct": "b", + "Explanation": "\"the volume of oil pumped to the tank = the volume of oil taken away from stationary cylinder . pi * 49 * 10 = pi * h * 100 * 100 ( h is distance that the oil level dropped ) h = 490 / 10,000 = 49 / 1000 = 0.049 ft the answer is b .\"" + }, + { + "Answer": 24, + "Options": "a ) 18 square inches , b ) 20 square inches , c ) 24 square inches , d ) 28 square inches , e ) 30 square inches", + "Correct": "c", + "Explanation": "\"total = a + b + c - ( sum of exactly 2 - group overlaps ) - 2 * ( all three ) + neither 80 % * 175 = 212 - 24 - 2 * ( all three ) + 0 2 * ( all three ) = 212 - 24 - 140 all three = 24 answer : c\"" + }, + { + "Answer": 3, + "Options": "['a ) 1', 'b ) 2', 'c ) 3', 'd ) 4', 'e ) 5']", + "Correct": "c", + "Explanation": "imo it should be c that is 3 reason : formed an equation . . . bat = b ball = c 2 b + 4 c = 200 1 b + 6 c = 220 solving both we get b that is bat = 40 and c that is ball = 30 new equation 210 to be divided in equal 3 b + 3 c = 210 3 * 40 + 3 * 30 = 210 120 + 90 = 210" + }, + { + "Answer": 216, + "Options": "a ) 200 , b ) 216 , c ) 345 , d ) 244 , e ) 242", + "Correct": "b", + "Explanation": "\"area of a parallelogram = base * height = 12 * 18 = 216 cm 2 answer : option b\"" + }, + { + "Answer": 32, + "Options": "a ) e = 16 , b ) e = 32 , c ) e = 64 , d ) 128 , e ) 512", + "Correct": "b", + "Explanation": "\"weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )\"" + }, + { + "Answer": 240, + "Options": "a ) 120 , b ) 772 , c ) 288 , d ) 266 , e ) 240", + "Correct": "e", + "Explanation": "\"the triangle with sides 26 cm , 24 cm and 20 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 24 * 20 = 240 cm 2 answer : e\"" + }, + { + "Answer": 5632, + "Options": "a ) 4830 , b ) 5632 , c ) 6420 , d ) 7500 , e ) 8960", + "Correct": "b", + "Explanation": "\"l = ( 48 - 16 ) m = 32 m , b = ( 38 - 16 ) m = 22 m , h = 8 m . volume of the box = ( 32 x 22 x 8 ) m 3 = 5632 m 3 . answer : option b\"" + }, + { + "Answer": 225, + "Options": "['a ) 225 sq m', 'b ) 186 sq m', 'c ) 586 sq m', 'd ) 287 sq m', 'e ) 296 sq m']", + "Correct": "a", + "Explanation": "15 * 15 = 225 sq m answer : a" + }, + { + "Answer": 115, + "Options": "a ) 144 , b ) 131 , c ) 115 , d ) 90 , e ) 45", + "Correct": "c", + "Explanation": "\"there are 10 business exec and in each handshake 2 business execs are involved . hence 10 c 2 = 45 also , each of 10 exec will shake hand with every 7 other chairmen for total of 70 handshake . total = 45 + 70 = 115 ans : c\"" + }, + { + "Answer": 157.07963267948966, + "Options": "a ) 250 , b ) 170 , c ) 148 , d ) 157 , e ) 150", + "Correct": "d", + "Explanation": "\"\u03c0 * 5 * 10 = 157 answer : d\"" + }, + { + "Answer": 360, + "Options": "a ) 290 cm 2 , b ) 360 cm 2 , c ) 270 cm 2 , d ) 280 cm 2 , e ) 260 cm 2", + "Correct": "b", + "Explanation": "\"area of a parallelogram = base * height = 30 * 12 = 360 cm 2 answer : b\"" + }, + { + "Answer": 90, + "Options": "a ) 70 , b ) 90 , c ) 60 , d ) 80 , e ) 292", + "Correct": "b", + "Explanation": "\"1 / 2 * 15 * 12 = 90 answer : b\"" + }, + { + "Answer": 3, + "Options": "['a ) 3 : 2', 'b ) 3 : 0', 'c ) 4 : 1', 'd ) 3 : 1', 'e ) 2 : 2']", + "Correct": "d", + "Explanation": "d = 3 d d = d a \u221a 2 = 3 d a \u221a 2 = d a = 3 d / \u221a 2 a = d / \u221a 2 = > 3 : 1 answer : d" + }, + { + "Answer": 240, + "Options": "a ) 189 cm 2 , b ) 150 cm 2 , c ) 240 cm 2 , d ) 177 cm 2 , e ) 187 cm 2", + "Correct": "c", + "Explanation": "\"1 / 2 * 30 ( 10 + 6 ) = 240 cm 2 answer : c\"" + }, + { + "Answer": 144, + "Options": "a ) 144 , b ) 772 , c ) 288 , d ) 266 , e ) 2848", + "Correct": "a", + "Explanation": "\"the triangle with sides 26 cm , 24 cm and 12 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 24 * 12 = 144 cm 2 answer : a\"" + }, + { + "Answer": 36, + "Options": "['a ) 27', 'b ) 36', 'c ) 42', 'd ) 64', 'e ) 147']", + "Correct": "b", + "Explanation": "112 ounces of a substance has a volume of 48 cubic inches 84 ounces of a substance has a volume of ( 48 / 112 ) * 84 = 36 cubic inches answer b" + }, + { + "Answer": 0.03, + "Options": "a ) 2.5 , b ) 0.025 , c ) 0.05 , d ) 0.03 , e ) 3", + "Correct": "d", + "Explanation": "\"the volume of oil pumped to the tank = the volume of oil taken away from stationary cylinder . pi * 25 * 12 = pi * h * 100 * 100 ( h is distance that the oil level dropped ) h = 300 / 10,000 = 3 / 100 = 0.03 ft the answer is d .\"" + }, + { + "Answer": 15, + "Options": "['a ) 10 feet', 'b ) 12 feet', 'c ) 13 feet', 'd ) 15 feet', 'e ) 18 feet']", + "Correct": "d", + "Explanation": "total circuit = 25 / 5 = 5 total feet squirrel travels = 5 * 3 = 15 feet answer : d" + }, + { + "Answer": 175.92918860102841, + "Options": "a ) 32 m 3 , b ) 36 m 3 , c ) 40 m 3 , d ) 44 m 3 , e ) 176 m 3", + "Correct": "e", + "Explanation": "\"solution volume = \u03c0 r 2 h \u2039 = \u203a ( 22 / 7 \u00d7 2 \u00d7 2 \u00d7 14 ) m 3 \u2039 = \u203a 176 m 3 . answer e\"" + }, + { + "Answer": 450, + "Options": "a ) 287 , b ) 269 , c ) 450 , d ) 200 , e ) 230", + "Correct": "c", + "Explanation": "\"d 2 / 2 = ( 30 * 30 ) / 2 = 450 answer : c\"" + }, + { + "Answer": 5120, + "Options": "a ) 2130 , b ) 3620 , c ) 4512 , d ) 5620 , e ) 5120", + "Correct": "e", + "Explanation": "\"clearly , l = ( 48 - 16 ) m = 32 m , b = ( 36 - 16 ) m = 20 m , h = 8 m . volume of the box = ( 32 x 20 x 8 ) m 3 = 5120 m ^ 3 . answer e\"" + }, + { + "Answer": 0.4375, + "Options": "['a ) 3 / 5', 'b ) 7 / 16', 'c ) 12 / 16', 'd ) 24 / 12', 'e ) 2 / 3']", + "Correct": "b", + "Explanation": "the questions asks us to find the surface which is not covered by the frame y i . e . , area of the surface not covered . where as circumference is the length along the edge of the circle , 2 * pi * r implies the length of the curve pi * r ^ 2 implies area enclosed by that curve . . hence area of the circle is considered for this problem area of the frame y = pi * r ^ 2 , where r = 6 = > pi * 36 area of the frame x = pi * 64 surface not covered by the frame y = pi * 64 - pi * 36 = pi * 28 fraction of frame x ' s surface is not covered by a frame y = pi * 28 / total area of the frame x = 28 / 64 = 7 / 16 answer is b" + }, + { + "Answer": 16, + "Options": "a ) 4 , b ) 16 , c ) 8 , d ) 8 \u221a 2 , e ) can not be determined from the information provided", + "Correct": "b", + "Explanation": "\"ans b . . 16 . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 64 or yz = 8 * \\ sqrt { 2 } . . therefore hyp = xy = 16\"" + }, + { + "Answer": 4913, + "Options": "['a ) 2334 cubic . cm', 'b ) 3356 cubic . cm', 'c ) 4913 cubic . cm', 'd ) 3478 cubic . cm', 'e ) none of these']", + "Correct": "c", + "Explanation": "explanation : let the edge of the cube bea . then , 6 a 2 = 1734 = > a = 17 cm . volume = a 3 = 173 = 4193 cm 3 answer : c" + }, + { + "Answer": 78, + "Options": "a ) 78 , b ) 40 , c ) 68 , d ) 88 , e ) none", + "Correct": "a", + "Explanation": "\"explanation we have : l = 30 ft and lb = 720 sq . ft . so , b = 24 ft . length of fencing = ( l + 2 b ) = ( 30 + 48 ) ft = 78 ft . answer a\"" + }, + { + "Answer": 10, + "Options": "a ) 28 , b ) 29 , c ) 10 , d ) 31 , e ) 32", + "Correct": "c", + "Explanation": "\"try filling the numbers into the answer y x y = find the closest to 100 . answer c\"" + }, + { + "Answer": 18, + "Options": "['a ) 9', 'b ) 18 \u2212 3 \u221a 3', 'c ) 18', 'd ) 18 + 3 \u221a 3', 'e ) 27']", + "Correct": "c", + "Explanation": "the altitude of an equilateral triangle is side * \u221a 3 / 2 . as perimeter of triangle acd is 9 + 3 \u221a 3 , ac + cd + ad = ( side + side / 2 + side * \u221a 3 / 2 ) = 9 + 3 \u221a 3 or side = 6 . perimeter of equilateral triangle , abc is 3 ( side ) or 18 . answer : ( optionc )" + }, + { + "Answer": 40, + "Options": "a ) 25 , b ) 43 , c ) 42 , d ) 40 , e ) 18", + "Correct": "d", + "Explanation": "\"area of carol ' s rectangle = 24 * 5 = 120 let width of jordan ' s rectangle = w since , the areas are equal 3 w = 120 = > w = 40 answer d\"" + }, + { + "Answer": 9, + "Options": "a ) 6 / \u03c0 , b ) 9 / \u03c0 , c ) 6 , d ) 9 , e ) 12", + "Correct": "d", + "Explanation": "\"given area of the base of a hemisphere is 3 = pi * r ^ 2 thus r = sqrt ( 3 / pi ) . surface area of whole sphere = 4 * pi * r ^ 2 . = 4 * pi * 3 / pi = 12 . since the hemisphere is half of a sphere the surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . but the total surface area = 6 + area of the base of a hemisphere . = 6 + 3 = 9 . answer is d ! !\"" + }, + { + "Answer": 25.132741228718345, + "Options": "['a ) 23.12', 'b ) 24.12', 'c ) 25.12', 'd ) 26.12', 'e ) 27.12']", + "Correct": "c", + "Explanation": "take r = 1 , h = 3 = 2 * 3.14 * r * r + 2 * 3.14 * r * h = 2 * 3.14 * r ( r + h ) = 2 * 3.14 * 1 ( 1 + 3 ) = 2 * 3.14 ( 4 ) = 25.12 answer : c" + }, + { + "Answer": 2, + "Options": "['a ) 1 : 1', 'b ) 1 : 2', 'c ) 2 : 3', 'd ) 2 : 1', 'e ) none of these']", + "Correct": "d", + "Explanation": "explanation : as far as questions of area or volume and surface area are concerned , it is all about formulas and very little logic . so its a sincere advice to get all formulas remembered before solving these questions . lets solve this , area of rectangle = l \u2217 b area of triangle = 1 / 2 l \u2217 b ratio = l \u2217 b : 1 / 2 l \u2217 b = 1 : 1 / 2 = 2 : 1 option d" + }, + { + "Answer": 200, + "Options": "['a ) 120 cm', 'b ) 200 cm', 'c ) 88 cm', 'd ) 666 cm', 'e ) 776 cm']", + "Correct": "b", + "Explanation": "area of each slab = 120 / 30 m 2 = 4 m 2 length of each slab \u221a 4 = 2 m = 200 cm b" + }, + { + "Answer": 6466.698709641254, + "Options": "a ) 2399 , b ) 3888 , c ) 2999 , d ) 5808 , e ) 6468", + "Correct": "e", + "Explanation": "\"explanation : area = ( 13.86 x 10000 ) sq . m = 138600 sq . m circumference = cost of fencing = rs . ( 1320 x 4.90 ) = rs . 6468 . answer : e ) 6468\"" + }, + { + "Answer": 3000, + "Options": "['a ) 3000 sq m', 'b ) 1878 sq m', 'c ) 2789 sq m', 'd ) 26811 sq m', 'e ) 29762 sq m']", + "Correct": "a", + "Explanation": "5 x + 12 x + 13 x = 300 = > x = 10 a = 50 , b = 120 , c = 130 s = ( 50 + 120 + 130 ) / 2 = 150 3000 sq m answer : a" + }, + { + "Answer": 16964.600329384884, + "Options": "a ) 900 , b ) 4000 , c ) 10000 , d ) 17000 , e ) 25000", + "Correct": "d", + "Explanation": "\"answer should be d . v = \\ pir ^ 2 h = \\ pi * 30 ^ 2 * 6 = approximately 17000\"" + }, + { + "Answer": 8, + "Options": "a ) 1 , b ) 2 , c ) 4 , d ) 8 , e ) 16", + "Correct": "d", + "Explanation": "\"as per the question - - width is negligible now , let l be the length of the fence = 2 pir l = 1 / 4 ( pir ^ 2 ) pir ^ 2 = 8 pir r = 8 answer : d\"" + }, + { + "Answer": 42, + "Options": "['a ) 42', 'b ) 45', 'c ) 47', 'd ) 49', 'e ) 56']", + "Correct": "a", + "Explanation": "number of cubes required = volume of box / volume of cube = 7 * 18 * 3 / 9 = 42 cubes answer : a" + }, + { + "Answer": 40401, + "Options": "a ) 44001 , b ) 44000 , c ) 40400 , d ) 40401 , e ) can not be determined", + "Correct": "d", + "Explanation": "\"explanatory answer the shape of the area used for growing cauliflower has remained a square in both the years . let the side of the square area used for growing cauliflower this year be x ft . therefore , the area of the ground used for cultivation this year = x 2 sq . ft . let the side of the square area used for growing cauliflower last year be y ft . therefore , the area of the ground used for cultivation last year = y 2 sq . ft . as the number of cauliflower grown has increased by 401 , the area would have increased by 401 sq ft because each cauliflower takes 1 sq ft space . hence , x 2 - y 2 = 401 ( x + y ) ( x - y ) = 401 . 401 is a prime number and hence it will have only two factors . i . e . , 401 and 1 . therefore , 401 can be expressed as product of 2 numbers in only way = 401 * 1 i . e . , ( x + y ) ( x - y ) = 401 * 1 so , ( x + y ) should be 401 and ( x - y ) should be 1 . solving the two equations we get x = 201 and y = 200 . therefore , number of cauliflower produced this year = x 2 = 2012 = 40401 alternative approach : use answer choices the area in both the years are squares of two numbers . that rules out choice a , b and c . as 44001,44000 and 40400 are not the square of any number . check choice d : if this year ' s produce is 40401 , last year ' s produce would have been 40401 - 401 = 40000 40000 is the square of 200 . so , 40401 is the answer . choice d .\"" + }, + { + "Answer": 90, + "Options": "['a ) 90', 'b ) 180', 'c ) 210', 'd ) 240', 'e ) 864']", + "Correct": "a", + "Explanation": "least number of cubes will be required when the cubes that could fit in are biggest . 3 is the biggest number that could divide all three , 27 , 15 and 6 . thus side of cube must be 3 , and total number of cubes = 27 / 3 * 15 / 3 * 6 / 3 = 90 ans a it is ." + }, + { + "Answer": 14, + "Options": "a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 13", + "Correct": "d", + "Explanation": "\"11 ^ 2 + 3 ^ 2 = 130 - - > 11 + 3 = 14 . d\"" + }, + { + "Answer": 7.5, + "Options": "a ) 7.6 , b ) 7.3 , c ) 7.2 , d ) 7.5 , e ) 8.0", + "Correct": "d", + "Explanation": "\"if we take a square with side length x and draw a diagonal , we get two isosceles right triangles . if we focus on one such right triangle , we see that the legs have length x . square 8 - inch flat - screen television the diagonal ( hypotenuse ) = 8 so , we can apply the pythagorean theorem to get x \u00b2 + x \u00b2 = 8 \u00b2 simplify : 2 x \u00b2 = 8 \u00b2 divide both sides by 2 to get : x \u00b2 = 8 \u00b2 / 2 since the area of the square = x \u00b2 , we can see that the area of this square is 8 \u00b2 / 2 square 7 - inch flat - screen television the diagonal ( hypotenuse ) = 7 so , we can apply the pythagorean theorem to get x \u00b2 + x \u00b2 = 7 \u00b2 simplify : 2 x \u00b2 = 7 \u00b2 divide both sides by 2 to get : x \u00b2 = 7 \u00b2 / 2 since the area of the square = x \u00b2 , we can see that the area of this square is 7 \u00b2 / 2 difference in areas = 8 \u00b2 / 2 - 7 \u00b2 / 2 = ( 8 \u00b2 - 7 \u00b2 ) / 2 = ( 64 - 49 ) / 2 = 15 / 2 = 7.5 d\"" + }, + { + "Answer": 21.00000000000002, + "Options": "['a ) 21 %', 'b ) 31 %', 'c ) 41 %', 'd ) 51 %', 'e ) none of these']", + "Correct": "a", + "Explanation": "since 4 x pi x radius x radius = surface area . therefore , net % change in area = ( x + y + xy / 100 ) % = [ 10 + 10 + ( 10 x 10 ) / 100 ] % or 21 % . answer : a" + }, + { + "Answer": 392, + "Options": "a ) 288 , b ) 289 , c ) 200 , d ) 112 , e ) 392", + "Correct": "e", + "Explanation": "\"d 2 / 2 = ( 28 * 28 ) / 2 = 392 answer : e\"" + }, + { + "Answer": 20, + "Options": "a ) 33 , b ) 45 , c ) 20 , d ) 77 , e ) 21", + "Correct": "c", + "Explanation": "\"r = 2 h = 5 \u03c0 * 2 * 2 * 5 = 20 \u03c0 cc answer : c\"" + }, + { + "Answer": 50, + "Options": "a ) 40 % , b ) 45 % , c ) 50 % , d ) 65 % , e ) 70 %", + "Correct": "c", + "Explanation": "\"let original length = x and original breadth = y . original area = xy . new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c\"" + }, + { + "Answer": 9900, + "Options": "a ) 110 , b ) 1100 , c ) 9900 , d ) 10000 , e ) 12100", + "Correct": "c", + "Explanation": "total values for x = 10 ; y = 11 x 1 , y 1 = 10 * 11 . . . . . . . . . . . . . . . . . . . . . . . coordinates of 1 st pnt x 2 , y 2 = 9 * 1 ( y 2 = y 1 ) . . . . . . . . . . . . . . . coordinates of 2 nd pnt y coordinates will be same as that of 1 st pnt bcoz it is parallel to x axis x 3 , y 3 = 1 * 10 ( x 2 = x 3 ) . . . . . . . . . . coordinates of 3 rd pt . x coordinates will be same as that of 2 nd point bcoz to make a right angle it has to be parallel to y axis tot ways = 10 * 11 * 9 * 1 * 1 * 10 = 9900 ans : c" + }, + { + "Answer": 4, + "Options": "a ) 15 , b ) 26 , c ) 28 , d ) 4 , e ) none of these", + "Correct": "d", + "Explanation": "\"let the number be x . then , x + x 2 = 20 ( x + 5 ) ( x - 4 ) = 0 x = 4 answer : d\"" + }, + { + "Answer": 64, + "Options": "a ) 34 , b ) 40 , c ) 64 , d ) 88 , e ) 92", + "Correct": "c", + "Explanation": "\"given that length and area , so we can find the breadth . length x breadth = area 20 x breadth = 440 breadth = 22 feet area to be fenced = 2 b + l = 2 ( 22 ) + 20 = 64 feet answer : c\"" + }, + { + "Answer": 240, + "Options": "a ) 240 , b ) 250 , c ) 260 , d ) 270 , e ) 280", + "Correct": "a", + "Explanation": "\"given that the area of the square = 3600 sq . units = > side of square = \u221a 3600 = 60 units the radius of the circle = side of the square = 60 units length of the rectangle = 2 / 5 * 60 = 24 units given that breadth = 10 units area of the rectangle = lb = 24 * 10 = 240 sq . units answer : option a\"" + }, + { + "Answer": 65, + "Options": "a ) 65 , b ) 80 , c ) 85 , d ) 90 , e ) 95", + "Correct": "a", + "Explanation": "\"in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 \u00b0 ) . given : x + ( x + 50 ) = 180 - - > x = 65 . answer : a .\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16", + "Correct": "a", + "Explanation": "\"total circuit = 16 / 4 = 4 total feet squirrel travels = 4 * 3 = 12 feet answer : a\"" + }, + { + "Answer": 126, + "Options": "['a ) 126 sq . ft', 'b ) 64 sq . ft', 'c ) 100 sq . ft', 'd ) 120 sq . ft', 'e ) 140 sq . ft']", + "Correct": "a", + "Explanation": "explanation : solution 1 length = 9 feet breadth = 37 \u2212 9 / 2 = 14 feet area = 9 \u00d7 14 = 126 square feet answer : option a" + }, + { + "Answer": 36, + "Options": "['a ) 20 cm', 'b ) 28 cm', 'c ) 36 cm', 'd ) 48 cm', 'e ) 40 cm']", + "Correct": "c", + "Explanation": "side of the 1 st square = 60 / 4 = 15 cm side of the 2 nd square = 48 / 4 = 12 cm area of the 3 rd square = 15 ^ 2 - 12 ^ 2 = 81 cm ^ 2 side of the 3 rd square = 9 cm required perimeter = 9 * 4 = 36 cm answer is c" + }, + { + "Answer": 24, + "Options": "a ) 23 a 2 cm 2 , b ) 84 a 2 cm 2 , c ) 64 a 2 cm 2 , d ) 24 a 2 cm 2 , e ) 14 a 2 cm 2", + "Correct": "d", + "Explanation": "\"6 a 2 = 6 * 2 a * 2 a = 24 a 2 answer : d\"" + }, + { + "Answer": 60, + "Options": "a ) 87 cm 2 , b ) 28 cm 2 , c ) 98 cm 2 , d ) 26 cm 2 , e ) 60 cm 2", + "Correct": "e", + "Explanation": "\"area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 48 / 2 = 60 cm 2 answer : e\"" + }, + { + "Answer": 628.3185307179587, + "Options": "a ) 330 , b ) 159 , c ) 150 , d ) 200 , e ) 628", + "Correct": "e", + "Explanation": "\"\u03c0 * 10 * 20 = 628 answer : e\"" + }, + { + "Answer": 3024, + "Options": "a ) 63 , b ) 336 , c ) 567 , d ) 3024 , e ) 5040", + "Correct": "d", + "Explanation": "all the cordinates are integer hence , possible ae values are { - 10 } , { - 11 } . . . . { - 17 } : 8 ways . . . . { 7 , - 1 } , { 70 } . . . . . . { 76 } : 8 ways 9 * 8 ways = 72 for ac values can be { 12 } , { 13 } . . . . { 17 } : 6 ways . . . . . . { 71 } , { 72 } . . . . . { 76 } : 6 ways 7 * 6 = 42 total = 72 * 42 = 3024 hence d" + }, + { + "Answer": 485.99999999999983, + "Options": "['a ) 486', 'b ) 255', 'c ) 2866', 'd ) 265', 'e ) 872']", + "Correct": "a", + "Explanation": "explanation : \\ inline \\ fn _ jvn a ^ 3 = 729 ; a = 9 surface area = ( 6 x 9 x 9 ) = 486 \\ inline \\ fn _ jvn cm ^ 2 answer : a ) 486 sq . cm" + }, + { + "Answer": 4, + "Options": "['a ) area', 'b ) circumference', 'c ) 4', 'd ) 2 \u03c0', 'e ) none of these']", + "Correct": "c", + "Explanation": "according to question , circumference of circle = area of circle or \u03c0 d = \u03c0 ( d \u2044 2 ) 2 [ where d = diameter ] \u2234 d = 4 answer c" + }, + { + "Answer": 113.09733552923255, + "Options": "['a ) 113 cm \u00b2', 'b ) 144 cm \u00b2', 'c ) 154 cm \u00b2', 'd ) 184 cm \u00b2', 'e ) 194 cm \u00b2']", + "Correct": "a", + "Explanation": "area of circle = \u03c0 r \u00b2 = 22 / 7 \u00d7 6 \u00d7 6 cm \u00b2 = 113 cm \u00b2 answer : a" + }, + { + "Answer": 120, + "Options": "a ) 100 , b ) 110 , c ) 120 , d ) 130 , e ) 140", + "Correct": "c", + "Explanation": "\"other side = ( ( 17 ) 2 - ( 15 ) 2 ) ( 1 / 2 ) = ( 289 - 225 ) ( 1 / 2 ) = ( 64 ) ( 1 / 2 ) = 8 m . area = ( 15 x 8 ) m 2 = 120 m 2 . option c\"" + }, + { + "Answer": 38.5, + "Options": "['a ) 76', 'b ) 65', 'c ) 59.5', 'd ) 49', 'e ) 38.5']", + "Correct": "e", + "Explanation": "area covered by picture = ( 8.5 - 3 ) * ( 10 - 3 ) = 5.5 * 7 = 38.5 answer e" + }, + { + "Answer": 18, + "Options": "['a ) 18', 'b ) 20', 'c ) 24', 'd ) 26', 'e ) 40']", + "Correct": "a", + "Explanation": "let the original side of the square be x . ( x - 8 ) * ( x - 6 ) = 120 = 10 * 12 x = 18 the answer is a ." + }, + { + "Answer": 38, + "Options": "a ) 2 , b ) 4 , c ) 16 , d ) 38 , e ) 40", + "Correct": "d", + "Explanation": "\"pythogoras will help here ! let the sides be x and diagonal be d then d ^ 2 = 2 x ^ 2 and area = x ^ 2 now plug in the given diagonal values to find x values and then subtract the areas ans will be 20 ^ 2 / 2 - 18 ^ 2 / 2 = 76 / 2 = 38 ans d .\"" + }, + { + "Answer": 1920, + "Options": "['a ) 1,408 square inches', 'b ) 1,920 square inches', 'c ) 1,936 square inches', 'd ) 2,304 square inches', 'e ) none of these']", + "Correct": "b", + "Explanation": "explanation : we have : ( l - b ) = 8 and 2 ( l + b ) = 176 or ( l + b ) = 88 . solving the two equations , we get : l = 48 and b = 40 . area = ( l x b ) = ( 48 x 40 ) in 2 = 1920 in 2 . correct answer : b" + }, + { + "Answer": 23.999999999999996, + "Options": "['a ) 24 sq units', 'b ) 48 sq units', 'c ) 24 under root 3', 'd ) 48 under root 3', 'e ) such a triangle does not exist']", + "Correct": "a", + "Explanation": "explanatory answer if two sides of a triangle and the included angle ' y ' is known , then the area of the triangle = 1 / 2 * ( product of sides ) * sin y substituting the values in the formula , we get 1 / 2 * 8 * 12 * sin 150 o = 1 / 2 * 8 * 12 * 1 / 2 . note : sin 150 o = 1 / 2 area = 24 sq units . choice a" + }, + { + "Answer": 0.5860000000000001, + "Options": "['a ) 0.586', 'b ) 0.687', 'c ) 0.784', 'd ) 0.874', 'e ) 0.974']", + "Correct": "a", + "Explanation": "if r be radius of smaller circle then distance b / n centres = \u221a 2 * r so , r + r \u221a 2 = r here , r = 1.414 = \u221a 2 = > r = ( \u221a 2 - 1 ) r r = 0 . 586 unit answer : a" + }, + { + "Answer": 140, + "Options": "['a ) 140', 'b ) 388', 'c ) 238', 'd ) 119', 'e ) 112']", + "Correct": "a", + "Explanation": "when folded along the breadth we have 2 ( l / 2 + b ) = 34 or l + 2 b = 34 . . . . . . . . . . . ( 1 ) when folded along the length , we have 2 ( l + b / 2 ) = 38 or 2 l + b = 38 . . . . . ( 2 ) from 1 & 2 we get l = 14 and b = 10 area of the paper = 14 * 10 = 140 sq cmv answer : a" + }, + { + "Answer": 69.00000000000001, + "Options": "['a ) 70 %', 'b ) 69 %', 'c ) 80 %', 'd ) 82 %', 'e ) 55 %']", + "Correct": "b", + "Explanation": "the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 30 % increase a surface = 6 * ( ( 1.3 a ) ^ 2 ) = 6 * 1.69 * a ^ 2 the increase in the surface area = ( 6 * 1.69 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 1.69 - 1 ) ) / ( 6 * a ^ 2 ) = 1.69 - 1 = 0.69 = 69 % answer : b" + }, + { + "Answer": 367.5663404700058, + "Options": "a ) 367 , b ) 378 , c ) 365 , d ) 26 , e ) 28", + "Correct": "a", + "Explanation": "\"\u03c0 * 13 * 9 = 367 answer : a\"" + }, + { + "Answer": 36, + "Options": "['a ) 50 %', 'b ) 46 %', 'c ) 36 %', 'd ) 26 %', 'e ) 38 %']", + "Correct": "c", + "Explanation": "let diameter of circle r , dr = 60 and diameter of circle s , ds = 100 radius of circle r , rr = 30 radius of circle s , rs = 50 area of circle r / area of circle s = ( pi * rr ^ 2 ) / ( pi * rs ^ 2 ) = ( 30 / 50 ) ^ 2 = ( 6 / 10 ) ^ 2 = 36 % answer : c" + }, + { + "Answer": 3, + "Options": "['a ) 2', 'b ) 4', 'c ) 1', 'd ) 5', 'e ) 3']", + "Correct": "e", + "Explanation": "4 / 3 \u03c0 r ( power 3 ) = 4 \u03c0 r ( power 2 ) r = 3 answer is e ." + }, + { + "Answer": 300, + "Options": "['a ) 300 square meters', 'b ) 400 square meters', 'c ) 500 square meters', 'd ) 600 square meters', 'e ) 700 square meters']", + "Correct": "a", + "Explanation": "if l and w be the original length and width of the rectangle and its area is given by l ? w after increase the length becomes 2 l and the width becomes 3 w . the area is then given by ( 2 l ) ? ( 3 w ) and is known . hence ( 2 l ) ? ( 3 w ) = 1800 solve the above equation to find l ? w 6 l ? w = 1800 l ? w = 1800 / 6 = 300 square meters , area of original rectangle correct answer a" + }, + { + "Answer": 20, + "Options": "a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21", + "Correct": "d", + "Explanation": "\"area of first rectangle is 12 * 15 = 180 hence area of second would be 9 x = 180 x x = 20 answer is d\"" + }, + { + "Answer": 164, + "Options": "['a ) 154 cm square', 'b ) 156 cm square', 'c ) 160 cm square', 'd ) 164 cm square', 'e ) none of these']", + "Correct": "d", + "Explanation": "explanation : surface area of a cuboid = 2 ( lb + bh + hl ) cm square so , surface area of a brick = 2 ( 10 * 4 + 4 * 3 + 3 * 10 ) cm square = 2 ( 82 ) cm square = 164 cm square option d" + }, + { + "Answer": 84, + "Options": "['a ) 80', 'b ) 82', 'c ) 84', 'd ) 86', 'e ) 88']", + "Correct": "c", + "Explanation": "let a = 13 cm , b = 14 cm . and c = 15 cm . s = 1 / 2 ( 13 + 14 + 15 ) = 21 , ( s - a ) = 8 , ( s - b ) = 7 and ( s - c ) = 6 area = \u221a 21 * 8 * 7 * 6 = 84 sq . cm answer c" + }, + { + "Answer": 3.3333333333333335, + "Options": "['a ) 6 cm', 'b ) 8.25 cm', 'c ) 11.25 cm', 'd ) 15.12 cm', 'e ) 3.33 cm']", + "Correct": "e", + "Explanation": "increase in volume = volume of the cube = 10 * 10 * 10 cm ^ 3 rise in water level = volume / area = 10 * 10 * 10 / 20 * 15 = 3.33 cm answer is e" + }, + { + "Answer": 42, + "Options": "a ) 2 , b ) 4 , c ) 16 , d ) 42 , e ) 40", + "Correct": "d", + "Explanation": "\"pythogoras will help here ! let the sides be x and diagonal be d then d ^ 2 = 2 x ^ 2 and area = x ^ 2 now plug in the given diagonal values to find x values and then subtract the areas ans will be 22 ^ 2 / 2 - 20 ^ 2 / 2 = 84 / 2 = 42 ans d .\"" + }, + { + "Answer": 4313.735577562732, + "Options": "a ) 3312 , b ) 2888 , c ) 4312 , d ) 2881 , e ) 1221", + "Correct": "c", + "Explanation": "\"let the radii of the smaller and the larger circles be s m and l m respectively . 2 \u220f s = 264 and 2 \u220f l = 352 s = 264 / 2 \u220f and l = 352 / 2 \u220f difference between the areas = \u220f l 2 - \u220f s 2 = \u220f { 1762 / \u220f 2 - 1322 / \u220f 2 } = 1762 / \u220f - 1322 / \u220f = ( 176 - 132 ) ( 176 + 132 ) / \u220f = ( 44 ) ( 308 ) / ( 22 / 7 ) = ( 2 ) ( 308 ) ( 7 ) = 4312 sq m answer : c\"" + }, + { + "Answer": 0.7, + "Options": "a ) 3.5 % , b ) 2.4 % , c ) 3 % , d ) 5 % , e ) 0.7 %", + "Correct": "e", + "Explanation": "\"say both sides of the rectangle are equal to 100 ( so consider that we have a square ) . in this case the area is 100 * 100 = 10,000 . now , the area obtained with wrong measurements would be 106 * 95 = 10,070 , which is 0.7 % greater than the actual area . answer : e .\"" + }, + { + "Answer": 14, + "Options": "a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 14", + "Correct": "e", + "Explanation": "solution : this problem is testing us on the rule that when we express a perfect square by its unique prime factors , every prime factor ' s exponent is an even number . let \u2019 s start by prime factorizing 3150 . 3150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2 3150 = 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 ( notice that the exponents of both 2 and 7 are not even numbers . this tells us that 3150 itself is not a perfect square . ) we also are given that 3150 multiplied by a is the square of an integer . we can write this as : 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 x a = square of an integer according to our rule , we need all unique prime factors ' exponents to be even numbers . thus , we need one more 2 and one more 7 . therefore , a = 7 x 2 = 14 answer is e ." + }, + { + "Answer": 15, + "Options": "['a ) 12 cm', 'b ) 15 cm', 'c ) 18 cm', 'd ) 21 cm', 'e ) 24 cm']", + "Correct": "b", + "Explanation": "2 l + 2 w = 5 w l = 3 w / 2 w * l = 150 3 w ^ 2 / 2 = 150 w ^ 2 = 100 w = 10 l = 3 ( 10 ) / 2 = 15 the answer is b ." + }, + { + "Answer": 2.4, + "Options": "a ) 3.6 cm , b ) 2.4 cm , c ) 4.8 cm , d ) 2.16 cm , e ) 3.2 cm", + "Correct": "b", + "Explanation": "\"look at the diagram below : now , in case when qy is perpendicular to pr , two right triangles pqr and pqy are similar : qy : qp = qr : pr - - > qy : 3 = 8 : 10 - - > qy = 2.4 . answer : b .\"" + }, + { + "Answer": 45.25714285714286, + "Options": "a ) 52.6 , b ) 45.3 , c ) 52.8 , d ) 52.1 , e ) 52.2", + "Correct": "b", + "Explanation": "\"36 / 360 * 22 / 7 * 12 * 12 = 45.3 m 2 answer : b\"" + }, + { + "Answer": 2030, + "Options": "a ) 2510 , b ) 2535 , c ) 2530 , d ) 2030 , e ) 2520", + "Correct": "d", + "Explanation": "\"length = breadth + 23 . therefore , 4 \u00d7 breadth + 2 \u00d7 23 = 186 m \u21d2 breadth = 35 m length = 35 + 23 = 58 m area = 58 \u00d7 35 = 2030 m 2 answer is d .\"" + }, + { + "Answer": 76800, + "Options": "a ) 76,800 , b ) 19,600 , c ) 20,000 , d ) 20,400 , e ) 20,800", + "Correct": "a", + "Explanation": "\"you can avoid a lot of work in this problem by recognizing that , with the info provided , the diagonal forms a triangle inside the rectangle with sides that have a 3 : 4 : 5 ratio . diagonal = 200 2 x + 2 y = 560 , or x + y = 280 a ^ 2 + b ^ 2 = c ^ 2 for each the sides of the triangle using the ratio 3 : 4 : 5 for sides , and knowing c = 400 , you can deduce the following a = 240 b = 320 240 x 320 = 76,800 a is the answer .\"" + }, + { + "Answer": 7, + "Options": "['a ) 9 cm', 'b ) 8 cm', 'c ) 7 cm', 'd ) 6 cm', 'e ) 5 cm']", + "Correct": "c", + "Explanation": "explanation : let the lengths of the line segments be x and x + 2 cm then , ( x + 2 ) 2 \u2212 x 2 = 32 x 2 + 4 x + 4 \u2212 x 2 = 324 x = 28 x = 7 cm option c" + }, + { + "Answer": 146, + "Options": "a ) 144 ft , b ) 88 ft , c ) 22 ft , d ) 112 ft , e ) 146 t", + "Correct": "e", + "Explanation": "\"given that length and area , so we can find the breadth . length x breadth = area 10 x breadth = 680 breadth = 68 feet area to be fenced = 2 b + l = 2 ( 68 ) + 20 = 146 feet answer : e ) 146 ft\"" + }, + { + "Answer": 88, + "Options": "a ) 88 feet , b ) 86 feet , c ) 84 feet , d ) 82 feet , e ) 83 feet", + "Correct": "a", + "Explanation": "\"explanation : we are given with length and area , so we can find the breadth . as length * breadth = area = > 20 * breadth = 680 = > breadth = 34 feet area to be fenced = 2 b + l = 2 * 34 + 20 = 88 feet answer : option a\"" + }, + { + "Answer": 127.5, + "Options": "a ) 277 , b ) 127.5 , c ) 150 , d ) 288 , e ) 212", + "Correct": "b", + "Explanation": "\"1 / 2 * 15 * 17 = 127.5 answer : b\"" + }, + { + "Answer": 150, + "Options": "a ) 150 , b ) 131 , c ) 115 , d ) 90 , e ) 45", + "Correct": "a", + "Explanation": "\"there are 12 business exec and in each handshake 2 business execs are involved . hence 12 c 2 = 66 also , each of 12 exec will shake hand with every 7 other chairmen for total of 84 handshake . total = 66 + 84 = 150 ans : a\"" + }, + { + "Answer": 80, + "Options": "a ) 50 , b ) 60 , c ) 11 , d ) 80 , e ) 90", + "Correct": "d", + "Explanation": "\"let l be the length and w be the width . l = ( 7 / 5 ) w perimeter : 2 l + 2 w = 384 , 2 ( 7 / 5 ) w + 2 w = 384 solve the above equation to find : w = 80 m and l = 112 m . correct answer d ) 80\"" + }, + { + "Answer": 100, + "Options": "a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 100", + "Correct": "e", + "Explanation": "\"alternate approach backsolving ( using answer options to reach the correct answer ) can work wonders here if one is fast in calculations . given perimeter is 300 so , 2 ( l + b ) = 300 or , l + b = 150 now use the answer options ( given length ; breath will be half the length ) ( a ) 40 l = 40 ; b = 20 l + b = 60 ( b ) 50 l = 50 ; b = 25 l + b = 75 ( c ) 60 l = 60 ; b = 30 l + b = 90 ( d ) 70 l = 70 ; b = 35 l + b = 105 ( e ) 100 l = 100 ; b = 50 l + b = 150 thus you see no , need of any calculations , u can reach the correct option only by checking options ; correct answer will be ( e )\"" + }, + { + "Answer": 21.000000000000018, + "Options": "['a ) 26 %', 'b ) 21 %', 'c ) 15 %', 'd ) 18 %', 'e ) 12 %']", + "Correct": "b", + "Explanation": "a = 1 / 2 x b x h or 1 / 2 x 2 a x a ( for simplification ) new h = 220 a / 100 = 22 a / 10 new b = ( 110 a x 100 ) = = 11 a / 10 new area = 1 / 2 ( 22 a x 11 a ) / ( 10 x 10 ) = ( 121 a \u00b2 / 100 ) increased area = = ( 121 a \u00b2 / 100 ) - a \u00b2 increase % = [ ( 21 a \u00b2 / 100 ) x ( 1 / a \u00b2 ) x 100 ] % = 21 % answer : b" + }, + { + "Answer": 130, + "Options": "a ) 130 cm , b ) 767 cm , c ) 88 cm , d ) 666 cm , e ) 776 cm", + "Correct": "a", + "Explanation": "\"area of each slab = 50.7 / 30 m 2 = 1.69 m 2 length of each slab \u221a 1.69 = 1.3 m = 130 cm\"" + }, + { + "Answer": 80, + "Options": "a ) 53 , b ) 66 , c ) 60 , d ) 85 , e ) 80", + "Correct": "e", + "Explanation": "\"yes , ensure that you understand the relation thoroughly ! cost per liter = k * fraction of spirit 80 cents is the cost of 2 liters of solution ( 1 part water , 1 part spirit ) . so cost per liter is 40 cents . fraction of spirit is 1 / 2 . 40 = k * ( 1 / 2 ) k = 80 cost per liter = 80 * ( 1 / 3 ) ( 1 part spirit , 2 parts water ) cost for 3 liters = 80 * ( 1 / 3 ) * 3 = 80 cents e . 80 cents\"" + }, + { + "Answer": 60.00000000000001, + "Options": "['a ) 42.5 m', 'b ) 60 m', 'c ) 4800 m', 'd ) data inadequate', 'e ) none of these']", + "Correct": "b", + "Explanation": "a 2 = 45 \u00d7 40 = 1800 \u2234 a = \u221a 1800 = 30 \u221a 2 \u2234 diagonal of the square = \u221a 2 a = \u221a 2 \u00d7 30 \u221a 2 = 30 \u00d7 2 = 60 m answer b" + }, + { + "Answer": 12, + "Options": "a ) 4 , b ) 8 , c ) 12 , d ) 15 , e ) 20", + "Correct": "c", + "Explanation": "\"i understand this might not be required but i used the equation of a circle . since the origin is at 0 , x ^ 2 + y ^ 2 = 5 ^ 2 . x , y could be + / - ( 0,5 or 5,0 ) - 4 possibilities . x , y could be + / - ( 3,4 or 4,3 ) - 8 possibilities . ans : w = c\"" + }, + { + "Answer": 7737.769850454057, + "Options": "a ) 7744 , b ) 8844 , c ) 5544 , d ) 4444 , e ) 3444", + "Correct": "a", + "Explanation": "\"length of wire = 2 pier = 2 * ( 22 / 7 ) * 56 = 352 cm side of the square = 352 / 4 = 88 cm area of the square = 88 * 88 = 7744 sq cm answer : a\"" + }, + { + "Answer": 80, + "Options": "a ) 73 , b ) 32 , c ) 34 , d ) 43 , e ) 80", + "Correct": "e", + "Explanation": "\"explanation : a / 50 = 8 * 8 = > a = 8 * 8 * 50 x * 2 x = 8 * 8 * 50 x = 40 = > 2 x = 80 answer : option e\"" + }, + { + "Answer": 1440, + "Options": "a ) 1440 , b ) 1200 , c ) 2832 , d ) 1299 , e ) 1236", + "Correct": "a", + "Explanation": "\"explanation : l * 30 = 1200 \u00e8 l = 40 40 + 30 + 50 = 120 120 * 12 = 1440 answer : option a\"" + }, + { + "Answer": 900, + "Options": "['a ) 900', 'b ) 1,600', 'c ) 2,500', 'd ) 3,600', 'e ) 4,900']", + "Correct": "a", + "Explanation": "the number needs to be divisible by 2 ^ 2 , 2 * 5 , and 2 * 3 ^ 2 . the smallest such perfect square is 2 ^ 2 * 3 ^ 2 * 5 ^ 2 = 900 the answer is a ." + }, + { + "Answer": 12, + "Options": "['a ) 4', 'b ) 8', 'c ) 12', 'd ) 15', 'e ) 20']", + "Correct": "c", + "Explanation": "i understand this might not be required but i used the equation of a circle . since the origin is at 0 , x ^ 2 + y ^ 2 = 5 ^ 2 . x , y could be + / - ( 0,5 or 5,0 ) - 4 possibilities . x , y could be + / - ( 3,4 or 4,3 ) - 8 possibilities . ans : j = c" + }, + { + "Answer": 36.666666666666664, + "Options": "a ) 36.7 , b ) 52.9 , c ) 52.8 , d ) 52.1 , e ) 52.2", + "Correct": "a", + "Explanation": "\"42 / 360 * 22 / 7 * 10 * 10 = 36.7 m 2 answer : a\"" + }, + { + "Answer": 346.3605900582747, + "Options": "['a ) 248', 'b ) 312.5', 'c ) 346.5', 'd ) 392.5', 'e ) 424']", + "Correct": "c", + "Explanation": "area covered by lamp = pi * r ^ 2 / 4 ( here we divide by 4 because lamp is put in the corner of the plot and only 1 / 4 part lit is of the plot ) where r = 21 m = length of part lit so area = ( 22 / 7 ) * 21 * 21 / 4 = 346.5 sq m answer : c" + }, + { + "Answer": 43.982297150257104, + "Options": "a ) 23.56 , b ) 23.59 , c ) 44.0 , d ) 23.53 , e ) 23.57", + "Correct": "c", + "Explanation": "\"let the side of the square be a cm . parameter of the rectangle = 2 ( 36 + 20 ) = 112 cm parameter of the square = 112 cm i . e . 4 a = 112 a = 28 diameter of the semicircle = 28 cm circimference of the semicircle = 1 / 2 ( \u00e2 \u02c6 \u008f ) ( 28 ) = 1 / 2 ( 22 / 7 ) ( 28 ) = 44 cm to two decimal places answer : c\"" + }, + { + "Answer": 0.016, + "Options": "a ) 1.6 , b ) 1 , c ) 0.4 , d ) 0.16 , e ) 0.016", + "Correct": "e", + "Explanation": "\"the volume of oil pumped to the tank = the volume of oil taken away from stationary cylinder . pi * 16 * 10 = pi * h * 100 * 100 ( h is distance that the oil level dropped ) h = 160 / 10,000 = 16 / 1000 = 0.016 ft the answer is e .\"" + }, + { + "Answer": 50, + "Options": "a ) 50 , b ) 70 , c ) 60 , d ) 20 , e ) 25", + "Correct": "a", + "Explanation": "\"d 2 / 2 = ( 10 * 10 ) / 2 = 50 answer : a\"" + }, + { + "Answer": 3, + "Options": "['a ) 0', 'b ) 1', 'c ) 2', 'd ) 3', 'e ) 4']", + "Correct": "d", + "Explanation": "let x = 6 q + 3 . then , x 2 = ( 6 q + 3 ) 2 = 36 q 2 + 36 q + 9 = 6 ( 6 q 2 + 6 q + 1 ) + 3 . so , when 2 n is divided by 4 , remainder = 3 . answer : d" + }, + { + "Answer": 77, + "Options": "['a ) 80', 'b ) 90', 'c ) 77', 'd ) 88', 'e ) 99']", + "Correct": "c", + "Explanation": "if i calculate it using the formulae , # diagonals = n ( n - 3 ) / 2 each vertex sends of n - 3 diagonals n = 15 - 1 then 14 * ( 14 - 3 ) / 2 = 77 correct option : c" + }, + { + "Answer": 972, + "Options": "a ) 640 , b ) 758 , c ) 862 , d ) 972 , e ) 1024", + "Correct": "d", + "Explanation": "\"2 hl + 2 hw = 2 lw h = lw / ( l + w ) volume = lwh = ( lw ) ^ 2 / ( l + w ) = 972 the answer is d .\"" + }, + { + "Answer": 600, + "Options": "a ) 450 , b ) 600 , c ) 750 , d ) 2400 , e ) 3200", + "Correct": "b", + "Explanation": "\"answer a ) 9600 yards need 1200 lbs 1 yard will need 1200 / 7200 = 1 / 6 lbs 3600 yards will need 1 / 6 * 3600 yards = 600 lbs b\"" + }, + { + "Answer": 1550, + "Options": "a ) 1350 , b ) 1550 , c ) 9676 , d ) 1679 , e ) 2691", + "Correct": "b", + "Explanation": "\"area = ( l + b + 2 d ) 2 d = ( 95 + 55 + 2.5 * 2 ) 2 * 2.5 = > 775 775 * 2 = rs . 1550 answer : b\"" + }, + { + "Answer": 45, + "Options": "a ) 38 cm 2 , b ) 27 cm 2 , c ) 45 cm 2 , d ) 25 cm 2 , e ) 35 cm 2", + "Correct": "c", + "Explanation": "\"area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 36 / 2 = 45 cm 2 answer : c\"" + }, + { + "Answer": 27, + "Options": "['a ) 4', 'b ) 27', 'c ) 12', 'd ) 16', 'e ) 18']", + "Correct": "b", + "Explanation": "let length of rectangle = l 9 ^ 2 = l * 3 = > l = 81 / 3 = 27 answer b" + }, + { + "Answer": 33.33333333333333, + "Options": "a ) 15 % , b ) 20 % , c ) 25 % , d ) 33 % , e ) 40 %", + "Correct": "d", + "Explanation": "\"sol . required change = ( 25 * 100 ) / ( 100 - 25 ) = 25 % d\"" + }, + { + "Answer": 65, + "Options": "['a ) 3', 'b ) 4', 'c ) 5', 'd ) 6', 'e ) 7']", + "Correct": "b", + "Explanation": "answer : b" + }, + { + "Answer": 16, + "Options": "a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20", + "Correct": "a", + "Explanation": "\"let x be the width of the garden . 3 x ^ 2 = 768 x ^ 2 = 256 x = 16 the answer is a .\"" + }, + { + "Answer": 121, + "Options": "a ) 11 cm \u00b2 , b ) 21 cm \u00b2 , c ) 22 cm \u00b2 , d ) 113 cm \u00b2 , e ) 121 cm \u00b2", + "Correct": "e", + "Explanation": "\"we know that the perimeter of square = 4 \u00d7 side side = 11 cm therefore , perimeter = 4 \u00d7 11 cm = 44 cm now , area of the square = ( side \u00d7 side ) sq . units = 11 \u00d7 11 cm \u00b2 = 121 cm \u00b2 answer : option e\"" + }, + { + "Answer": 120, + "Options": "a ) 100 , b ) 777 , c ) 998 , d ) 729 , e ) 120", + "Correct": "e", + "Explanation": "\"120 % answer : e\"" + }, + { + "Answer": 33.1, + "Options": "['a ) 33.1', 'b ) 33.5', 'c ) 33.7', 'd ) 33.2', 'e ) 33.9']", + "Correct": "a", + "Explanation": "100 \u00d7 ( 110 ) / 100 \u00d7 ( 110 ) / 100 \u00d7 ( 110 ) / 100 = > 1331 / 100 = 33.1 % answer is a ." + }, + { + "Answer": 104.80000000000005, + "Options": "a ) 75 % , b ) 80 % , c ) 104.8 % , d ) 150.5 % , e ) 180 %", + "Correct": "c", + "Explanation": "\"let length of each side of square a be 10 area of a = 10 ^ 2 = 100 since , length of each side of square a is increased by 100 percent to make square b length of each side of square b = 2 * 10 = 20 area of b = 20 ^ 2 = 400 since , length of the side of square b is increased by 60 percent to make square c length of each side of square c = 1.6 * 20 = 32 area of c = 32 ^ 2 = 1024 difference in areas of c and cummulative areas of a and b = 1024 - ( 400 + 100 ) = 524 percent is the area of square c greater than the sum of the areas of squares a and b = ( 524 / 500 ) * 100 % = 104.8 % answer c\"" + }, + { + "Answer": 225, + "Options": "a ) 144 , b ) 169 , c ) 196 , d ) 121 , e ) 225", + "Correct": "e", + "Explanation": "\"we know that the perimeter of square = 4 \u00e3 \u2014 side side = 15 cm therefore , perimeter = 4 \u00e3 \u2014 15 cm = 60 cm now , area of the square = ( side \u00e3 \u2014 side ) sq . units = 15 \u00e3 \u2014 15 cm \u00e2 \u00b2 = 225 cm \u00e2 \u00b2 answer : e\"" + }, + { + "Answer": 7.0710678118654755, + "Options": "a ) 5 , b ) 6 , c ) 7.07 , d ) 8 , e ) 9", + "Correct": "c", + "Explanation": "\"side of triangle is a then perimeter = a + a + a . sqrt 2 ( right angle and pythagorus ) = 2 a + a . sqrt 2 = 10 + 10 sqrt 2 or , a . ( 2 + sqrt 2 ) = 10 ( 1 + sqrt 2 ) , a = 10 * ( 1 + sqrt 2 ) / 2 + sqrt 2 = 10 * 2.414 / 3.414 = 0.707 * 10 then hypotenuse = 7.07 c\"" + }, + { + "Answer": 24000, + "Options": "a ) 42500 m cube , b ) 20000 m cube , c ) 44140 m cube , d ) 24000 m cube , e ) none of these", + "Correct": "d", + "Explanation": "\"explanation : l = ( 100 - 20 ) m = 80 m , [ because 10 + 10 = 20 ] b = ( 50 - 20 ) m = 30 m , h = 10 m . volume of the box = ( 80 x 30 x 8 ) m cube = 24000 m cube . option d\"" + }, + { + "Answer": 67.65800860900399, + "Options": "['a ) 68', 'b ) 83', 'c ) 57', 'd ) 61', 'e ) 62']", + "Correct": "a", + "Explanation": "area of star = \u221a 3 / 4 * ( 12 ) ^ 2 + 3 * \u221a 3 / 4 * ( 12 / 3 ) ^ 2 = 48 \u221a 3 if r be radius of circle then r = 6 / cos 30 = > r = 12 / \u221a 3 = > r ^ 2 = 48 area of circle = pi * 48 area of the circle not enclosed by the star = 48 * pi - 48 \u221a 3 = 48 ( 3.14 - 1.732 ) = 68 ( approax ) answer : a" + }, + { + "Answer": 68, + "Options": "a ) 50 , b ) 74 , c ) 37 , d ) 77 , e ) 68", + "Correct": "e", + "Explanation": "e 68 68 regions . each new tangent increases the non - enclosed areas by two" + }, + { + "Answer": 126, + "Options": "['a ) 120 m', 'b ) 122 m', 'c ) 124 m', 'd ) 126 m', 'e ) 128 m']", + "Correct": "d", + "Explanation": "explanation : let 4 x and 3 x be sides of the rectangle we know that area of rectangle = l \u00d7 b 4 x \u00d7 3 x = 972 12 x 2 = 972 x 2 = 81 x = 9 therefore length = 4 x = 4 \u00d7 9 = 36 m breadth = 3 x = 3 \u00d7 9 = 27 m therefore perimeter = 2 ( l + b ) = 2 ( 36 + 27 ) = 126 m answer : option d" + }, + { + "Answer": 18, + "Options": "a ) 16 , b ) 77 , c ) 25 , d ) 87 , e ) 18", + "Correct": "e", + "Explanation": "\"explanation : let the integer be x . then , x + x 2 = 342 x 2 + x - 342 = 0 ( x + 19 ) ( x \u2013 18 ) = 0 x = 18 answer : e\"" + }, + { + "Answer": 144, + "Options": "['a ) 56', 'b ) 80', 'c ) 100', 'd ) 120', 'e ) 144']", + "Correct": "e", + "Explanation": "w = 6 c 5 * ( 5 - 1 ) ! ( select 5 out of 6 and arrange them in circular manner ) = 6 * 4 ! = 6 * 24 = 144 answer - e" + }, + { + "Answer": 6202.751823533447, + "Options": "a ) 2399 , b ) 6204 , c ) 2999 , d ) 5808 , e ) 2888", + "Correct": "b", + "Explanation": "\"explanation : area = ( 13.86 x 10000 ) sq . m = 138600 sq . m circumference = cost of fencing = rs . ( 1320 x 4.70 ) = rs . 6204 . answer : b ) 6204\"" + }, + { + "Answer": 125, + "Options": "a ) 125 % , b ) 150 % , c ) 100 % , d ) 90 % , e ) 85 %", + "Correct": "a", + "Explanation": "\"the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 50 % increase a surface = 6 * ( ( 1.5 a ) ^ 2 ) = 6 * 2.25 * a ^ 2 the increase in the surface area = ( 6 * 2.25 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 2.25 - 1 ) ) / ( 6 * a ^ 2 ) = 2.25 - 1 = 1.25 = 125 % answer : a\"" + }, + { + "Answer": 240, + "Options": "a ) 240 cm 2 , b ) 384 cm 2 , c ) 279 cm 2 , d ) 200 cm 2 , e ) 297 cm 2", + "Correct": "a", + "Explanation": "\"area of a parallelogram = base * height = 24 * 10 = 240 cm 2 answer : a\"" + }, + { + "Answer": 74, + "Options": "a ) 44 ft , b ) 88 ft , c ) 74 ft , d ) 11 ft , e ) 66 ft", + "Correct": "c", + "Explanation": "\"given that length and area , so we can find the breadth . length x breadth = area 40 x breadth = 680 breadth = 17 feet area to be fenced = 2 b + l = 2 ( 17 ) + 40 = 74 feet answer : c ) 74 ft\"" + }, + { + "Answer": 4, + "Options": "['a ) 64', 'b ) 4', 'c ) 16', 'd ) 9', 'e ) 5']", + "Correct": "b", + "Explanation": "explanation : distance covered by roy in 1 / 2 hr = 4 kmtherefore , side of the square = 4 / 2 = 2 kmhence , area = 2 \u00d7 2 = 4 square km answer : b" + }, + { + "Answer": 7, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "e", + "Explanation": "if x is the number in the corner square , then the sum of all the numbers in the squares is equal to the sum of the numbers in the five squares aligned vertically plus the sum of the numbers in the five squares aligned horizontally minus x . hence , 1 + 2 + \u00b7 \u00b7 \u00b7 + 9 = 32 + 20 \u2212 x . the sum on the left is 45 , so x = 52 \u2212 45 = 7 . correct answer e" + }, + { + "Answer": 37500, + "Options": "['a ) 18750 sq . m', 'b ) 37500 sq . m', 'c ) 40000 sq . m', 'd ) 48000 sq . m', 'e ) none of these']", + "Correct": "b", + "Explanation": "solution so length = 250 m ; breadth = 150 m area = ( 250 x 150 ) m \u00b2 = 37500 m \u00b2 answer b" + }, + { + "Answer": 15, + "Options": "['a ) 17', 'b ) 16', 'c ) 15', 'd ) 14', 'e ) 13']", + "Correct": "c", + "Explanation": "7 ^ 2 + 5 ^ 2 + 3 ^ 2 = 49 + 25 + 9 = 83 7 + 5 + 3 = 15 hence answer is c" + }, + { + "Answer": 157.07963267948966, + "Options": "a ) 150 , b ) 155 , c ) 158 , d ) 157 , e ) 190", + "Correct": "d", + "Explanation": "\"\u03c0 * 10 * 5 = 157 answer : d\"" + }, + { + "Answer": 40, + "Options": "['a ) 10', 'b ) 20', 'c ) 30', 'd ) 40', 'e ) 80']", + "Correct": "d", + "Explanation": "two sides each = x the third = 2 x and the wall length is thus 2 x too x * 2 x = 2 x ^ 2 = 200 ie x ^ 2 = 100 ie x = 10 l = 20 w = 10 total lenght of fence = 2 * 10 + 20 = 40 my answer is d" + }, + { + "Answer": 30.000000000000178, + "Options": "['a ) 30', 'b ) 36', 'c ) 48', 'd ) 60', 'e ) 65']", + "Correct": "a", + "Explanation": "( - 2 , - 3 ) is in 3 rd quadrant , ( 4 , - 3 ) is in 4 th quadrant while ( 28,7 ) is in 1 st quadrant . also , y coordinate of ( - 2 , - 3 ) and ( 4 , - 3 ) is same so they lie on same horizontal line . so base of triangle = sqrt [ ( - 3 + 3 ) ^ 2 + ( 4 + 2 ) ^ 2 ] = 6 and height of triangle = 7 - ( - 3 ) = 10 so area of triangle = 1 / 2 * 6 * 10 = 30 hence option ( a ) ," + }, + { + "Answer": 7, + "Options": "['a ) 2', 'b ) 4', 'c ) 6', 'd ) 7', 'e ) 12']", + "Correct": "d", + "Explanation": "we can find the radius of all the three cases of cylinders . the only crux to find the answer faster is that : voulme is pi * r ^ 2 * h . the volume is a function of r ^ 2 . so r has to be the highest to find the largest volume . so r = 7 for the surface 8 * 12 face . volume = 343 pi answer d" + }, + { + "Answer": 11, + "Options": "a ) 3 : 8 , b ) 3 : 6 , c ) 3 : 7 , d ) 11 : 1 , e ) 3 : 3", + "Correct": "d", + "Explanation": "\"d = 11 d d = d a \u221a 2 = 11 d a \u221a 2 = d a = 11 d / \u221a 2 a = d / \u221a 2 = > 11 : 1 answer : d\"" + }, + { + "Answer": 270, + "Options": "['a ) 370 sq . units', 'b ) 270 sq . units', 'c ) 170 sq . units', 'd ) 470 sq . units', 'e ) 570 sq . units']", + "Correct": "b", + "Explanation": "given that the area of the square = 2025 sq . units = > side of square = \u221a 2025 = 45 units the radius of the circle = side of the square = 45 units breath of the rectangle = 3 / 5 * 45 = 27 units given that length = 10 units area of the rectangle = lb = 27 * 10 = 270 sq . units answer : b" + }, + { + "Answer": 105, + "Options": "a ) 145 cm 2 , b ) 105 cm 2 , c ) 125 cm 2 , d ) 115 cm 2 , e ) 135 cm 2", + "Correct": "b", + "Explanation": "\"the triangle with sides 30 cm , 21 cm and 10 cm is right angled , where the hypotenuse is 30 cm . area of the triangle = 1 / 2 * 21 * 10 = 105 cm 2 answer : b\"" + }, + { + "Answer": 91.91300234460846, + "Options": "a ) 100 , b ) 120 , c ) 91.2 , d ) 180 , e ) none", + "Correct": "c", + "Explanation": "\"solution other side = \u221a ( 17 ) 2 - ( 16 ) 2 = \u221a 289 - 256 = \u221a 33 = 5.7 m . \u2234 area = ( 16 x 5.7 ) m 2 = 91.2 m 2 . answer c\"" + }, + { + "Answer": 10.25, + "Options": "a ) 15.00 % , b ) 10.25 % , c ) 10.00 % , d ) 12.25 % , e ) 12.50 %", + "Correct": "b", + "Explanation": "\"a = 100 a 2 = 10000 a = 105 a 2 = 11025 - - - - - - - - - - - - - - - - 10000 - - - - - - - - - 1025 100 - - - - - - - ? = > 10.25 % answer : b\"" + }, + { + "Answer": 0.545415391248228, + "Options": "['a ) 5 / 12', 'b ) 2 / 5', 'c ) 0.5451', 'd ) 3 / 4', 'e ) 5 / 6']", + "Correct": "c", + "Explanation": "c . it is a circle inscribed in a square . square side = 24 - - - > square ( table ) area = 24 ^ 2 circle diameter = 20 - - - > circle area = pir ^ 2 = 100 pi ( where pi = ~ 3.14 ) covered fraction = 100 * 3.14 / 24 * 24 = ~ 314 / 24 * 24 = 0.5451 c" + }, + { + "Answer": 420, + "Options": "['a ) 120', 'b ) 150', 'c ) 200', 'd ) 270', 'e ) 420']", + "Correct": "e", + "Explanation": "to make a triangle , you need 2 checkpoints from one track and 1 from the other . you can not have all 3 from the same track since then the points will be in a line ( assuming straight line of track ) you select 2 checkpoints from the first track and one from the second or two from the second track and one from the first . 6 c 2 * 10 c 1 + 10 c 2 * 6 c 1 = 150 + 270 = 420 answer ( e )" + }, + { + "Answer": 40, + "Options": "a ) 42 , b ) 40 , c ) 38 , d ) 36 , e ) 48", + "Correct": "b", + "Explanation": "\"if we take a square with side length x and draw a diagonal , we get two isosceles right triangles . if we focus on one such right triangle , we see that the legs have length x . square 21 - inch flat - screen television the diagonal ( hypotenuse ) = 21 so , we can apply the pythagorean theorem to get x \u00b2 + x \u00b2 = 21 \u00b2 simplify : 2 x \u00b2 = 21 \u00b2 divide both sides by 2 to get : x \u00b2 = 21 \u00b2 / 2 since the area of the square = x \u00b2 , we can see that the area of this square is 21 \u00b2 / 2 square 19 - inch flat - screen television the diagonal ( hypotenuse ) = 19 so , we can apply the pythagorean theorem to get x \u00b2 + x \u00b2 = 19 \u00b2 simplify : 2 x \u00b2 = 19 \u00b2 divide both sides by 2 to get : x \u00b2 = 19 \u00b2 / 2 since the area of the square = x \u00b2 , we can see that the area of this square is 19 \u00b2 / 2 difference in areas = 21 \u00b2 / 2 - 19 \u00b2 / 2 = ( 21 + 19 ) ( 21 - 19 ) / 2 = 40 b\"" + }, + { + "Answer": 20, + "Options": "a ) 40 , b ) 35 , c ) 20 , d ) 25 , e ) 30", + "Correct": "c", + "Explanation": "\"c 20 240 pairs of bangles = 480 bangles = 40 dozens . 40 \u00f7 2 = 20 boxes .\"" + }, + { + "Answer": 4, + "Options": "['a ) 0', 'b ) 1', 'c ) 3', 'd ) 4', 'e ) 2']", + "Correct": "d", + "Explanation": "let the number be x and on dividing x by 5 , we get k as quotient and 3 as remainder . x = 5 k + 3 x ^ 2 = ( 5 k + 3 ) ^ 2 = ( 25 k ^ 2 + 30 k + 9 ) = 5 ( 5 k ^ 2 + 6 k + 1 ) + 4 on dividing x ^ 2 by 5 , we get 4 as remainder . answer is d" + }, + { + "Answer": 4, + "Options": "['a ) 3 cm', 'b ) 4 cm', 'c ) 6 cm', 'd ) 8 cm', 'e ) none']", + "Correct": "b", + "Explanation": "solution 4 \u00ee r 2 = 2 \u00ee 4 x 8 \u00e2 \u2021 \u2019 r 2 = ( 4 x 8 / 2 ) \u00e2 \u2021 \u2019 16 \u00e2 \u2021 \u2019 r = 4 cm . answer b" + }, + { + "Answer": 32, + "Options": "['a ) 4', 'b ) 8', 'c ) 16', 'd ) 32', 'e ) 64']", + "Correct": "d", + "Explanation": "two sides each = x the third = 2 x and the wall side is thus 2 x too x * 2 x = 2 x ^ 2 = 128 ie x ^ 2 = 64 ie x = 8 l = 16 w = 8 total lenght of table ' s free sides = 2 * 8 + 16 = 32 my answer is d" + }, + { + "Answer": 24, + "Options": "['a ) 36', 'b ) 32', 'c ) 24', 'd ) 21', 'e ) 15']", + "Correct": "c", + "Explanation": "27 cubic centimetre cubes gives side = 3 cm so if : l * w * h is 9 * 12 * 8 , then max . cube we can have are 3 * 4 * 2 = 24 l * w * h is 9 * 8 * 12 , then max . cube we can have are 3 * 2 * 4 = 24 l * w * h is 12 * 8 * 9 , then max . cube we can have are 4 * 2 * 3 = 24 l * w * h is 12 * 9 * 8 , then max . cube we can have are 4 * 3 * 2 = 24 l * w * h is 8 * 12 * 9 , then max . cube we can have are 2 * 4 * 3 = 24 l * w * h is 8 * 9 * 12 , then max . cube we can have are 2 * 3 * 4 = 24 in all cases we get r = 24 cubes . ans . c" + }, + { + "Answer": 70, + "Options": "a ) 56 , b ) 88 , c ) 70 , d ) 116 , e ) 120", + "Correct": "c", + "Explanation": "\"area of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 10 + 10 = 20 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 20 * 7 = 70 c is the answer\"" + }, + { + "Answer": 0.25, + "Options": "['a ) 0.25 % less', 'b ) 1 % less', 'c ) equal to each other', 'd ) 1 % more', 'e ) 9 % more']", + "Correct": "a", + "Explanation": "wish the question specified that we are talking about corresponding height . base of a = 21 / 20 * base of b height of a = 19 / 20 * height of b area of a = ( 1 / 2 ) * base of a * height of a = 21 / 20 * 19 / 20 * area of b = 399 / 400 * area of b area of a is 0.25 % less than the area of b . answer ( a )" + }, + { + "Answer": 343, + "Options": "a ) 125 cm 3 , b ) 343 cm 3 , c ) 250 cm 3 , d ) 625 cm 3 , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : edge of cude = 28 / 4 = 7 cm volume = a * a * a = 7 * 7 * 7 = 343 cm cube option b\"" + }, + { + "Answer": 80, + "Options": "['a ) 20', 'b ) 40', 'c ) 60', 'd ) 80', 'e ) 100']", + "Correct": "d", + "Explanation": "explanation : when all the dimensions of a three dimensional object are in fact doubled , then the capacity increases by a factor of 2 x 2 x 2 = 2 ^ 3 = 8 . thus the capacity of the new sandbox is 8 x 10 = 80 cubic feet . answer : option d" + }, + { + "Answer": 52.8, + "Options": "a ) 56.8 m 2 , b ) 82.9 m 2 , c ) 52.8 m 2 , d ) 17.9 m 2 , e ) 72.9 m 2", + "Correct": "c", + "Explanation": "\"42 / 360 * 22 / 7 * 12 * 12 = 52.8 m 2 answer : c\"" + }, + { + "Answer": 15, + "Options": "a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18", + "Correct": "b", + "Explanation": "\"let x be the width of the garden . 3 x ^ 2 = 675 x ^ 2 = 225 x = 15 the answer is b .\"" + }, + { + "Answer": 36, + "Options": "a ) 44 , b ) 42 , c ) 40 , d ) 38 , e ) 36", + "Correct": "e", + "Explanation": "\"isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side , the longer side with side 12 will be divided into 3 parts = 6 , 3 and 3 ( making one square and two right triangles ) for the right triangle , height will be = ( 5 ^ 2 - 3 ^ 2 ) ^ 1 / 2 = 4 and the area of trapezoid = 1 / 2 ( b 1 + b 2 ) h = 1 / 2 * 18 * 4 = 36 e\"" + }, + { + "Answer": 4456.443887106987, + "Options": "['a ) rs . 4233', 'b ) rs . 4350', 'c ) rs . 4457', 'd ) rs . 4670', 'e ) rs . 4756']", + "Correct": "c", + "Explanation": "area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . \u03c0 r 2 = 175600 \u21d4 ( r ) 2 = ( 175600 x ( 7 / 22 ) ) \u21d4 r = 236.37 m . circumference = 2 \u03c0 r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 3 ) = rs . 4457 . c" + }, + { + "Answer": 50, + "Options": "a ) 40 % , b ) 45 % , c ) 50 % , d ) 60 % , e ) 67 %", + "Correct": "c", + "Explanation": "\"let original length = x and original breadth = y . original area = xy . new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c\"" + }, + { + "Answer": 153.93804002589985, + "Options": "a ) 151 cm \u00b2 , b ) 152 cm \u00b2 , c ) 154 cm \u00b2 , d ) 155 cm \u00b2 , e ) 157 cm \u00b2", + "Correct": "c", + "Explanation": "\"circumference of circle = 2 \u03c0 r = 2 \u00d7 22 / 7 \u00d7 7 = 44 cm area of circle = \u03c0 r \u00b2 = 22 / 7 \u00d7 7 \u00d7 7 cm \u00b2 = 154 cm \u00b2 answer : c\"" + }, + { + "Answer": 3, + "Options": "a ) 27 , b ) 3 , c ) 6 , d ) 8 , e ) 12", + "Correct": "b", + "Explanation": "\"we can find the radius of all the three cases of cylinders . the only crux to find the answer faster is that : voulme is pi * r ^ 2 * h . the volume is a function of r ^ 2 . so r has to be the highest to find the largest volume . so r = 3 for the surface 8 * 12 face . volume = 27 pi answer b\"" + }, + { + "Answer": 104, + "Options": "['a ) 100 m 2', 'b ) 104 m 2', 'c ) 106 m 2', 'd ) 108 m 2', 'e ) 160 m 2']", + "Correct": "b", + "Explanation": "surface area of a cuboid = 2 ( lb + bh + lh ) = 2 ( 6 * 5 + 5 * 2 + 6 * 2 ) = 2 ( 30 + 10 + 12 ) = 2 * 52 = 104 m 2 answer : b" + }, + { + "Answer": 8, + "Options": "['a ) 8', 'b ) 9', 'c ) 10', 'd ) 11', 'e ) 16']", + "Correct": "a", + "Explanation": "let t be the number of trees . then the length required for trees on the sidewalk will be 1 * t = t to maximize the number of trees , the number of 20 feet spaces between trees should be 1 less than total number of trees . for example , if there are 3 trees , then there should be 2 spaces between them . so the number of 20 feet spaces will be t - 1 . then , the length of sidewalk required for 20 feet spaces will be 20 * ( t - 1 ) it is given that total length of sidewalk is 148 feet . or 20 ( t - 1 ) + t = 148 or 20 t - 20 + t = 148 or 21 t = 168 or t = 8 answer : - a" + }, + { + "Answer": 0.001, + "Options": "a ) 0.005 , b ) 0.002 , c ) 0.001 , d ) 0.0005 , e ) 0.0002", + "Correct": "c", + "Explanation": "\"it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 1 then x = 1 / 1000 = 0.001 . the answer is c\"" + }, + { + "Answer": 8, + "Options": "a ) 3 cm , b ) 4 cm , c ) 6 cm , d ) 8 cm , e ) none", + "Correct": "d", + "Explanation": "\"solution 4 \u00ee r 2 = 2 \u00ee 8 x 16 \u00e2 \u2021 \u2019 r 2 = ( 8 x 16 / 2 ) \u00e2 \u2021 \u2019 64 \u00e2 \u2021 \u2019 r = 8 cm . answer d\"" + }, + { + "Answer": 30, + "Options": "a ) 11 , b ) 17 , c ) 18 , d ) 101 , e ) 30", + "Correct": "e", + "Explanation": "\"let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 2700 3 b 2 = 2700 b 2 = 900 = 30 ( b > 0 ) b = 30 m . answer : e\"" + }, + { + "Answer": 52, + "Options": "a ) 14 , b ) 52 , c ) 54 , d ) 180 , e ) 240", + "Correct": "b", + "Explanation": "\"area = length x breadth 240 = 40 x breadth so , breadth = 6 units fencing required is - breadth + breadth + length 6 + 6 + 40 = > 52 feet answer must be ( b ) 52\"" + }, + { + "Answer": 3, + "Options": "a ) 3 : 1 , b ) 3 : 2 , c ) 3 : 5 , d ) 3 : 7 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : let the edges be a and b of two cubes , then a 3 / b 3 = 27 / 1 = > ( a / b ) 3 = ( 3 / 1 ) 3 a / b = 3 / 1 = > a : b = 3 : 1 option a\"" + }, + { + "Answer": 63, + "Options": "a ) 58 , b ) 70 , c ) 63 , d ) 65 , e ) 72", + "Correct": "c", + "Explanation": "1 / 2 bh = 1 / 2 ( 2 a + 1 ) ( 2 a + 6 ) now 4 a - 2 = 2 a + 6 2 a = 8 . a = 4 therefore , a ( 0,0 ) ; b ( 0,14 ) ; c ( 9,14 ) 1 / 2 * 9 * 14 = 63 answer : c" + }, + { + "Answer": 28, + "Options": "a ) 28 , b ) 40 , c ) 68 , d ) 88 , e ) 78", + "Correct": "a", + "Explanation": "\"we have : l = 20 ft and lb = 80 sq . ft . so , b = 4 ft . length of fencing = ( l + 2 b ) = ( 20 + 8 ) ft = 28 ft . answer : a\"" + }, + { + "Answer": 50, + "Options": "a ) 50 cm 2 , b ) 100 cm 2 , c ) 150 cm 2 , d ) 200 cm 2 , e ) 250 cm 2", + "Correct": "a", + "Explanation": "\"1 / 2 * 10 ( 7 + 3 ) = 50 cm 2 answer : a\"" + }, + { + "Answer": 45, + "Options": "a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50", + "Correct": "d", + "Explanation": "\"area of first rectangle is 15 * 24 = 360 hence area of second would be 8 x = 360 x x = 45 answer is d\"" + }, + { + "Answer": 6, + "Options": "['a ) l = 2 , w = 9', 'b ) l = 5 , w = 8', 'c ) l = 6 , w = 4', 'd ) l = 1 , w = 7', 'e ) l = 2 , w = 3']", + "Correct": "c", + "Explanation": "let length l = x , width w = x \u2212 2 and perimeter = p \u2234 p = 2 l + 2 w = 2 x + 2 ( x \u2212 2 ) 20 = 2 x + 2 x \u2212 4 4 x = 24 x = 6 l = 6 cm and w = l \u2212 2 = 4 cm answer is c ." + }, + { + "Answer": 216, + "Options": "a ) 216 , b ) 48 , c ) 64 , d ) 80 , e ) 100", + "Correct": "a", + "Explanation": "\"volume = 27 = side ^ 3 i . e . side of cube = 3 new cube has dimensions 6 , 6 , and 6 as all sides are twice of teh side of first cube volume = 6 * 6 * 6 = 216 square feet answer : option a\"" + }, + { + "Answer": 320, + "Options": "a ) 198 cm 2 , b ) 320 cm 2 , c ) 279 cm 2 , d ) 128 cm 2 , e ) 297 cm 2", + "Correct": "b", + "Explanation": "\"area of a parallelogram = base * height = 20 * 16 = 320 cm 2 answer : b\"" + }, + { + "Answer": 75, + "Options": "['a ) 77.77 %', 'b ) 75 %', 'c ) 67.5 %', 'd ) 87.5 %', 'e ) none of these']", + "Correct": "b", + "Explanation": "explanation : let the volume of sphere p be 64 parts . therefore volume of sphere q = > 64 \u2212 ( 37 / 64 ) % of 64 . = > 64 \u2212 37 = 27 parts . the volume of r is : - = > 27 \u2212 ( 19 / 27 ) \u00d7 27 . = > 27 \u2212 19 = 8 parts . volume ratio : = > p : q : r = 64 : 27 : 8 . radius ratio : = > p : q : r = 4 : 3 : 2 . the surface area will be 16 : 9 : 5 . surface area of r is less than the surface area of sphere p . = > 16 k \u2212 4 k = 12 k . now , = > ( 12 k / 16 k ) \u00d7 100 . = > 75 % . hence , the surface area of sphere r is less than the surface area of sphere p by 75 % . answer : b" + }, + { + "Answer": 153.93804002589985, + "Options": "['a ) 121 sq m', 'b ) 184 sq m', 'c ) 174 sq m', 'd ) 124 sq m', 'e ) 154 sq m']", + "Correct": "e", + "Explanation": "the area of circle = pie * r ^ 2 = 22 / 7 * 7 * 7 = 154 sq m answer : e" + }, + { + "Answer": 1.0033333333333334, + "Options": "a ) 1 meter , b ) 2 meter , c ) 3 meter , d ) 4 meter , e ) 5 meter", + "Correct": "a", + "Explanation": "solution we first note that mc = 20 - 5 = 15 the quadrilateral mnbc is a trapezoid and its area a is given by a = ( 1 / 2 ) \u00d7 10 \u00d7 ( x + mc ) = 5 ( x + 15 ) 40 % of the area of the rectangle is equal to 40 % \u00d7 ( 20 \u00d7 10 ) = ( 40 / 100 ) \u00d7 200 = 80 since the area of mnbc is equal to 40 % the area of the rectangle , we can write 5 ( x + 15 ) = 80 5 x + 75 = 80 5 x = 5 x = 1 meter answer is a" + }, + { + "Answer": 144, + "Options": "a ) 144 m 2 , b ) 120 m 2 , c ) 108 m 2 , d ) 158 m 2 , e ) none of these", + "Correct": "a", + "Explanation": "\"area of the outer rectangle = 24 \u00e3 \u2014 16 = 384 m 2 area of the inner rectangle = 20 \u00e3 \u2014 12 = 240 m 2 required area = ( 304 \u00e2 \u20ac \u201c 180 ) = 144 m 2 answer a\"" + }, + { + "Answer": 144, + "Options": "a ) 225 sq m , b ) 144 sq m , c ) 586 sq m , d ) 287 sq m , e ) 296 sq m", + "Correct": "b", + "Explanation": "\"12 * 12 = 144 sq m answer : b\"" + }, + { + "Answer": 0.8666666666666666, + "Options": "['a ) 13 / 15 ohms', 'b ) 15 / 13 ohms', 'c ) 5 / 8 ohms', 'd ) 3 / 7 ohms', 'e ) 45 / 18 ohms']", + "Correct": "a", + "Explanation": "the wording is a bit confusing , though basically we are told that 1 / r = 1 / 2 + 1 / 5 + 1 / 6 , from which it follows that r = 13 / 15 ohms option : a" + }, + { + "Answer": 10625, + "Options": "a ) 1288 , b ) 1299 , c ) 10625 , d ) 10000 , e ) 2887", + "Correct": "c", + "Explanation": "\"100 * 100 = 10000 125 * 85 = 10625 answer : c\"" + }, + { + "Answer": 18, + "Options": "['a ) 18 cm', 'b ) 20 cm', 'c ) 22 cm', 'd ) 24 cm', 'e ) 25 cm']", + "Correct": "a", + "Explanation": "2 ( l + b ) = 5 b 1 2 l + 2 b = 5 b 3 b = 2 l b = 2 l 3 then , area = 216 cm 2 l x b = 216 l x 2 l = 216 3 l 2 = 324 l = 18 cm . a" + }, + { + "Answer": 6, + "Options": "a ) 5 , b ) 6 , c ) 10 , d ) 13 , e ) 28", + "Correct": "b", + "Explanation": "\"suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 48 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , number of tiles = ( r - 2 ) * ( c + 4 ) = 48 comparing both of them we get c * r = ( r - 2 ) * ( c + 4 ) = > 4 r - 2 c = 8 c = 2 r - 4 putting it in c * r = 48 ( 2 r - 4 ) * r = 48 2 r ^ 2 - 4 r - 48 = 0 r can not be negative so r = 6 and c = 8 so , answer will be b\"" + }, + { + "Answer": 4, + "Options": "['a ) 9', 'b ) 7', 'c ) 4', 'd ) 8', 'e ) 6']", + "Correct": "c", + "Explanation": "first calculate the surface area of the cube . the cube is made of 6 squares with the sides measuring 6.5 cm each . the surface area of 1 side of the cube is 42.25 cm . multiply the surface area of the 1 side by 6 will give you the cube ' s total surface area . the cubes surface area is 253.5 cm . now we know that the surface area of the ball is 253.5 cm . to find out the surface area of a sphere you need to square the radius , then multiply by pi , and multiply by the number 4 . going backwards to find the radius - you will need to dived the surface area by 4 . then divide by pi . then determine the square root of the answer . the radius is 4.460 . rounding to the nearest whole number the radius is 4 . the correct answer is ( c ) ." + }, + { + "Answer": 3672, + "Options": "a ) 3672 , b ) 920 , c ) 7290 , d ) 6928 , e ) 3729", + "Correct": "a", + "Explanation": "\"explanation : let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 54 = rs . 3672 . answer : option a\"" + }, + { + "Answer": 6.0008333333333335, + "Options": "a ) 6 min , b ) 5 min , c ) 5.5 min , d ) 4 min , e ) 3 min", + "Correct": "a", + "Explanation": "\"area of a square field = 7201 sq m let the side of square = a a ^ 2 = 7201 = > a = 84.86 diagonal = ( 2 ) ^ ( 1 / 2 ) * a = 1.414 * 84.86 = 120 speed of lady = 1.2 km / hour = 1200 m / hour = 20 m / min time taken by lady to cross the field diagonally = 120 / 20 = 6 min answer a\"" + }, + { + "Answer": 8, + "Options": "['a ) 8', 'b ) 7', 'c ) 6', 'd ) 5', 'e ) 2']", + "Correct": "a", + "Explanation": "2 x * x = 128 = > x = 8 answer : a" + }, + { + "Answer": 44, + "Options": "['a ) 40 h', 'b ) 44 h', 'c ) 38 h', 'd ) 20 h', 'e ) 22 h']", + "Correct": "b", + "Explanation": "time at which they meet at starting point = lcm of 2 , 4 and 5.5 = 44 h answer : b" + }, + { + "Answer": 40, + "Options": "['a ) 40', 'b ) 38', 'c ) 27', 'd ) 29', 'e ) 11']", + "Correct": "a", + "Explanation": "explanation : d = \u221a 2 l answer : a ) 40" + }, + { + "Answer": 37.5, + "Options": "['a ) 37.2 %', 'b ) 37.5 %', 'c ) 30.2 %', 'd ) 37.7 %', 'e ) 33.2 %']", + "Correct": "b", + "Explanation": "explanation : 100 * 100 = 10000 110 * 125 = 13750 - - - - - - - - - - - 3750 10000 - - - - - - 3750 100 - - - - - - - ? = > 37.5 % answer : option b" + }, + { + "Answer": 49.99999999999999, + "Options": "a ) 13 , b ) 33 , c ) 50 , d ) 51 , e ) 52", + "Correct": "c", + "Explanation": "\"the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . it means there is no effect of change in volume of water to the costing of the solution so a solution of 1 liter of spirit and 2 liters of water will cost 50 cents answer = 50 answer : c\"" + }, + { + "Answer": 55, + "Options": "a ) 50 , b ) 55 , c ) 60 , d ) 65 , e ) 70", + "Correct": "b", + "Explanation": "\"the number of males is 180 - 110 = 70 . the number of males with advanced degrees is 70 - 35 = 35 . the number of females with advanced degrees is 90 - 35 = 55 . the answer is b .\"" + }, + { + "Answer": 1, + "Options": "['a ) 1 %', 'b ) 10 %', 'c ) 100 %', 'd ) 500 %', 'e ) 1000 %']", + "Correct": "a", + "Explanation": "let x be the original length of one side . then the original area is x ^ 2 . the new square has sides of length 10 x , so the area is 100 x ^ 2 . the area of the original square is 1 / 100 = 1 % times the area of the new square . the answer is a ." + }, + { + "Answer": 3.5, + "Options": "a ) 3.1 feet , b ) 3.2 feet , c ) 3.3 feet , d ) 3.4 feet , e ) 3.5 feet", + "Correct": "e", + "Explanation": "\"we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 8 = 42 42 / 12 = 3.5 feet answer : e\"" + }, + { + "Answer": 1200, + "Options": "a ) 3348 , b ) 3898 , c ) 1200 , d ) 2881 , e ) 7881", + "Correct": "c", + "Explanation": "answer : c ) 1200" + }, + { + "Answer": 168, + "Options": "a ) 120 cm 2 , b ) 112 cm 2 , c ) 776 cm 2 , d ) 666 cm 2 , e ) 168 cm 2", + "Correct": "e", + "Explanation": "\"the triangle with sides 30 cm , 28 cm and 12 cm is right angled , where the hypotenuse is 30 cm . area of the triangle = 1 / 2 * 28 * 12 = 168 cm 2 answer : e\"" + }, + { + "Answer": 8, + "Options": "a ) 8 m , b ) 10 m , c ) 12 m , d ) 15 m , e ) 17 m", + "Correct": "a", + "Explanation": "\"let the length of the hall be x m breadth of the hall = 1 x / 2 m area of the hall = length * breadth 128 = x * 1 x / 2 x \u00b2 = 256 x = 16 difference between the length and breadth of the hall = x - 1 x / 2 = x / 2 = 16 / 2 = 8 m answer : a\"" + }, + { + "Answer": 40, + "Options": "['a ) 20', 'b ) 30', 'c ) 40', 'd ) 56', 'e ) 65']", + "Correct": "c", + "Explanation": "sol . according to question ( l - 5 ) ( b + 5 ) - lb = 75 and l = 2 b so , b = 20 , l = 40 ans . ( c )" + }, + { + "Answer": 24, + "Options": "a ) 20 cm , b ) 24 cm , c ) 32 cm , d ) 28 cm , e ) 30 cm", + "Correct": "b", + "Explanation": "\"side of the 1 st square = 40 / 4 = 10 cm side of the 2 nd square = 32 / 4 = 8 cm area of the 3 rd square = 10 ^ 2 - 8 ^ 2 = 36 cm ^ 2 side of the 3 rd square = 6 cm required perimeter = 6 * 4 = 24 cm answer is b\"" + }, + { + "Answer": 9600, + "Options": "a ) 1288 , b ) 9600 , c ) 1000 , d ) 10000 , e ) 2887", + "Correct": "b", + "Explanation": "\"100 * 100 = 10000 120 * 80 = 9600 answer : b\"" + }, + { + "Answer": 6, + "Options": "a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7", + "Correct": "d", + "Explanation": "\"if n is a perfect square and a perfect cube , then n = a ^ 6 for some integer a . the numbers are 1 ^ 6 = 1 , 2 ^ 6 = 64 , 3 ^ 6 = 729 , 4 ^ 6 = 4096 , 5 ^ 6 = 15,625 , 6 ^ = 46,656 . the answer is d .\"" + }, + { + "Answer": 25, + "Options": "['a ) 10', 'b ) 15', 'c ) 20', 'd ) 25', 'e ) 30']", + "Correct": "d", + "Explanation": "the base of the isosceles triangle is 65 - 20 - 20 = 25 units the answer is d ." + }, + { + "Answer": 24, + "Options": "a ) 4 , b ) 8 , c ) 12 , d ) 24 , e ) 18", + "Correct": "d", + "Explanation": "\"let length of rectangle = l 12 ^ 2 = l * 4 = > l = 144 / 6 = 24 answer d\"" + }, + { + "Answer": 616.2479396518188, + "Options": "['a ) 88 cm 2', 'b ) 154 cm 2', 'c ) 1250 cm 2', 'd ) 616 cm 2', 'e ) none of these']", + "Correct": "d", + "Explanation": "perimeter of the circle = 2 \u03c0 r = 2 ( 18 + 26 ) \u21d2 2 \u00d7 22 \u2044 7 \u00d7 r = 88 \u21d2 r = 14 \u2234 area of the circle = \u03c0 r 2 = 22 \u2044 7 \u00d7 14 \u00d7 14 = 616 cm 2 answer d" + }, + { + "Answer": 3, + "Options": "['a ) 0', 'b ) 1', 'c ) 2', 'd ) 3', 'e ) 4']", + "Correct": "d", + "Explanation": "first break down 200 into 20 * 20 and further into the prime factors 2 * 2 * 5 * 2 * 2 * 5 . now we are looking for all the possible pairs ( 2 numbers ) of squares whose product results in 400 . 1 st : 2 ^ 2 * 10 ^ 2 ( i . e . the first two 2 ' s and two times 2 * 5 = 10 ) 2 nd : 4 ^ 2 * 5 ^ 2 ( i . e . two times 2 * 2 = 4 = 4 ^ 2 and 5 ^ 2 ) . 3 rd : 1 ^ 2 * 20 ^ 2 ( i . e . two times 2 * 2 * 5 and 1 ^ 2 = 1 ) answer d ." + }, + { + "Answer": 56, + "Options": "a ) 48 , b ) 32 , c ) 24 , d ) 56 , e ) 12", + "Correct": "d", + "Explanation": "\"for example our cube have a side 1 meter , so we have 1 cubical meter in this cube and this cubical meter weigth 7 pounds if we take cube with side 2 meters we will have 8 cubical meters in this cube 8 meters * 7 pounds = 56 pounds so answer is d and similar but more theoretical approach : if we have sides a and b than they have equal ration with their areas : a / b = a ^ 2 / b ^ 2 and they have equal ration with their volumes : a / b = a ^ 3 / b ^ 3 we have two sides 1 / 2 so their volume will be in ratio 1 / 8 weight of one cube * volume of another cube 7 * 8 = 56 so answer is d\"" + }, + { + "Answer": 39, + "Options": "a ) 39 . , b ) 40 . , c ) 42 . , d ) 44 . , e ) 46 .", + "Correct": "a", + "Explanation": "\"let the width = x x * 4 x = 676 x ^ 2 = 169 x = 13 length = 4 * 13 = 52 difference = 52 - 13 = 39 a is the answer\"" + }, + { + "Answer": 21.908902300206645, + "Options": "['a ) 32 m', 'b ) 12 m', 'c ) 20 m', 'd ) 22 m', 'e ) 25 m']", + "Correct": "d", + "Explanation": "length = 75 % of breadth . length \u00d7 breadth = 360 m 2 \u21d2 75 % of breadth \u00d7 breadth = 360 m 2 \u21d2 75 / 100 \u00d7 breadth \u00d7 breadth = 360 m 2 \u21d2 breadth \u00d7 breadth = 480 m 2 \u21d2 breadth = 22 m answer : d" + }, + { + "Answer": 71.9822971502571, + "Options": "a ) 72 , b ) 76 , c ) 80 , d ) 84 , e ) 88", + "Correct": "a", + "Explanation": "\"the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 14 + 2 * 14 which is about 72 . the answer is a .\"" + }, + { + "Answer": 0.7, + "Options": "a ) 0.11 % , b ) 0.7 % , c ) 0.4 % , d ) 0.6 % , e ) 0.8 %", + "Correct": "b", + "Explanation": "\"let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 53 / 50 ) x ( 19 / 20 ) y = ( 144 / 143 ) ( xy ) error in measurement = ( 144 / 143 ) xy - xy = ( 1 / 143 ) xy error percentage = [ ( 1 / 143 ) xy ( 1 / xy ) 100 ] % = ( 7 / 10 ) % = 0.7 % . answer is b .\"" + }, + { + "Answer": 25, + "Options": "a ) 35 % , b ) 25 % , c ) 20 % , d ) 15 % , e ) 10 %", + "Correct": "b", + "Explanation": "\"let diameter of circle r , dr = 50 and diameter of circle s , ds = 100 radius of circle r , rr = 25 radius of circle s , rs = 50 area of circle r / area of circle s = ( pi * rr ^ 2 ) / ( pi * rs ^ 2 ) = ( 25 / 50 ) ^ 2 = ( 5 / 10 ) ^ 2 = 25 % answer : b\"" + }, + { + "Answer": 12, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12", + "Correct": "e", + "Explanation": "\"let x be the width of the garden . 3 x ^ 2 = 432 x ^ 2 = 144 x = 12 the answer is e .\"" + }, + { + "Answer": 216, + "Options": "a ) 216 cm 3 , b ) 400 cm 3 , c ) 250 cm 3 , d ) 625 cm 3 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : edge of cude = 24 / 4 = 6 cm volume = a * a * a = 6 * 6 * 6 = 216 cm cube option a\"" + }, + { + "Answer": 38.5, + "Options": "['a ) 76', 'b ) 65', 'c ) 59.5', 'd ) 49', 'e ) 38.5']", + "Correct": "e", + "Explanation": "area covered by photograph = ( 8.5 - 3 ) * ( 10 - 3 ) = 5.5 * 7 = 38.5 answer e" + }, + { + "Answer": 9801, + "Options": "['a ) 9001', 'b ) 9621', 'c ) 9431', 'd ) 9801', 'e ) 9601']", + "Correct": "d", + "Explanation": "square of ( 100 - 1 ) = 10000 + 1 - 200 9801 answer d" + }, + { + "Answer": 100, + "Options": "a ) 50 % , b ) 87 % , c ) 100 % , d ) 187 % , e ) 200 %", + "Correct": "c", + "Explanation": "\"let ' s just look at the dimensions ( no calculation needed ) . with dimension 11 the same , the other dimension 11 is twice 5.5 then the area will be double which means 100 % greater . the answer is c .\"" + }, + { + "Answer": 26960.847359767075, + "Options": "a ) 29960 sq m , b ) 26950 sq m , c ) 43120 sq m , d ) 27680 sq m , e ) 27786 sq m", + "Correct": "b", + "Explanation": "\"let the radii of the smaller and the larger circles be s m and l m respectively . 2 \u220f s = 396 and 2 \u220f l = 704 s = 396 / 2 \u220f and l = 704 / 2 \u220f difference between the areas = \u220f l ^ 2 - \u220f s ^ 2 = \u220f { 198 ^ 2 / \u220f ^ 2 - 352 ^ 2 / \u220f ^ 2 } = 198 ^ 2 / \u220f - 352 ^ 2 / \u220f = ( 198 - 352 ) ( 198 + 352 ) / \u220f = ( 154 ) ( 550 ) / ( 22 / 7 ) = 26950 sq m answer : b\"" + }, + { + "Answer": 1880, + "Options": "a ) $ 1220 , b ) $ 1330 , c ) $ 1550 , d ) $ 1770 , e ) $ 1880", + "Correct": "e", + "Explanation": "\"the total surface area is 2 ( 3 * 4 + 4 * 5 + 3 * 5 ) = 94 square feet the total cost is 94 * $ 20 = $ 1880 the answer is e .\"" + }, + { + "Answer": 0.7853981633974483, + "Options": "['a ) 11 / 14', 'b ) 1 / 14', 'c ) 13 / 14', 'd ) 12 / 14', 'e ) 5 / 14']", + "Correct": "a", + "Explanation": "let the side of square = a unit so area of square = a ^ 2 diameter of inscribed circle = side of square = a radius of circle = a / 2 area of circle = ( 22 / 7 ) ( a / 2 ) ^ 2 ratio of area of circle to square = { ( 22 / 7 ) ( a / 2 ) ^ 2 } / a ^ 2 = 11 / 14 answer : a" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 27 , c ) 98 , d ) 27 , e ) 29", + "Correct": "a", + "Explanation": "\"lb = 3 * 4 = 12 answer : a\"" + }, + { + "Answer": 8, + "Options": "a ) 8 , b ) 6 , c ) 4 , d ) 3 , e ) 1", + "Correct": "a", + "Explanation": "\"6 a 2 = 24 a = 2 = > a 3 = 8 cc answer : a\"" + }, + { + "Answer": 5, + "Options": "a ) 4 , b ) 6 , c ) 5 , d ) 15 , e ) 20", + "Correct": "c", + "Explanation": "number of triangles can be formed out of 6 points = 6 c 3 = 20 number of quadrilaterals can be formed out of 6 points = 6 c 4 = 15 20 - 15 = 5 . answer = c" + }, + { + "Answer": 720, + "Options": "['a ) 120 m \u00b3', 'b ) 400 m \u00b3', 'c ) 660 m \u00b3', 'd ) 720 cm m \u00b3', 'e ) none']", + "Correct": "d", + "Explanation": "sol . let the length , breadth and height of the box be , l , b , and h respectively , then , volume = lbh = \u221a ( lbh ) \u00b2 = \u221a lb * bh * lh = \u221a 120 * 72 * 60 = 720 cm \u00b3 answer d" + }, + { + "Answer": 2480, + "Options": "a ) 1940 , b ) 2480 , c ) 2460 , d ) 2500 , e ) 1980", + "Correct": "b", + "Explanation": "\"area of the rhombus = 1 / 2 d 1 d 2 = ( 1 / 2 \u00e3 \u2014 62 \u00e3 \u2014 80 ) cm ( power ) 2 = 62 \u00e3 \u2014 40 = 2480 cm ( power ) 2 answer is b .\"" + }, + { + "Answer": 60, + "Options": "a ) 65 , b ) 63 , c ) 52 , d ) 60 , e ) 68", + "Correct": "d", + "Explanation": "\"area of carol ' s rectangle = 24 * 5 = 120 let width of jordan ' s rectangle = w since , the areas are equal 2 w = 120 = > w = 60 answer d\"" + }, + { + "Answer": 140, + "Options": "a ) 140 cm , b ) 767 cm , c ) 88 cm , d ) 666 cm , e ) 776 cm", + "Correct": "a", + "Explanation": "\"area of each slab = 58.8 / 30 m 2 = 1.96 m 2 length of each slab \u221a 1.96 = 1.4 m = 140 cm\"" + }, + { + "Answer": 289, + "Options": "a ) 225 , b ) 777 , c ) 266 , d ) 289 , e ) 261", + "Correct": "d", + "Explanation": "\"17 * 17 = 289 sq m answer : d\"" + }, + { + "Answer": 600, + "Options": "a ) 54 , b ) 600 , c ) 81 , d ) 108 , e ) 120", + "Correct": "b", + "Explanation": "\"volume of larger cube = 125 = 5 ^ 3 side of larger cube = 5 volume of smaller cube = 1 - - > side of smaller cube = 1 surface area of larger cube = 6 * 5 ^ 2 = 150 surface area of 27 smaller cubes = 125 * 6 * 1 = 750 difference = 750 - 150 = 600 answer : b\"" + }, + { + "Answer": 2.6, + "Options": "a ) 3.5 % , b ) 2.4 % , c ) 3 % , d ) 5 % , e ) 2.6 %", + "Correct": "e", + "Explanation": "\"let the sides of the rectangle be a and b . actual area of the rectangle without error = ab new side a ( 8 % in excess ) = a + 0.08 a = 1.08 a new side b ( 5 % in deficit ) = b - 0.05 b = 0.95 b area of the new rectangle = ( 1.08 a ) ( 0.95 b ) = ( 1.0260 ) ab say a = 1 and b = 1 area of the original rectangle = 1 area of the new rectangle = 1.026 change in the area calculation = . 026 error percentage in the area calculated = 2.6 % answer : e\"" + }, + { + "Answer": 20000, + "Options": "['a ) 20,000 square meters', 'b ) 10,000 square meters', 'c ) 30,000 square meters', 'd ) 40,000 square meters', 'e ) 50,000 square meters']", + "Correct": "a", + "Explanation": "let us first find the distance d jogged distance = rate * time = ( 12 km / hr ) * 30 minutes = ( 12 km / hr ) * 0.5 hr = 6 km the distance of 6 km corresponds to 10 perimeters and therefore 1 perimeter is equal to 6 km / 10 = 0.6 km = 0.6 * 1000 meters = 600 meters let l and w be the length and width of the field . the length is twice the width . hence l = 2 w the perimeter is 600 meters and is given by 2 ( l + w ) = 600 substitute l by 2 w 2 ( 2 w + w ) = 600 simplify and solve for w 4 w + 2 w = 600 6 w = 600 w = 100 find l l = 2 w = 200 find the area a of the rectangle a = l * w = 200 * 100 = 20,000 square meters correct answer a" + }, + { + "Answer": 8, + "Options": "a ) 24 , b ) 8 , c ) 16 , d ) 0 , e ) 4", + "Correct": "b", + "Explanation": "\"there are 64 small cubes , hence one side side of the big cube is 3 \u221a 64 = 4 cm number of small cubes having only one faces coloured = ( x - 2 ) ^ 3 here , x = side of big cube / side of small cube x = 4 / 1 x = 4 required number = ( 4 - 2 ) ^ 3 = 8 answer : b\"" + }, + { + "Answer": 6, + "Options": "['a ) 6', 'b ) 7', 'c ) 8', 'd ) 9', 'e ) 10']", + "Correct": "a", + "Explanation": "as we know that for a right angle triangle the are is 1 / 2 * base * height we know the base = 3 we need to calculate the height hypotenuse = h = 5 base = b = 3 height = c = ? as per pythagoras h ^ 2 = b ^ 2 + c ^ 2 5 ^ 2 = 3 ^ 2 + c ^ 2 25 = 9 + c ^ 2 c ^ 2 = 25 - 9 c ^ 2 = 16 c = 4 height = 4 area = 1 / 2 * base * height = 1 / 2 * 3 * 4 = 6 square units ans : a" + }, + { + "Answer": 75, + "Options": "a ) 144 , b ) 131 , c ) 115 , d ) 90 , e ) 75", + "Correct": "e", + "Explanation": "\"there are 10 business exec and in each handshake 2 business execs are involved . hence 10 c 2 = 45 also , each of 10 exec will shake hand with every 3 other chairmen for total of 30 handshake . total = 45 + 30 = 75 ans : e\"" + }, + { + "Answer": 9, + "Options": "a ) 4 , b ) 7 , c ) 8 , d ) 9 , e ) 26", + "Correct": "d", + "Explanation": "\"this question can be solved algebraically or by testing the answers . we ' re told that a rectangle has an area of 117 and a perimeter of 44 . we ' re asked for the length of one of the shorter sides of the rectangle . since the answers are all integers , and the area is 117 , the shorter side will almost certainly be less than 10 ( since 10 x 10 = 100 , but we ' re not dealing with a square ) . answer b ( 7 ) does not divide evenly into 117 , so the correct answer is let ' s test answer d : 9 if . . . the shorter side = 9 . . . the area = 117 . . . . 117 / 9 = 13 = the longer side perimeter = 9 + 9 + 13 + 13 = 44 d\"" + }, + { + "Answer": 28, + "Options": "a ) 54 , b ) 32 , c ) 75 , d ) 28 , e ) 11", + "Correct": "d", + "Explanation": "\"a / 8 = 7 * 7 = > a = 7 * 7 * 8 x * 2 x = 7 * 7 * 8 x = 14 = > 2 x = 28 answer : d\"" + }, + { + "Answer": 60, + "Options": "a ) 60 , b ) 70 , c ) 80 , d ) 90 , e ) 100", + "Correct": "a", + "Explanation": "\"the number of males is 200 - 120 = 80 . the number of males with advanced degrees is 80 - 40 = 40 . the number of females with advanced degrees is 100 - 40 = 60 . the answer is a .\"" + }, + { + "Answer": 43.99999999999999, + "Options": "a ) 38 % , b ) 40 % , c ) 44 % , d ) 48 % , e ) 50 %", + "Correct": "c", + "Explanation": "let original length = x metres and original breadth = y metres . original area = ( xy ) m 2 . new length = 120 x m = 6 x m . 100 5 new breadth = 120 y m = 6 y m . 100 5 new area = 6 x x 6 y m 2 = 36 xy m 2 . 5 5 25 the difference between the original area = xy and new - area 36 / 25 xy is = ( 36 / 25 ) xy - xy = xy ( 36 / 25 - 1 ) = xy ( 11 / 25 ) or ( 11 / 25 ) xy increase % = 11 xy x 1 x 100 % = 44 % . 25 xy c )" + }, + { + "Answer": 140, + "Options": "a ) 140 cm 2 , b ) 150 cm 2 , c ) 168 cm 2 , d ) 182 cm 2 , e ) 200 cm 2", + "Correct": "a", + "Explanation": "\"1 / 2 * 28 ( 8 + 2 ) = 140 cm 2 answer : a\"" + }, + { + "Answer": 8, + "Options": "a ) 64 , b ) 32 , c ) 8 , d ) 4 , e ) 2", + "Correct": "c", + "Explanation": "\"let the positive number be x x ^ 2 = ( ( 16 ) ^ ( 1 / 2 ) ) ^ 3 = > x ^ 2 = 4 ^ 3 = 64 = > x = 8 answer c\"" + }, + { + "Answer": 2744, + "Options": "a ) 2812 , b ) 8231 , c ) 2734 , d ) 2744 , e ) 4254", + "Correct": "d", + "Explanation": "\"a volume of 4 l can be kept in 1 hemisphere therefore , a volume of 10976 l can be kept in ( 10976 / 4 ) hemispheres ans . 2744 answer : d\"" + }, + { + "Answer": 50, + "Options": "a ) 14 , b ) 47 , c ) 50 , d ) 180 , e ) 240", + "Correct": "c", + "Explanation": "\"area = length x breadth 200 = 40 x breadth so , breadth = 5 units fencing required is - breadth + breadth + length 5 + 5 + 40 = > 50 feet answer must be ( c ) 50\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 8 , c ) 6 , d ) 10 , e ) 16", + "Correct": "a", + "Explanation": "\"1 ) draw a simple cube 2 ) draw 9 squares on each face of the cube ( so that it looks like a rubik ' s cube ) - this is what the cube will look like when it ' s cut into 27 equal smaller cubes . 3 ) remember that the outside of the cube is the part that ' s painted . . . . the mini - cubes with 2 painted sides are all on the edge of the cube , in themiddleof the edge . there are 4 in front , 4 in back and 4 more on thestripthat runs around the left / top / right / bottom of the cube . p = 4 + 4 + 4 = 12 . answer a\"" + }, + { + "Answer": 1250, + "Options": "a ) 1350 , b ) 1971 , c ) 9676 , d ) 1679 , e ) 1250", + "Correct": "e", + "Explanation": "\"area = ( l + b + 2 d ) 2 d = ( 65 + 55 + 2.5 * 2 ) 2 * 2.5 = > 625 625 * 2 = rs . 1250 answer : e\"" + }, + { + "Answer": 32, + "Options": "a ) 32 . , b ) 40 . , c ) 42 . , d ) 44 . , e ) 46 .", + "Correct": "a", + "Explanation": "\"answer is a : 42 let w be the width , so length is 3 w . therefore : w * 4 w = 768 , solving for , w = 16 , so 3 w - w = 2 w = 2 * 16 = 32\"" + }, + { + "Answer": 192, + "Options": "a ) 432 sq m , b ) 192 sq m , c ) 452 sq m , d ) 428 sq m , e ) 528 sq m", + "Correct": "b", + "Explanation": "\"2 ( 3 x + x ) = 64 l = 24 b = 8 lb = 24 * 8 = 192 answer : b\"" + }, + { + "Answer": 512, + "Options": "a ) 8 cc , b ) 9 cc , c ) 512 cc , d ) 4 cc , e ) 6 cc", + "Correct": "c", + "Explanation": "\"6 a 2 = 384 = 6 * 64 a = 8 = > a 3 = 512 cc answer : c\"" + }, + { + "Answer": 33.333333333333336, + "Options": "a ) 20 cm , b ) 25 cm , c ) 26 cm , d ) 100 / 3 cm , e ) 23 cm", + "Correct": "d", + "Explanation": "explanation : let breadth = x . then , length = 2 x . then , ( 2 x - 5 ) ( x + 4 ) - 2 x * x = 75 = > 3 x - 25 = 75 = > x = 100 / 3 . length of the rectangle = 100 / 3 cm . answer : option d" + }, + { + "Answer": 8, + "Options": "['a ) 1 : 4', 'b ) 8 : 1', 'c ) 4 : 1', 'd ) 3 : 1', 'e ) 1 : 3']", + "Correct": "b", + "Explanation": "a - - - - - - - - - - - - b - - - - - - - - e | | 50 % | g - - - - - - - - - - - - | - - - - - - - - f | | | 75 % | d - - - - - - - - - - - c remaining square 75 % and remaining rectangle 50 % rectangle share 25 % area of square so , ab x ag = ( ad x ab ) / 4 ad = 4 ag - - - - - - - - - - - - - - - - - - ( 1 ) square share half the area of rectangle so , ag x ab = ( ae x ag ) / 2 ab = ae / 2 - - - - - - - - - - - - - - - - - - ( 2 ) in square all sides are equal i . e . ab = bc = cd = ad so , equation ( 1 ) and ( 2 ) both are equal ae / 2 = 4 ag ae / ag = 8 ae : ag = 8 : 1 answer : b" + }, + { + "Answer": 26, + "Options": "a ) 34 , b ) 40 , c ) 68 , d ) 88 , e ) 26", + "Correct": "e", + "Explanation": "\"we have : l = 20 ft and lb = 60 sq . ft . so , b = 3 ft . length of fencing = ( l + 2 b ) = ( 20 + 6 ) ft = 26 ft . answer : e\"" + }, + { + "Answer": 6, + "Options": "['a ) 4 tiles', 'b ) 5 tiles', 'c ) 6 tiles', 'd ) 7 tiles', 'e ) 8 tiles']", + "Correct": "c", + "Explanation": "lcm of 16,24 = 48 48 * 48 is the minimum size of square made with 16 by 24 tiles number of tiles required = area of square / area of one tile = 48 * 48 / ( 16 * 24 ) = 6 tiles answer : c" + }, + { + "Answer": 144, + "Options": "a ) 144 , b ) 121 , c ) 169 , d ) 196 , e ) 100", + "Correct": "a", + "Explanation": "\"we know that the perimeter of square = 4 \u00e3 \u2014 side side = 12 cm therefore , perimeter = 4 \u00e3 \u2014 12 cm = 48 cm now , area of the square = ( side \u00e3 \u2014 side ) sq . units = 12 \u00e3 \u2014 12 cm \u00e2 \u00b2 = 144 cm \u00e2 \u00b2 answer : a\"" + }, + { + "Answer": 200, + "Options": "['a ) rs . 200', 'b ) rs . 672', 'c ) rs . 546', 'd ) rs . 876', 'e ) none of these']", + "Correct": "a", + "Explanation": "explanation : surface area of a cube = 6 x 5 ^ 2 = 150 sq . ft quantity of paint required = ( 150 / 15 ) = 10 kg cost of painting = 20 x 10 = rs . 200 answer : a" + }, + { + "Answer": 90, + "Options": "['a ) 90', 'b ) 110', 'c ) 130', 'd ) 140', 'e ) 150']", + "Correct": "a", + "Explanation": "the triangle with sides 26 cm , 18 cm and 10 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 18 * 10 = 90 cm 2 answer : option a" + }, + { + "Answer": 3, + "Options": "a ) 3 , b ) 8 , c ) 12 , d ) 16 , e ) 18", + "Correct": "a", + "Explanation": "\"let length of rectangle = l 3 ^ 2 = l * 3 = > l = 9 / 3 = 3 answer a\"" + }, + { + "Answer": 5, + "Options": "a ) 2 , b ) 4 , c ) 5 , d ) 8 , e ) 12", + "Correct": "c", + "Explanation": "\"we can find the radius of all the three cases of cylinders . the only crux to find the answer faster is that : voulme is pi * r ^ 2 * h . the volume is a function of r ^ 2 . so r has to be the highest to find the largest volume . so r = 5 for the surface 8 * 12 face . volume = 125 pi answer c\"" + }, + { + "Answer": 20, + "Options": "a ) 18 square meters , b ) 20 square meters , c ) 24 square meters , d ) 28 square meters , e ) 30 square meters", + "Correct": "b", + "Explanation": "\"total = rug 1 + rug 2 + rug 3 - { overlap of exactly 2 rugs } - 2 * { overlap of exactly 3 rugs } 140 = 204 - 24 - 2 * { overlap of exactly 2 rugs } - - > { overlap of exactly 3 rugs } = 20 . answer : b .\"" + }, + { + "Answer": 4725, + "Options": "a ) 4350 , b ) 4725 , c ) 4328 , d ) 4329 , e ) 4829", + "Correct": "b", + "Explanation": "\"area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 2.5 * 2 ) 2 * 2.5 = > 675 675 * 7 = rs . 4725 answer : b\"" + }, + { + "Answer": 139, + "Options": "['a ) 128', 'b ) 158', 'c ) 178', 'd ) 139', 'e ) 140']", + "Correct": "d", + "Explanation": "root 92555 = 304.228 and 304 ^ 2 = 92416 92555 - 92416 = 139 should be subtracted from 92555 to make it a perfect square answer : d" + }, + { + "Answer": 108, + "Options": "a ) 96 , b ) 100 , c ) 104 , d ) 108 , e ) 112", + "Correct": "d", + "Explanation": "\"2 hl + 2 hw = 2 lw h = lw / ( l + w ) volume = lwh = ( lw ) ^ 2 / ( l + w ) = 108 the answer is d .\"" + }, + { + "Answer": 96, + "Options": "a ) 73 , b ) 32 , c ) 34 , d ) 43 , e ) 96", + "Correct": "e", + "Explanation": "\"explanation : a / 72 = 8 * 8 = > a = 8 * 8 * 72 x * 2 x = 8 * 8 * 72 x = 48 = > 2 x = 96 answer : option e\"" + }, + { + "Answer": 226.98006922186255, + "Options": "a ) 154 cm 2 , b ) 308 m 2 , c ) 227 m 2 , d ) 407 m 2 , e ) none of these", + "Correct": "c", + "Explanation": "\"area of the shaded portion = 1 \u2044 4 \u00d7 \u03c0 \u00d7 ( 17 ) 2 = 227 m 2 answer c\"" + }, + { + "Answer": 704, + "Options": "a ) 281 , b ) 284 , c ) 704 , d ) 640 , e ) 920", + "Correct": "c", + "Explanation": "\"area of a parallelogram = base * height = 32 * 22 = 704 cm 2 answer : c\"" + }, + { + "Answer": 2600, + "Options": "a ) 2288 , b ) 2779 , c ) 2779 , d ) 3900 , e ) 2600", + "Correct": "e", + "Explanation": "\"area = ( l + b \u00e2 \u20ac \u201c d ) d ( 80 + 60 \u00e2 \u20ac \u201c 10 ) 10 = > 1300 m 2 1300 * 2 = rs . 2600 answer : e\"" + }, + { + "Answer": 2, + "Options": "a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) none of the above", + "Correct": "a", + "Explanation": "\"the answer is a it takes 3 distinct points to define a circle . only 2 are given here . the two points essentially identify a single chord of the circle c . since no other information is provided , however , the radius of the circle can essentially be anything . all this information tell us is that the radius isgreater 2\"" + }, + { + "Answer": 30, + "Options": "['a ) 24', 'b ) 26', 'c ) 28', 'd ) 30', 'e ) 32']", + "Correct": "d", + "Explanation": "area of first rectangle is 12 * 15 = 180 hence area of second would be 6 x = 180 x x = 30 answer is d" + }, + { + "Answer": 24, + "Options": "['a ) 24', 'b ) 64', 'c ) 81', 'd ) 108', 'e ) 120']", + "Correct": "a", + "Explanation": "volume of larger cube = 8 = 2 ^ 3 side of larger cube = 2 volume of smaller cube = 1 - - > side of smaller cube = 1 surface area of larger cube = 6 * 2 ^ 2 = 24 surface area of 27 smaller cubes = 8 * 6 * 1 = 48 difference = 48 - 24 = 24 answer : a" + }, + { + "Answer": 12, + "Options": "['a ) 5 m', 'b ) 12 m', 'c ) 13 m', 'd ) 14.5 m', 'e ) 15.5 m']", + "Correct": "b", + "Explanation": "let , length = x meters and breadth = y meters then xy = 60 and ( x 2 + y 2 ) + x = 5 therefore , x = 60 and ( x 2 + y 2 ) = ( 5 y - x ) 2 or xy = 60 and 24 y 2 - 10 xy = 0 . therefore , 24 y 2 - 10 * 60 = 0 or y 2 = 25 or = 5 . therefore , x = ( 60 / 5 ) m = 12 m . so , length of the carpet = 12 m answer : b" + }, + { + "Answer": 8, + "Options": "['a ) a 8', 'b ) b 22', 'c ) c 27', 'd ) d 40', 'e ) e 51']", + "Correct": "a", + "Explanation": "l = 48 / 12 = 4 ft w = 72 / 12 = 6 ft area of paper = 24 area of cube = 4 * side ^ 2 side of cube = 2 v of cube = 8" + }, + { + "Answer": 287.9999999999999, + "Options": "a ) 123 , b ) 167 , c ) 178 , d ) 199 , e ) 288", + "Correct": "e", + "Explanation": "\"lets suppose length = l , breadth = b , depth = d front face area = l * w = 1 / 2 w * d ( l = 1 / 2 d or d = 2 l ) top face area = w * d side face area = w * d = 1.5 d * l ( w = 1.5 l ) volume = l * w * d = 5184 l * 1.5 l * 2 l = 5184 l = 12 side face area = l * d = l * 2 l = 12 * 2 * 12 = 288 e is the answer\"" + }, + { + "Answer": 276, + "Options": "a ) 200 , b ) 276 , c ) 230 , d ) 240 , e ) 250", + "Correct": "b", + "Explanation": "\"let no of sits in vip enclosure is x then x * 45 + 20 ( 320 - x ) = 7500 or 25 x = 7500 - 6400 , x = 1100 / 25 = 44 vip = 44 general 320 - 44 = 276 b\"" + }, + { + "Answer": 225, + "Options": "a ) $ 200 , b ) $ 240 , c ) $ 480 , d ) $ 225 , e ) $ 1,920", + "Correct": "d", + "Explanation": "\"the width of the rectangular floor ( 6 m ) is a multiple of one side of the square ( 2 m ) , and the length of the floor ( 10 m ) is also a multiple of the side of the square . so the number of carpets to cover the floor is ( 6 / 2 ) * ( 10 / 2 ) = 15 . the total cost is 15 * 15 = $ 225 . the answer is , therefore , d .\"" + }, + { + "Answer": 100, + "Options": "a ) 50 % , b ) 87 % , c ) 100 % , d ) 187 % , e ) 200 %", + "Correct": "c", + "Explanation": "\"let ' s just look at the dimensions ( no calculation needed ) . with dimension 11 the same , the other dimension 9 is twice 4.5 then the area will be double which means 100 % greater . the answer is c .\"" + }, + { + "Answer": 90, + "Options": "a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90", + "Correct": "e", + "Explanation": "\"let l be the length and w be the width . l = ( 7 / 5 ) w perimeter : 2 l + 2 w = 432 , 2 ( 7 / 5 ) w + 2 w = 432 solve the above equation to find : w = 90 m and l = 126 m . correct answer e ) 90\"" + }, + { + "Answer": 2520, + "Options": "['a ) 1220 m ^ 2', 'b ) 1520 m ^ 2', 'c ) 2520 m ^ 2', 'd ) 2600 m ^ 2', 'e ) 3420 m ^ 2']", + "Correct": "c", + "Explanation": "we have : ( l - b ) = 23 and 2 ( l + b ) = 206 or ( l + b ) = 103 . solving the two equations , we get : l = 63 and b = 40 . area = ( l x b ) = ( 63 x 40 ) m 2 = 2520 m ^ 2 c" + }, + { + "Answer": 2812, + "Options": "a ) 2812 , b ) 8231 , c ) 2734 , d ) 4222 , e ) 4254", + "Correct": "a", + "Explanation": "\"a volume of 4 l can be kept in 1 hemisphere therefore , a volume of 11248 l can be kept in ( 11248 / 4 ) hemispheres ans . 2812 answer : a\"" + }, + { + "Answer": 8, + "Options": "a ) 9 , b ) 2 , c ) 12 , d ) 14 , e ) 8", + "Correct": "e", + "Explanation": "let the numbers be x and y then x 2 - y 2 = 39 and x - y = 3 we get x + y = 13 solving x - y = 3 , x + y = 13 x = 8 , y = 5 larger number 8 answer e" + }, + { + "Answer": 150, + "Options": "a ) 188 cm 2 , b ) 150 cm 2 , c ) 168 cm 2 , d ) 198 cm 2 , e ) 987 cm 2", + "Correct": "b", + "Explanation": "\"1 / 2 * 20 ( 9 + 6 ) = 150 cm 2 answer : b\"" + }, + { + "Answer": 0.3055555555555555, + "Options": "['a ) 11 / 36', 'b ) 23 / 10', 'c ) 5 / 14', 'd ) 22 / 11', 'e ) 3 / 4']", + "Correct": "a", + "Explanation": "the questions asks us to find the surface which is not covered by the plate i . e . , area of the surface not covered . where as circumference is the length along the edge of the circle , 2 * pi * r implies the length of the curve pi * r ^ 2 implies area enclosed by that curve . . hence area of the circle is considered for this problem area of the big plate = pi * r ^ 2 , where r = 6 = > pi * 36 area of the small plate = pi * 25 surface not covered by the plate = pi * 36 - pi * 25 = pi * 11 fraction of big plate ' s surface is not covered by small plate = pi * 11 / total area of the big plate = > pi * 11 / pi * 36 answer a" + }, + { + "Answer": 0.1, + "Options": "a ) 1 / 10 , b ) 2 / 10 , c ) 3 / 10 , d ) 4 / 10 , e ) 5 / 10", + "Correct": "a", + "Explanation": "total no . of triangles that can b made with the vetices hexagon = 6 c 3 = 20 no . of possible outcomes i . e . no . of equality triangles = 2 . . ' . probability = 2 / 20 = 1 / 10 answer : a" + }, + { + "Answer": 36, + "Options": "a ) 38 . , b ) 40 . , c ) 36 . , d ) 44 . , e ) 46 .", + "Correct": "c", + "Explanation": "\"let the width = x x * 4 x = 576 x ^ 2 = 144 x = 12 length = 4 * 12 = 48 difference = 48 - 12 = 36 c is the answer\"" + }, + { + "Answer": 9801, + "Options": "a ) 9801 , b ) 10,000 , c ) 14,400 , d ) 12,696 , e ) can not be determined", + "Correct": "a", + "Explanation": "\"let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 197 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 197 ( x + y ) ( x - y ) = 197 197 is a prime number and thus it will be ( 99 + 98 ) * ( 99 - 98 ) . thus x = 99 and y = 98 x ^ 2 = 99 ^ 2 = 9801 the answer is a .\"" + }, + { + "Answer": 5, + "Options": "a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25", + "Correct": "a", + "Explanation": "\"l * w = 50 : area , l is the length and w is the width . 2 l + 2 w = 30 : perimeter l = 15 - w : solve for l ( 15 - w ) * w = 30 : substitute in the area equation w = 5 and l = 10 correct answer a\"" + }, + { + "Answer": 180, + "Options": "a ) 140 , b ) 150 , c ) 160 , d ) 170 , e ) 180", + "Correct": "e", + "Explanation": "\"given that the area of the square = 2025 sq . units = > side of square = \u221a 2025 = 45 units the radius of the circle = side of the square = 45 units length of the rectangle = 2 / 5 * 45 = 18 units given that breadth = 10 units area of the rectangle = lb = 18 * 10 = 180 sq . units answer : option e\"" + }, + { + "Answer": 125, + "Options": "['a ) 125 %', 'b ) 129 %', 'c ) 185 %', 'd ) 725 %', 'e ) 145 %']", + "Correct": "a", + "Explanation": "let the edge = a cm so increase by 50 % = = total surface area of original cube = tsa of new cube = = = increase in area = = increase % = = 125 % answer : a" + }, + { + "Answer": 8, + "Options": "['a ) 8 cm', 'b ) 9 cm', 'c ) 10 cm', 'd ) 11 cm', 'e ) 12 cm']", + "Correct": "a", + "Explanation": "d 1 = 4 ? 2 = > area = 1 / 2 d 12 = 1 / 2 * ( 4 ? 2 ) 2 = 16 cm 2 area of new square = ( 2 * 16 ) cm 2 = 32 cm 2 therefore 1 / 2 * d 22 = 32 = > d 22 = 64 = > d 2 = 8 cm answer a" + }, + { + "Answer": 2734, + "Options": "['a ) 2812', 'b ) 8231', 'c ) 2734', 'd ) 4222', 'e ) 4254']", + "Correct": "c", + "Explanation": "a volume of 4 l can be kept in 1 hemisphere therefore , a volume of 10936 l can be kept in ( 10936 / 4 ) hemispheres ans . 2734 answer : c" + }, + { + "Answer": 192, + "Options": "['a ) 185', 'b ) 132', 'c ) 165', 'd ) 192', 'e ) 212']", + "Correct": "d", + "Explanation": "breadth = \u221a 20 ^ 2 - 16 ^ 2 = \u221a 144 = 12 cm area = 16 * 12 = 192 sq . cm answer d" + }, + { + "Answer": 216, + "Options": "['a ) 90 \u00b0', 'b ) 135 \u00b0', 'c ) 216 \u00b0', 'd ) 240 \u00b0', 'e ) 270 \u00b0']", + "Correct": "c", + "Explanation": "the percent of the budget for salaries is 100 - ( 20 + 9 + 5 + 4 + 2 ) = 60 % 100 % of the circle is 360 degrees . then ( 60 % / 100 % ) * 360 = 216 degrees the answer is c ." + }, + { + "Answer": 50, + "Options": "a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 65 %", + "Correct": "c", + "Explanation": "\"let original length = x and original breadth = y . original area = xy . new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c\"" + }, + { + "Answer": 485.99999999999983, + "Options": "a ) 486 , b ) 556 , c ) 255 , d ) 287 , e ) 267", + "Correct": "a", + "Explanation": "\"a 3 = 729 = > a = 9 6 a 2 = 6 * 9 * 9 = 486 answer : a\"" + }, + { + "Answer": 32, + "Options": "['a ) 16', 'b ) 20', 'c ) 36', 'd ) 32', 'e ) 28']", + "Correct": "d", + "Explanation": "volume of cube = lbh = 4 new cube l , b , h are increases of 2 l , 2 b , 2 h new volume of cube = 2 l * 2 b * 2 h = 8 * lbh = 8 * 4 = 32 answer : d" + }, + { + "Answer": 48, + "Options": "['a ) 48', 'b ) 56', 'c ) 68', 'd ) 87', 'e ) 92']", + "Correct": "a", + "Explanation": "sol . monthly rent per square feet = 1440 / ( 20 * 18 ) = 4 & annual rent per square feet = 12 * 4 = 48 answer : a" + }, + { + "Answer": 10000, + "Options": "['a ) 10000', 'b ) 10008', 'c ) 10005', 'd ) 10004', 'e ) 10001']", + "Correct": "a", + "Explanation": "100 * 100 = 10000 125 * 80 = 10000 no change answer : a" + }, + { + "Answer": 48, + "Options": "['a ) 48', 'b ) 49', 'c ) 50', 'd ) 51', 'e ) 52']", + "Correct": "a", + "Explanation": "no . of such cubes = volume of material / volume of one cube ( 12 * 18 * 6 ) / ( 3 * 3 * 3 ) = 48 answer : a" + }, + { + "Answer": 1200, + "Options": "['a ) 1100', 'b ) 1200', 'c ) 1300', 'd ) 1400', 'e ) 1500']", + "Correct": "b", + "Explanation": "area of 4 wall = sum of area of floor and celling 2 ( l + b ) * h = 2 ( l * b ) ( 15 + 12 ) * h = 2 ( 12 * 15 ) on solving h = 20 / 3 m volume = l * b * h = 12 * 15 * 20 / 3 = 1200 m ^ 3 answer : b" + }, + { + "Answer": 148, + "Options": "a ) 124 m 2 , b ) 128 m 2 , c ) 138 m 2 , d ) 148 m 2 , e ) none of these", + "Correct": "d", + "Explanation": "\"area of the outer rectangle = 25 \u00e3 \u2014 16 = 400 m 2 area of the inner rectangle = 21 \u00e3 \u2014 12 = 252 m 2 required area = ( 400 \u00e2 \u20ac \u201c 252 ) = 148 m 2 answer d\"" + }, + { + "Answer": 240, + "Options": "a ) 180 , b ) 270 , c ) 340 , d ) 140 , e ) 240", + "Correct": "e", + "Explanation": "\"sol . x * 8 x = 6 * 1200 x = 30 length = 8 * 30 = 240 e\"" + }, + { + "Answer": 720, + "Options": "['a ) 259200 cm 3', 'b ) 86400 cm 3', 'c ) 720 cm 3', 'd ) can not be determined', 'e ) none of these']", + "Correct": "c", + "Explanation": "volume of the box = \u221a 120 \u00d7 72 \u00d7 60 = 720 cm 3 answer c" + }, + { + "Answer": 44, + "Options": "a ) 42 % , b ) 43 % , c ) 45 % , d ) 44 % , e ) 46 %", + "Correct": "d", + "Explanation": "let original length = l original breadth = b then original area = lb length is increased by 20 % \u21d2 new length = l \u00d7 120100 = 1.2 l breadth is increased by 20 % \u21d2 new breadth = b \u00d7 120100 = 1.2 b new area = 1.2 l \u00d7 1.2 b = 1.44 lb increase in area = new area - original area = 1.44 lb \u2212 lb = 0.44 lb percentage increase in area = increase in areaoriginal area \u00d7 100 = 0.44 lblb \u00d7 100 = 44 % answer is d ." + }, + { + "Answer": 9, + "Options": "['a ) 9', 'b ) 10', 'c ) 11', 'd ) 12', 'e ) 13']", + "Correct": "a", + "Explanation": "the triangle is symmetric about the x - axis . the part above the x - axis forms a triangle with a base of 3 and a height of 3 . the area of this part is ( 1 / 2 ) ( 3 ) ( 3 ) . we can double this to find the area of the whole triangle . the total area is ( 2 ) ( 1 / 2 ) ( 3 ) ( 3 ) = 9 . the answer is a ." + }, + { + "Answer": 1, + "Options": "['a ) 9 % less', 'b ) 1 % less', 'c ) equal to each other', 'd ) 1 % more', 'e ) 9 % more']", + "Correct": "b", + "Explanation": "base of a = 11 / 10 * base of b height of a = 9 / 10 * height of b area of a = ( 1 / 2 ) * base of a * height of a = 11 / 10 * 9 / 10 * area of b = 99 / 100 * area of b area of a is 1 % less than the area of b . answer ( b )" + }, + { + "Answer": 3740, + "Options": "a ) s . 3944 , b ) s . 3948 , c ) s . 3942 , d ) s . 3965 , e ) s . 3740", + "Correct": "e", + "Explanation": "\"let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 55 = rs . 3740 . answer : e\"" + }, + { + "Answer": 32, + "Options": "['a ) 27', 'b ) 43', 'c ) 11', 'd ) 32', 'e ) 45']", + "Correct": "d", + "Explanation": "d 32 the next cube number below 64 ( 4 \u00d7 4 \u00d7 4 ) is 27 ( 3 \u00d7 3 \u00d7 3 ) . in order to construct a solid cube , therefore , with none left over , 59 \u2013 27 = 32 blocks need to be taken away ." + }, + { + "Answer": 4, + "Options": "a ) 5 % , b ) 10 % , c ) 15 % , d ) 14 % , e ) 4 %", + "Correct": "e", + "Explanation": "\"let diameter of circle r , dr = 20 and diameter of circle s , ds = 100 radius of circle r , rr = 10 radius of circle s , rs = 50 area of circle r / area of circle s = ( pi * rr ^ 2 ) / ( pi * rs ^ 2 ) = ( 10 / 50 ) ^ 2 = ( 2 / 10 ) ^ 2 = 4 % answer : e\"" + }, + { + "Answer": 3, + "Options": "a ) 5 m , b ) 4 m , c ) 2 m , d ) 3 m , e ) 6 m", + "Correct": "d", + "Explanation": "\"area of the park = 60 * 40 = 2400 m ^ 2 given area of the lawn = 2109 m ^ 2 total area of the cross roads = 2400 - 2109 = 291 m ^ 2 assume that the width of the cross road = x = area of road 1 + road 2 - common area cross road = 60 x + 40 x - x ^ 2 total area of cross road = 60 x + 40 x - x ^ 2 = 291 m ^ 2 ( x - 97 ) ( x - 3 ) = 0 x = 3 answer d\"" + }, + { + "Answer": 192.28324559588634, + "Options": "['a ) 168 cm \u00b3', 'b ) 192 cm \u00b3', 'c ) 228 cm \u00b3', 'd ) 236 cm \u00b3', 'e ) none']", + "Correct": "b", + "Explanation": "sol . difference in capacities = [ 8 * 8 * 14 - 22 / 7 * 4 * 4 * 14 ] cm \u00b3 = 192 cm \u00b3 answer b" + }, + { + "Answer": 338, + "Options": "a ) 287 , b ) 269 , c ) 338 , d ) 200 , e ) 230", + "Correct": "c", + "Explanation": "\"d 2 / 2 = ( 26 * 26 ) / 2 = 338 answer : c\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 8 , c ) 6 , d ) 10 , e ) 16", + "Correct": "a", + "Explanation": "\"1 ) draw a simple cube 2 ) draw 9 squares on each face of the cube ( so that it looks like a rubik ' s cube ) - this is what the cube will look like when it ' s cut into 27 equal smaller cubes . 3 ) remember that the outside of the cube is the part that ' s painted . . . . the mini - cubes with 2 painted sides are all on the edge of the cube , in themiddleof the edge . there are 4 in front , 4 in back and 4 more on thestripthat runs around the left / top / right / bottom of the cube . j = 4 + 4 + 4 = 12 . answer a\"" + }, + { + "Answer": 1296, + "Options": "['a ) 1296', 'b ) 1369', 'c ) 1681', 'd ) 1764', 'e ) 2500']", + "Correct": "a", + "Explanation": "let \u2019 s call the two perfect squares x ^ 2 and y ^ 2 , respectively . then the given information translates as x ^ 2 + 148 = y ^ 2 . subtracting x ^ 2 gives 148 = y ^ 2 \u2212 x ^ 2 , a difference of squares . this , in turn , factors as ( y + x ) ( y \u2212 x ) = 148 . the next step is tricky . it begins with factoring 148 , which breaks down as 2 \u2217 2 \u2217 37 . since we \u2019 re dealing with perfect squares , x and y are positive integers , and ( y + x ) and ( y \u2212 x ) must be paired integer factors of 148 . the options are 148 \u2217 1,74 \u2217 2 , and 37 \u2217 4 . but our number properties establish that ( y + x ) and ( y \u2212 x ) must be either both odd or both even , so only 74 \u2217 2 is an actual possibility . and because for any positive integers ( y + x ) > ( y \u2212 x ) , we can conclude that y + x = 74 and y \u2013 x = 2 . solving by elimination , 2 y = 76 , y = 38 , and x = 36 . finally , we just need to square 36 . but rather than multiplying it out , note that 36 ^ 2 ends in 6 \u2013 as does only one answer , choice a . this answer must be the one we want ." + }, + { + "Answer": 49, + "Options": "a ) 5 square inches , b ) 10 square inches , c ) 49 square inches , d ) 25 square inches , e ) 350 square inches", + "Correct": "c", + "Explanation": "\"in the first case each can buy one pizza of $ 10 and one pizza of $ 20 . in square inches that would be ( 14 * 14 = 196 ) for the small pizza and ( 21 * 21 = 441 ) for the large pizza . in total sq inches that would be ( 196 + 441 ) * 2 = 1274 sq inches . in the second case if they pool their money together they can buy 3 large pizzas . in terms of square inches that would be 3 * 441 = 1323 sq inches . hence , the difference is 49 square inches more ( 1323 - 1274 ) . the correct answer is c\"" + }, + { + "Answer": 307.8760800517997, + "Options": "a ) 308 , b ) 369 , c ) 434 , d ) 476 , e ) 513", + "Correct": "a", + "Explanation": "\"cone curved surface area = \u00ef \u20ac rl 22 / 7 \u00e3 \u2014 7 \u00e3 \u2014 14 = 22 \u00e3 \u2014 14 = 308 m ( power 2 ) answer is a .\"" + }, + { + "Answer": 1323, + "Options": "['a ) 1299', 'b ) 1305', 'c ) 1311', 'd ) 1317', 'e ) 1323']", + "Correct": "e", + "Explanation": "the total number of ways we can choose three dots is 21 c 3 = 1330 . we can form seven equilateral triangles from these twenty - one dots . there are 1330 - 7 = 1323 combinations which do not form an equilateral triangle . the answer is e ." + }, + { + "Answer": 87.98229536926875, + "Options": "['a ) 76', 'b ) 55', 'c ) 88', 'd ) 21', 'e ) 11']", + "Correct": "c", + "Explanation": "the area of circle = pie * r ^ 2 = 616 = > r = 14 2 * 22 / 7 * 14 = 88 answer : c" + }, + { + "Answer": 141.3716694115407, + "Options": "a ) 26 , b ) 134 , c ) 141 , d ) 190 , e ) 28", + "Correct": "c", + "Explanation": "\"\u03c0 * 15 * 3 = 141 answer : c\"" + }, + { + "Answer": 288, + "Options": "a ) 54 , b ) 64 , c ) 81 , d ) 288 , e ) 120", + "Correct": "d", + "Explanation": "\"volume of larger cube = 64 = 4 ^ 3 side of larger cube = 4 volume of smaller cube = 1 - - > side of smaller cube = 1 surface area of larger cube = 6 * 4 ^ 2 = 96 surface area of 27 smaller cubes = 64 * 6 * 1 = 384 difference = 384 - 96 = 288 answer : d\"" + }, + { + "Answer": 75, + "Options": "a ) a ) 72 , b ) b ) 828 , c ) c ) 729 , d ) d ) 75 , e ) e ) 35", + "Correct": "d", + "Explanation": "\"explanation : area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 60 / 2 = 35 cm 2 answer : option d\"" + }, + { + "Answer": 400, + "Options": "a ) 200 sq m , b ) 186 sq m , c ) 586 sq m , d ) 287 sq m , e ) 400 sq m", + "Correct": "e", + "Explanation": "\"20 * 20 = 400 sq m answer : e\"" + }, + { + "Answer": 43.99999999999999, + "Options": "a ) 44 % , b ) 46 % , c ) 48 % , d ) 50 % , e ) 51 %", + "Correct": "a", + "Explanation": "\"let original length = x metres and original breadth = y metres . original area = ( xy ) m 2 . new length = 120 x m = 6 x m . 100 5 new breadth = 120 y m = 6 y m . 100 5 new area = 6 x x 6 y m 2 = 36 xy m 2 . 5 5 25 the difference between the original area = xy and new - area 36 / 25 xy is = ( 36 / 25 ) xy - xy = xy ( 36 / 25 - 1 ) = xy ( 11 / 25 ) or ( 11 / 25 ) xy increase % = 11 xy x 1 x 100 % = 44 % . 25 xy a\"" + }, + { + "Answer": 6, + "Options": "['a ) 3', 'b ) 4', 'c ) 5', 'd ) 6', 'e ) 7']", + "Correct": "d", + "Explanation": "if n is a perfect square and a perfect cube , then n = a ^ 6 for some integer a . the numbers are 1 ^ 6 = 1 , 2 ^ 6 = 64 , 3 ^ 6 = 729 , 4 ^ 6 = 4096 , 5 ^ 6 = 15,625 , 6 ^ = 46,656 . the answer is d ." + }, + { + "Answer": 7, + "Options": "['a ) 4', 'b ) 5', 'c ) 6', 'd ) 7', 'e ) 8']", + "Correct": "d", + "Explanation": "5 * 8 ^ 2 + 2 * 8 ^ 1 + 4 * 8 ^ 0 = 6 * k ^ 2 + 6 * k ^ 1 + 4 * k ^ 0 320 + 16 + 4 = 6 ( k ^ 2 ) + 6 k + 4 340 = 6 ( k ^ 2 ) + 6 k + 4 6 ( k ^ 2 ) + 6 k + 4 - 340 = 0 6 ( k ^ 2 ) + 6 k - 336 = 0 dividing by 6 ; ( k ^ 2 ) + k - 56 = 0 solving this quadratic equation we get , k = 7 and k = - 8 thus k = 7 answer : d" + }, + { + "Answer": 4456.443887106987, + "Options": "['a ) rs . 4000', 'b ) rs . 4450', 'c ) rs . 4457', 'd ) rs . 4560', 'e ) rs . 5457']", + "Correct": "c", + "Explanation": "area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . \u03c0 r 2 = 175600 \u21d4 ( r ) 2 = ( 175600 x ( 7 / 22 ) ) \u21d4 r = 236.37 m . circumference = 2 \u03c0 r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 3 ) = rs . 4457 . c" + }, + { + "Answer": 100, + "Options": "['a ) 400 %', 'b ) 200 %', 'c ) 300 %', 'd ) 100 %', 'e ) 800 %']", + "Correct": "d", + "Explanation": "the area of the circle is increased by 300 % , thus the area is increased 4 times . the area of a circle it proportional to the square of the diameter ( area = \u03c0 d ^ 2 / 4 ) , therefore the diameter must increase 2 times ( diameter increase 2 times = area increase 4 times ) , which is increase by 100 % . answer : d ." + }, + { + "Answer": 800, + "Options": "a ) 802 , b ) 800 , c ) 829 , d ) 389 , e ) 245", + "Correct": "b", + "Explanation": "\"area of the square = s * s = 5 ( 125 * 64 ) = > s = 25 * 8 = 200 cm perimeter of the square = 4 * 200 = 800 cm . answer : b\"" + }, + { + "Answer": 989.6016858807849, + "Options": "['a ) 660', 'b ) 770', 'c ) 880', 'd ) 900', 'e ) 990']", + "Correct": "e", + "Explanation": "cone curved surface area = \u00ef \u20ac rl 22 / 7 \u00e3 \u2014 21 \u00e3 \u2014 15 = 66 \u00e3 \u2014 15 = 990 m ( power 2 ) answer is e ." + }, + { + "Answer": 11.111111111111107, + "Options": "a ) 10 % , b ) 11.1 % , c ) 25 % , d ) 30 % , e ) 35 %", + "Correct": "b", + "Explanation": "\"sol . required change = ( 10 * 100 ) / ( 100 - 10 ) = 11.1 % b\"" + }, + { + "Answer": 48, + "Options": "['a ) 18 m', 'b ) 28 m', 'c ) 38 m', 'd ) 42 m', 'e ) 48 m']", + "Correct": "e", + "Explanation": "area of square = side \u00d7 side given ; area of square = 144 m \u00b2 therefore , side \u00b2 = 144 m \u00b2 therefore , side = \u221a ( 144 m \u00b2 ) = \u221a ( 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 3 ) m \u00b2 = 2 \u00d7 2 \u00d7 3 m = 12 m now , the perimeter of the square = 4 x side = 4 \u00d7 12 m = 48 m answer : e" + }, + { + "Answer": 9, + "Options": "a ) 4 , b ) 8 , c ) 12 , d ) 9 , e ) 18", + "Correct": "d", + "Explanation": "\"let length of rectangle = l 6 ^ 2 = l * 4 = > l = 36 / 4 = 9 answer d\"" + }, + { + "Answer": 3.9999999999999996, + "Options": "['a ) 4', 'b ) 5', 'c ) 7', 'd ) 8', 'e ) 9']", + "Correct": "a", + "Explanation": "if sides are 7 , vol = 7 ^ 3 = 343 75 % = 257.25 , 85 % = 291.55 so vol above water , between 85.75 and 51.45 - - > too big if side are 4 , vol = 64 75 % = 48 , 85 % = 54.4 vol above water between 16 and 9.6 so 4 should be the answer . check option c , if sides are 5 , vol = 125 75 % = 93.75 , . 85 % = 106.25 vol above water between 18.75 - 31.25 ( sides are 4 cubic centimeters ) a" + }, + { + "Answer": 1051.5489993525034, + "Options": "['a ) 1050 sq . m', 'b ) 3850 sq . m', 'c ) 950 sq . m', 'd ) 1075 sq . m', 'e ) 1065 sq . m']", + "Correct": "a", + "Explanation": "area ungrazed is given by total area - 4 * area grazed by each horse = 70 * 70 - 4 * ( 90 / 360 ) * pi * ( 70 / 2 ) ^ 2 as the angle made by the horse is 90 degree , so applying the area of the sector , = theta / 360 * pi * radius ^ 2 above = 70 * 70 - pi * ( 70 / 2 ) * ( 70 / 2 ) = 70 * 70 { 1 - pi / 4 } = 70 * 70 { 6 / ( 7 * 4 ) } , expanding pi = 22 / 7 = ( 70 * 70 * 6 ) / ( 7 * 4 ) = 1050 sq m answer : a" + }, + { + "Answer": 876, + "Options": "a ) rs . 850 , b ) rs . 860 , c ) rs . 876 , d ) rs . 886 , e ) none of these", + "Correct": "c", + "Explanation": "\"explanation : we will first calculate the surface area of cube , then we will calculate the quantity of paint required to get answer . here we go , surface area = 6 a 2 = 6 \u2217 8 ( 2 ) = 384 sq feet quantity required = 38416 = 24 kg cost of painting = 36.50 \u2217 24 = rs . 876 option c\"" + }, + { + "Answer": 3, + "Options": "['a ) 5', 'b ) 4', 'c ) 3', 'd ) 2', 'e ) 1']", + "Correct": "c", + "Explanation": "calculate the volume of the larger cylinder and divide it by the volume of the smaller cylinder . volume of cylinder = \u03c0 r 2 h larger cylinder volume = 226.19 smaller cylinder volume = 62.83 therefore the number of smaller cylinders can be filled to capacity = 226.19 / 62.83 = 3.6 answer is c only 3 smaller cylinders can be filled to capacity ." + }, + { + "Answer": 42.06195997410015, + "Options": "['a ) 12', 'b ) 32', 'c ) 42', 'd ) 52', 'e ) 58']", + "Correct": "c", + "Explanation": "required area = 14 * 14 - ( 4 * 1 / 4 * 22 / 7 * 7 * 7 ) sq cm = 196 - 154 = 42 sq cm . answer : c" + }, + { + "Answer": 48, + "Options": "a ) 38 . , b ) 40 . , c ) 42 . , d ) 44 . , e ) 48 .", + "Correct": "e", + "Explanation": "\"answer is e : 48 let w be the width , so length is 5 w . therefore : w * 5 w = 720 , solving for , w = 12 , so 5 w - w = 4 w = 4 * 12 = 48\"" + }, + { + "Answer": 2, + "Options": "['a ) 4 m', 'b ) 3 m', 'c ) 2 m', 'd ) 1 m', 'e ) none of these']", + "Correct": "c", + "Explanation": "let the width of the path = w m then , length of plot with path = ( 15 + 2 w ) m and breadth of plot with path = ( 10 + 2 w ) m therefore , area of rectangular plot ( without path ) = 15 \u00d7 10 = 150 m 2 and area of rectangular plot ( with path ) = 150 + 54 = 204 m 2 hence , ( 15 + 2 w ) \u00d7 ( 10 + 2 w ) = 204 \u21d2 4 w 2 + 50 w \u2013 54 = 0 \u21d2 2 w 2 + 25 w \u2013 27 = 0 \u21d2 ( w \u2013 2 ) ( w + 27 ) = 0 thus w = 2 or \u2013 27 \u2234 with of the path = 2 m answer c" + }, + { + "Answer": 100, + "Options": "['a ) 50 %', 'b ) 87 %', 'c ) 100 %', 'd ) 187 %', 'e ) 200 %']", + "Correct": "c", + "Explanation": "let ' s just look at the dimensions ( no calculation needed ) . with dimension 11 the same , the other dimension 13 is twice 6.5 then the area will be double which means 100 % greater . the answer is c ." + }, + { + "Answer": 60, + "Options": "a ) 30 , b ) 45 , c ) 60 , d ) 75 , e ) 90", + "Correct": "c", + "Explanation": "\"c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be 60 . c\"" + }, + { + "Answer": 375, + "Options": "a ) 295 cm 2 , b ) 385 cm 2 , c ) 275 cm 2 , d ) 375 cm 2 , e ) 285 cm 2", + "Correct": "d", + "Explanation": "\"area of a parallelogram = base * height = 25 * 15 = 375 cm 2 answer : d\"" + }, + { + "Answer": 31.41592653589793, + "Options": "a ) 32 m 3 , b ) 31.4 m 3 , c ) 40 m 3 , d ) 44 m 3 , e ) none", + "Correct": "b", + "Explanation": "\"solution volume = \u03c0 r 2 h \u2039 = \u203a ( 22 / 7 \u00d7 1 \u00d7 1 \u00d7 10 ) m 3 \u2039 = \u203a 31.4 m 3 . answer b\"" + }, + { + "Answer": 32, + "Options": "a ) 16 , b ) r = 32 , c ) r = 64 , d ) 128 , e ) 512", + "Correct": "b", + "Explanation": "\"weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )\"" + }, + { + "Answer": 55, + "Options": "a ) 55 , b ) 80 , c ) 85 , d ) 90 , e ) 95", + "Correct": "a", + "Explanation": "in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 \u00b0 ) . given : x + ( x + 70 ) = 180 - - > x = 55 . answer : a ." + }, + { + "Answer": 20, + "Options": "['a ) 13 1 / 2', 'b ) 20', 'c ) 18 3 / 4', 'd ) 21', 'e ) 24']", + "Correct": "b", + "Explanation": "the area of a rectangle is : area = length x width we are given that floor x is 10 feet by 18 feet and that floor y is 9 feet wide . so we can say : length of x = 10 width of x = 18 width of y = 9 length of y = n we also can say : area of floor x = area of floor y ( length of x ) ( width of x ) = ( length of y ) ( width of y ) ( 10 ) ( 18 ) = 9 n ( 10 ) ( 2 ) = n 20 = n answer b ." + }, + { + "Answer": 9060, + "Options": "a ) s . 9060 , b ) s . 4520 , c ) s . 4527 , d ) s . 4530 , e ) s . 4521", + "Correct": "a", + "Explanation": "\"area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 10 = rs . 9060 answer : a\"" + }, + { + "Answer": 10398.369069916303, + "Options": "a ) 4457 , b ) 10400 , c ) 4235 , d ) 4547 , e ) 4675", + "Correct": "b", + "Explanation": "\"explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . \u03c0 r 2 = 175600 \u21d4 ( r ) 2 = ( 175600 x ( 7 / 22 ) ) \u21d4 r = 236.37 m . circumference = 2 \u03c0 r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 7 ) = rs . 10400 . answer : option b\"" + }, + { + "Answer": 135.01111065390137, + "Options": "a ) 134.4 , b ) 120 , c ) 150 , d ) 180 , e ) none", + "Correct": "a", + "Explanation": "\"solution other side = \u221a ( 17 ) 2 - ( 14 ) 2 = \u221a 289 - 196 = \u221a 93 = 9.6 m . \u2234 area = ( 14 x 9.6 ) m 2 = 134.4 m 2 . answer a\"" + }, + { + "Answer": 48, + "Options": "a ) 44 , b ) 48 , c ) 46 , d ) 47 , e ) 50", + "Correct": "b", + "Explanation": "\"isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side , the longer side with side 15 will be divided into 3 parts = 9 , 3 and 3 ( making one square and two right triangles ) for the right triangle , height will be = ( 5 ^ 2 - 3 ^ 2 ) ^ 1 / 2 = 4 and the area of trapezoid = 1 / 2 ( b 1 + b 2 ) h = 1 / 2 * 24 * 4 = 48 b\"" + }, + { + "Answer": 1, + "Options": "['a ) 100 km', 'b ) 1000 km', 'c ) 1 million km', 'd ) 1 billion km', 'e ) none']", + "Correct": "d", + "Explanation": "after 1 hold , thickness will be 2 mm after 2 hold , thich ness will be 4 mm after 50 th hold thick ness will be 2 ^ 50 mm . . converting to km . . . . gives 1 billion km answer : d" + }, + { + "Answer": 4, + "Options": "a ) 12 h , b ) 10 h , c ) 8 h , d ) 4 h , e ) none of these", + "Correct": "d", + "Explanation": "explanation area of field = 625 km 2 . then , each side of field = \u221a 625 = 25 km distance covered by the horse = perimeter of square field = 25 \u00d7 4 = 100 km \u2234 time taken by horse = distances / peed = 100 / 25 = 4 h answer d" + }, + { + "Answer": 900, + "Options": "a ) 600 , b ) 700 , c ) 800 , d ) 900 , e ) 1000", + "Correct": "d", + "Explanation": "\"2 hl + 2 hw = 2 lw h = lw / ( l + w ) volume = lwh = ( lw ) ^ 2 / ( l + w ) = 900 the answer is d .\"" + }, + { + "Answer": 85.76470588235294, + "Options": "['a ) 25.7', 'b ) 72.7', 'c ) 70.7', 'd ) 85.7', 'e ) 56.7']", + "Correct": "d", + "Explanation": "since the mirror is 42 inches in all sides , it must be a square . area of a square is a = a ^ 2 ; 54 ^ 2 = 2916 . area of rectangle is double of that 2 * 2916 = 5832 . now a = lw and we need find w so a / l = w ; 5832 / 68 = 85.7 answer ! answer is d" + }, + { + "Answer": 3, + "Options": "['a ) 8 cm', 'b ) 6 cm', 'c ) 4 cm', 'd ) 3 cm', 'e ) none']", + "Correct": "d", + "Explanation": "sol . let the height of the cone be h cm . then , 1 / 3 \u220f * 6 * 6 * h = 4 / 3 \u220f * 3 * 3 * 3 \u21d2 h = [ 36 * 3 / 36 ] = 3 cm . answer d" + }, + { + "Answer": 28, + "Options": "['a ) 24', 'b ) 28', 'c ) 32', 'd ) 36', 'e ) 40']", + "Correct": "b", + "Explanation": "let x be the length of one side of the square garden . x ^ 2 = 4 x + 21 x ^ 2 - 4 x - 21 = 0 ( x - 7 ) ( x + 3 ) = 0 x = 7 , - 3 p = 4 ( 7 ) = 28 the answer is b ." + }, + { + "Answer": 43, + "Options": "a ) 43.0 , b ) 44.0 , c ) 43.5 , d ) 45.0 , e ) 42.0", + "Correct": "a", + "Explanation": "\"100 * 100 = 10000 110 * 130 = 14300 - - - - - - - - - - 4300 10000 - - - - - - - 4300 100 - - - - - - - 43.00 answer a\"" + }, + { + "Answer": 125, + "Options": "a ) 168 , b ) 125 , c ) 186 , d ) 197 , e ) 191", + "Correct": "b", + "Explanation": "\"explanation : take radius 100 . then surface area is 4 \u00d7 \u03c0 \u03c0 \u00d7 100 \u00d7 100 . after increase radius by 50 % the radius becomes 100 + 50 % of 100 = 150 then new surface area is 4 \u00d7 \u03c0 \u03c0 \u00d7 150 \u00d7 150 then put the values into formula of percentage = 4 \u03c0 1502 \u2212 4 \u03c0 10024 \u03c0 1002 \u00d7 1004 \u03c0 1502 \u2212 4 \u03c0 10024 \u03c0 1002 \u00d7 100 = 125 % answer : b\"" + }, + { + "Answer": 21, + "Options": "['a ) 20', 'b ) 21', 'c ) 22', 'd ) 23', 'e ) 24']", + "Correct": "b", + "Explanation": "the volume the box is : length * width * depth = 7 * 6 * 2 = 84 cubic feet . 84 cubic feet / 4 cubic feet per hour = 21 hours . it will take 21 hours to fill the box . the answer is b ." + }, + { + "Answer": 750, + "Options": "a ) 850 cm 2 , b ) 750 cm 2 , c ) 450 cm 2 , d ) 550 cm 2 , e ) 650 cm 2", + "Correct": "b", + "Explanation": "\"the triangle with sides 65 cm , 60 cm and 25 cm is right angled , where the hypotenuse is 65 cm . area of the triangle = 1 / 2 * 60 * 25 = 750 cm 2 answer : b\"" + }, + { + "Answer": 3, + "Options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "c", + "Explanation": "a = # of adults price for on adult = $ 1.00 e = # of kids price for on kid ( accompanying an adult ) = $ 0.75 t = total ( $ ) $ 3.25 t = price for an adult * a + price for on kid * e 3.25 = $ 1 * a + $ 0.75 * e 3.25 = a + $ 0.75 * e because the kids have to be accompanying by an adult , a = 1 $ 3.25 = 1 + $ 0.75 * e $ 3.25 - 1 = 1 - 1 + $ 0.75 * e $ 2.25 = $ 0.75 * e $ 2.25 / $ 0.75 = ( $ 0.75 * e ) / $ 0.75 3 = e = number of kids accompanying an adult . correct option : c ) 3 kids" + }, + { + "Answer": 12, + "Options": "['a ) 6', 'b ) 8', 'c ) 10', 'd ) 12', 'e ) 16']", + "Correct": "d", + "Explanation": "1 ) if the two sides are co - prime , sum of sides - 1 . . 2 ) and if not co - prime , sum of sides - hcf of sides . . the difference is related to the diagonal passing through a vertex of squares at some place . . here 6 and 8 are not co - primes , so ans = 6 + 8 \u2212 hcf ( 6,8 ) = 14 \u2212 2 = 12 answer : d" + }, + { + "Answer": 170, + "Options": "['a ) 875', 'b ) 170', 'c ) 1425', 'd ) 2025', 'e ) 2500']", + "Correct": "b", + "Explanation": "there ' s a direct formula for this . number of diagonals in a regular polygon = [ n * ( n - 3 ) ] / 2 , n = number of sides of the regular polygon . here , n = 20 . plugging it in , we get 170 diagonals ! answer ( b ) ." + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 8 , c ) 6 , d ) 10 , e ) 16", + "Correct": "a", + "Explanation": "\"1 ) draw a simple cube 2 ) draw 9 squares on each face of the cube ( so that it looks like a rubik ' s cube ) - this is what the cube will look like when it ' s cut into 27 equal smaller cubes . 3 ) remember that the outside of the cube is the part that ' s painted . . . . the mini - cubes with 2 painted sides are all on the edge of the cube , in themiddleof the edge . there are 4 in front , 4 in back and 4 more on thestripthat runs around the left / top / right / bottom of the cube . h = 4 + 4 + 4 = 12 . answer a\"" + }, + { + "Answer": 9200, + "Options": "a ) 1288 , b ) 1299 , c ) 1000 , d ) 10000 , e ) 9200", + "Correct": "e", + "Explanation": "\"100 * 100 = 10000 115 * 80 = 9200 answer : e\"" + }, + { + "Answer": 210, + "Options": "a ) 210 cm 2 , b ) 150 cm 2 , c ) 168 cm 2 , d ) 198 cm 2 , e ) 987 cm 2", + "Correct": "a", + "Explanation": "\"1 / 2 * 28 ( 9 + 6 ) = 210 cm 2 answer : a\"" + }, + { + "Answer": 108, + "Options": "a ) 30 square inches , b ) 108 square inches , c ) 68 square inches , d ) 89 square inches , e ) 92 square inches", + "Correct": "b", + "Explanation": "\"if the width is 6 in and the length is 3 times the width , then the length is 3 * 6 = 18 in the area is given by 6 * 18 = 108 square inches correct answer b\"" + }, + { + "Answer": 48, + "Options": "a ) 30 square inches , b ) 75 square inches , c ) 68 square inches , d ) 48 square inches , e ) 92 square inches", + "Correct": "d", + "Explanation": "\"if the width is 4 in and the length is 3 times the width , then the length is 3 * 4 = 12 in the area is given by 4 * 12 = 48 square inches correct answer d\"" + }, + { + "Answer": 72, + "Options": "['a ) 27 sq . m', 'b ) 126 sq . m', 'c ) 84 sq . m', 'd ) 18 sq . m', 'e ) 72 sq . m']", + "Correct": "e", + "Explanation": "a = b * h = > a = 12 * 6 = 72 sq . m . answer : ( e )" + }, + { + "Answer": 40, + "Options": "a ) 28 , b ) 40 , c ) 30 , d ) 31 , e ) 32", + "Correct": "b", + "Explanation": "\"try filling the numbers into the answer y x y = find the closest to 900 . answer b\"" + }, + { + "Answer": 172800, + "Options": "['a ) 172,800', 'b ) 19,600', 'c ) 20,000', 'd ) 20,400', 'e ) 20,800']", + "Correct": "a", + "Explanation": "you can avoid a lot of work in this problem by recognizing that , with the info provided , the diagonal forms a triangle inside the rectangle with sides that have a 3 : 4 : 5 ratio . diagonal = 200 2 x + 2 y = 560 , or x + y = 280 a ^ 2 + b ^ 2 = c ^ 2 for each the sides of the triangle using the ratio 3 : 4 : 5 for sides , and knowing c = 600 , you can deduce the following a = 360 b = 480 360 x 480 = 172,800 a is the answer ." + }, + { + "Answer": 4, + "Options": "['a ) 4', 'b ) 5', 'c ) 6', 'd ) 3', 'e ) 7']", + "Correct": "a", + "Explanation": "54000 = 2 ^ 1 * 3 ^ 3 * 10 ^ 3 to make it ps * 2 ^ 2 or 4 answer : a" + }, + { + "Answer": 27, + "Options": "['a ) 3', 'b ) 27', 'c ) 13', 'd ) 12', 'e ) 15']", + "Correct": "b", + "Explanation": "volume of prism = area of base * height = 1 / 2 * ( square root of 9 ) * ( square root of 9 ) * 6 = 27 answer : b" + }, + { + "Answer": 16, + "Options": "a ) 16 % , b ) 18 % , c ) 20 % , d ) 22 % , e ) 24 %", + "Correct": "a", + "Explanation": "\"let diameter of circle r , dr = 40 and diameter of circle s , ds = 100 radius of circle r , rr = 20 radius of circle s , rs = 50 area of circle r / area of circle s = ( pi * rr ^ 2 ) / ( pi * rs ^ 2 ) = ( 20 / 50 ) ^ 2 = ( 4 / 10 ) ^ 2 = 16 % answer : a\"" + }, + { + "Answer": 34.14213562373095, + "Options": "['a ) 25', 'b ) 36', 'c ) 25', 'd ) 30', 'e ) 34.14']", + "Correct": "e", + "Explanation": "an isosceles right angled triangle has both the base and height same . the area of an isosceles triangle = 1 / 2 * base * height since height = base 1 / 2 * height * height = 1 / 2 * height ^ 2 = 50 height ^ 2 = 100 height = 10 = base since we know the base and height . we will calculate the hypotenuse using pythagoras base ^ 2 + height ^ 2 = hypotenuse ^ 2 10 ^ 2 + 10 ^ 2 = hypotenuse ^ 2 hypotenuse ^ 2 = 200 hypotenuse = 14.14 perimeter of the triangle = 10 + 10 + 14.14 = 34.14 ans : e" + }, + { + "Answer": 51.41592653589793, + "Options": "a ) 27 , b ) 33 , c ) 39 , d ) 45 , e ) 51", + "Correct": "e", + "Explanation": "\"the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 10 + 2 * 10 which is about 51 . the answer is e .\"" + }, + { + "Answer": 25, + "Options": "a ) 11 , b ) 25 , c ) 787 , d ) 122 , e ) 12", + "Correct": "b", + "Explanation": "\"1 / 2 * 10 * 5 = 25 m 2 answer : b\"" + }, + { + "Answer": 54, + "Options": "a ) 65 , b ) 62 , c ) 58 , d ) 54 , e ) 60", + "Correct": "d", + "Explanation": "\"if i calculate it using the formulae , # diagonals = n ( n - 3 ) / 2 each vertex sends of n - 3 diagonals n = 13 - 1 then 12 * ( 12 - 3 ) / 2 = 54 correct option : d\"" + }, + { + "Answer": 38, + "Options": "['a ) 42', 'b ) 38', 'c ) 28', 'd ) 57', 'e ) 49']", + "Correct": "b", + "Explanation": "let l and w be the length and width of the garden . the statement ` ` the length of a rectangular garden is 2 feet longer than 3 times its width ' ' may be formulated by l = 2 + 3 w the formula for the perimeter is given by p = 2 l + 2 w substitute p and l in the above equation by 100 and 2 + 3 w respectively to obtain 100 = 2 ( 2 + 3 w ) + 2 w solve for w and l w = 12 and l = 2 + 3 w = 38 . check that the perimeter of the rectangular garden is 100 p = 2 l + 2 w = 76 + 24 = 100 correct answer b" + }, + { + "Answer": 95.99999999999997, + "Options": "a ) 95 % , b ) 90 % , c ) 85 % , d ) 96 % , e ) 25 %", + "Correct": "d", + "Explanation": "\"the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 40 % increase a surface = 6 * ( ( 1.4 a ) ^ 2 ) = 6 * 1.96 * a ^ 2 the increase in the surface area = ( 6 * 1.96 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 1.96 - 1 ) ) / ( 6 * a ^ 2 ) = 1.96 - 1 = 0.96 = 96 % answer : d\"" + }, + { + "Answer": 36, + "Options": "a ) 54 , b ) 36 , c ) 75 , d ) 28 , e ) 11", + "Correct": "b", + "Explanation": "\"a / 8 = 9 * 9 = > a = 9 * 9 * 8 x * 2 x = 9 * 9 * 8 x = 18 = > 2 x = 36 answer : b\"" + }, + { + "Answer": 3.6666666666666665, + "Options": "a ) 3.1 feet , b ) 3.66 feet , c ) 3.3 feet , d ) 3.4 feet , e ) 3.5 feet", + "Correct": "b", + "Explanation": "\"we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 10 = 40 44 / 12 = 3.66 feet answer : b\"" + }, + { + "Answer": 0.1111111111111111, + "Options": "a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 5 , e ) 1 / 3", + "Correct": "a", + "Explanation": "\"if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 8,12 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives w = 1 / 9 . a\"" + }, + { + "Answer": 31.5, + "Options": "a ) 21.5 , b ) 31.5 , c ) 41.5 , d ) 61.5 , e ) 71.5", + "Correct": "b", + "Explanation": "\"since the mirror is 42 inches in all sides , it must be a square . area of a square is a = a ^ 2 ; 21 ^ 2 = 441 . area of rectangle is double of that 2 * 441 = 882 . now a = lw and we need find w so a / l = w ; 882 / 28 = 31.5 answer ! answer is b\"" + }, + { + "Answer": 225, + "Options": "['a ) 100', 'b ) 256', 'c ) 225', 'd ) 81', 'e ) 144']", + "Correct": "c", + "Explanation": "a square can be considered as a set of two right angled triangles joined from the hypotenuse . since the sides are 10 units each . the height and base of both the triangles is 10 each . area of a right angled triangle is 1 / 2 * base * height area of both the triangles is 2 * 1 / 2 * base * height . since both triangles are similar . = base * height = 15 * 15 = 225 ans : c" + }, + { + "Answer": 240, + "Options": "['a ) 180 cm', 'b ) 220 cm', 'c ) 240 cm', 'd ) 270 cm', 'e ) 300 cm']", + "Correct": "c", + "Explanation": "we have 40 for first triangle , when we join mid - points of first triangle we get the second equilateral traingle then the length of second one is 20 and continues . so we have 40 , 20,10 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 40 / 1 - ( 1 / 2 ) = 80 equilateral triangle perimeter is 3 a = 3 * 80 = 240 . so option c ." + }, + { + "Answer": 9856, + "Options": "['a ) 4920 cm 2', 'b ) 4727 cm 2', 'c ) 9856 cm 2', 'd ) 19712 cm 2', 'e ) none']", + "Correct": "c", + "Explanation": "sol . let the original radius be r . then , original surface area = 4 \u03c0 r 2 = 2464 cm 2 ( given ) . new radius = 2 r . \u2234 new surface area = 4 \u03c0 ( 2 r ) 2 = 4 x 4 \u03c0 r 2 = ( 4 x 2464 ) cm 2 = 9856 cm 2 answer c" + }, + { + "Answer": 24, + "Options": "a ) 24 , b ) 32 , c ) 75 , d ) 28 , e ) 11", + "Correct": "a", + "Explanation": "\"a / 8 = 6 * 6 = > a = 6 * 6 * 8 x * 2 x = 6 * 6 * 8 x = 12 = > 2 x = 24 answer : a\"" + }, + { + "Answer": 3, + "Options": "a ) 11 , b ) 10 , c ) 787 , d ) 3 , e ) 12", + "Correct": "d", + "Explanation": "\"1 / 2 * 2 * 3 = 3 m 2 answer : d\"" + }, + { + "Answer": 24.999999999999993, + "Options": "a ) 14 % , b ) 15 % , c ) 25 % , d ) 30 % , e ) 35 %", + "Correct": "c", + "Explanation": "\"sol . required change = ( 20 * 100 ) / ( 100 - 20 ) = 25 % c\"" + }, + { + "Answer": 200, + "Options": "a ) 200 , b ) 384 , c ) 200 , d ) 244 , e ) 242", + "Correct": "c", + "Explanation": "\"area of a parallelogram = base * height = 10 * 20 = 200 cm 2 answer : option c\"" + }, + { + "Answer": 5, + "Options": "a ) 10 metres , b ) 5 metres , c ) 7.5 metres , d ) data inadequate , e ) none of these", + "Correct": "b", + "Explanation": "\"l \u00d7 b = 15 \u00d7 b \u2234 l = 15 m and l \u2013 b = 10 \u2234 b = 15 \u2013 10 = 5 m answer b\"" + }, + { + "Answer": 6342, + "Options": "a ) s . 4538 , b ) s . 6342 , c ) s . 4518 , d ) s . 4530 , e ) s . 4517", + "Correct": "b", + "Explanation": "\"area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 7 = rs . 6342 answer : b\"" + }, + { + "Answer": 8281, + "Options": "['a ) 6564', 'b ) 7372', 'c ) 8281', 'd ) 9331', 'e ) can not be determined']", + "Correct": "c", + "Explanation": "let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 181 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 181 ( x + y ) ( x - y ) = 181 181 is a prime number and thus it will be ( 91 + 90 ) * ( 91 - 90 ) . thus x = 91 and y = 90 x ^ 2 = 91 ^ 2 = 8281 the answer is c ." + }, + { + "Answer": 15, + "Options": "['a ) 225 square inches', 'b ) 45 square inches', 'c ) 25 square inches', 'd ) 15 square inches', 'e ) 10 square inches']", + "Correct": "d", + "Explanation": "definitely ( d ) 5 * 3 = 15 sq inches the question asks to find the greatest area of the faces of a cuboid the possible area of the faces are - length * breadth , breadth * height & height * length the possible areas are - 6 , 10 & 15 thus 15 is the greatest possible area . . . . answer : d" + }, + { + "Answer": 30, + "Options": "a ) 88 m 2 , b ) 30 m 2 , c ) 66 m 2 , d ) 77 m 2 , e ) 31 m 2", + "Correct": "b", + "Explanation": "\"1 / 2 * 12 * 5 = 30 m 2 answer : b\"" + }, + { + "Answer": 82.25000000000003, + "Options": "a ) 38.25 % , b ) 40.25 % , c ) 82.25 % , d ) 50 % , e ) 65 %", + "Correct": "c", + "Explanation": "if sides are a and b , after increase sides would be 1.35 a and 1.35 b . percentage increase in area = ( 1.35 a * 1.35 b - ab ) * 100 / ab = 82.25 answer : c" + }, + { + "Answer": 43.99999999999999, + "Options": "a ) 44 % , b ) 45 % , c ) 50 % , d ) 55 % , e ) 60 %", + "Correct": "a", + "Explanation": "\"let original length = x metres and original breadth = y metres . original area = ( xy ) m 2 . new length = 120 x m = 6 x m . 100 5 new breadth = 120 y m = 6 y m . 100 5 new area = 6 x x 6 y m 2 = 36 xy m 2 . 5 5 25 the difference between the original area = xy and new - area 36 / 25 xy is = ( 36 / 25 ) xy - xy = xy ( 36 / 25 - 1 ) = xy ( 11 / 25 ) or ( 11 / 25 ) xy increase % = 11 xy x 1 x 100 % = 44 % . a )\"" + }, + { + "Answer": 24, + "Options": "['a ) 36', 'b ) 32', 'c ) 24', 'd ) 21', 'e ) 15']", + "Correct": "c", + "Explanation": "27 cubic centimetre cubes gives side = 3 cm so if : l * w * h is 9 * 12 * 8 , then max . cube we can have are 3 * 4 * 2 = 24 l * w * h is 9 * 8 * 12 , then max . cube we can have are 3 * 2 * 4 = 24 l * w * h is 12 * 8 * 9 , then max . cube we can have are 4 * 2 * 3 = 24 l * w * h is 12 * 9 * 8 , then max . cube we can have are 4 * 3 * 2 = 24 l * w * h is 8 * 12 * 9 , then max . cube we can have are 2 * 4 * 3 = 24 l * w * h is 8 * 9 * 12 , then max . cube we can have are 2 * 3 * 4 = 24 in all cases we get e = 24 cubes . ans . c" + }, + { + "Answer": 7, + "Options": "a ) 3 cm , b ) 4 cm , c ) 6 cm , d ) 7 cm , e ) none", + "Correct": "d", + "Explanation": "\"solution 4 \u00ee r 2 = 2 \u00ee 7 x 14 \u00e2 \u2021 \u2019 r 2 = ( 7 x 14 / 2 ) \u00e2 \u2021 \u2019 49 \u00e2 \u2021 \u2019 r = 7 cm . answer d\"" + }, + { + "Answer": 20.75, + "Options": "a ) 21.25 , b ) 22.75 , c ) 19.25 , d ) 20.75 , e ) 22.25", + "Correct": "d", + "Explanation": "\"100 * 100 = 10000 105 * 115 = 12075 - - - - - - - - - - - 2075 10000 - - - - - - 2075 100 - - - - - ? = > 20.75 answer d\"" + }, + { + "Answer": 2, + "Options": "['a ) 2 : 1', 'b ) 3 : 2', 'c ) 3 : 5', 'd ) 3 : 7', 'e ) none of these']", + "Correct": "a", + "Explanation": "explanation : let the edges be a and b of two cubes , then a 3 / b 3 = 8 / 1 = > ( a / b ) 3 = ( 2 / 1 ) 3 a / b = 2 / 1 = > a : b = 2 : 1 option a" + }, + { + "Answer": 8, + "Options": "a ) 10 metres , b ) 8 metres , c ) 7.5 metres , d ) data inadequate , e ) none of these", + "Correct": "b", + "Explanation": "\"l \u00d7 b = 18 \u00d7 b \u2234 l = 18 m and l \u2013 b = 10 \u2234 b = 18 \u2013 10 = 8 m answer b\"" + }, + { + "Answer": 9.899494936611665, + "Options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9.899", + "Correct": "e", + "Explanation": "\"side of triangle is a then perimeter = a + a + a . sqrt 2 ( right angle and pythagorus ) = 2 a + a . sqrt 2 = 14 + 14 sqrt 2 or , a . ( 2 + sqrt 2 ) = 14 ( 1 + sqrt 2 ) , a = 14 * ( 1 + sqrt 2 ) / 2 + sqrt 2 = 14 * 2.414 / 3.414 = then hypotenuse = 9.899 e\"" + }, + { + "Answer": 4.04, + "Options": "a ) 4 % , b ) 4.04 % , c ) 4.15 % , d ) 5 % , e ) 5.24 %", + "Correct": "b", + "Explanation": "\"100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 102 x 102 ) cm 2 . ( a 2 - a 1 ) = [ ( 102 ) 2 - ( 100 ) 2 ] = ( 102 + 100 ) x ( 102 - 100 ) = 404 cm 2 . percentage error = 404 x 100 % = 4.04 % 100 x 100 b\"" + }, + { + "Answer": 640.3822465077428, + "Options": "a ) 540.72 , b ) 740.64 , c ) 640.64 , d ) 620.45 , e ) 725.26", + "Correct": "c", + "Explanation": "\"req . area = \u00ef \u20ac [ ( 37.8 ) 2 \u00e2 \u20ac \u201c ( 35 ) 2 ] = 22 \u00e2 \u0081 \u201e 7 \u00e3 \u2014 ( 72.8 \u00e3 \u2014 2.8 ) [ since a 2 - b 2 = ( a + b ) ( a - b ) ] = 22 \u00e3 \u2014 72.8 \u00e3 \u2014 0.4 = 640.64 sq m answer c\"" + }, + { + "Answer": 416, + "Options": "a ) 297 cm 2 , b ) 384 cm 2 , c ) 672 cm 2 , d ) 416 cm 2 , e ) 286 cm 2", + "Correct": "d", + "Explanation": "\"area of a parallelogram = base * height = 26 * 16 = 416 cm 2 answer : d\"" + }, + { + "Answer": 3944, + "Options": "a ) 3944 , b ) 3932 , c ) 3929 , d ) 3926 , e ) 3902", + "Correct": "a", + "Explanation": "\"let the side of the square plot be a foot a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 foot cost of building the fence = 68 * 58 = rs . 3944 . answer : a\"" + }, + { + "Answer": 0.1111111111111111, + "Options": "a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 5 , e ) 1 / 3", + "Correct": "a", + "Explanation": "\"if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 8,12 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives d = 1 / 9 . a\"" + }, + { + "Answer": 0.1111111111111111, + "Options": "['a ) 1 / 9', 'b ) 1 / 8', 'c ) 1 / 6', 'd ) 1 / 5', 'e ) 1 / 3']", + "Correct": "a", + "Explanation": "if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 8,12 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives c = 1 / 9 . a" + }, + { + "Answer": 1200, + "Options": "a ) rs . 1200 , b ) rs . 672 , c ) rs . 546 , d ) rs . 876 , e ) none of these", + "Correct": "a", + "Explanation": "\"explanation : surface area of a cube = 6 x 10 ^ 2 = 600 s q . ft quantity of paint required = ( 600 / 20 ) = 30 kg cost of painting = 40 x 30 = rs . 1200 answer : a\"" + }, + { + "Answer": 5040, + "Options": "['a ) 1320 sq . metres', 'b ) 3260 sq . metres', 'c ) 4280 sq . metres', 'd ) 5040 sq . metres', 'e ) none of these']", + "Correct": "d", + "Explanation": "let the length and breadth be 7 x and 5 x respectively . then , p = 2 ( 7 x + 5 x ) = 288 \u00e2 \u2021 \u2019 x = 12 area = 7 \u00e3 \u2014 12 \u00e3 \u2014 5 \u00e3 \u2014 12 = 5040 sq . m . answer d" + }, + { + "Answer": 4800, + "Options": "a ) 4830 , b ) 5120 , c ) 6420 , d ) 4800 , e ) 8960", + "Correct": "d", + "Explanation": "\"l = ( 46 - 16 ) m = 30 m , b = ( 36 - 16 ) m = 20 m , h = 8 m . volume of the box = ( 30 x 20 x 8 ) m 3 = 4800 m 3 . answer : option d\"" + }, + { + "Answer": 40, + "Options": "a ) 32 , b ) 34 , c ) 38 , d ) 40 , e ) 42", + "Correct": "d", + "Explanation": "\"least number of cubes will be required when the cubes that could fit in are biggest . 9 is the biggest number that could divide all three , 36 , 45 and 18 . thus side of cube must be 9 , and total number of cubes = 36 / 9 * 45 / 9 * 18 / 9 = 40 ans d .\"" + }, + { + "Answer": 1800, + "Options": "['a ) 3000', 'b ) 900', 'c ) 1800', 'd ) 360', 'e ) none of these']", + "Correct": "c", + "Explanation": "area of cube = 6 \u00d7 ( side ) 2 = 6 \u00d7 10 \u00d7 10 = 600 square feet . cost to paint outside of the cube = 600 \u2044 20 \u00d7 60 = 1800 answer c" + }, + { + "Answer": 12, + "Options": "a ) 4 , b ) 8 , c ) 12 , d ) 15 , e ) 20", + "Correct": "c", + "Explanation": "\"i understand this might not be required but i used the equation of a circle . since the origin is at 0 , x ^ 2 + y ^ 2 = 5 ^ 2 . x , y could be + / - ( 0,5 or 5,0 ) - 4 possibilities . x , y could be + / - ( 3,4 or 4,3 ) - 8 possibilities . ans : q = c\"" + }, + { + "Answer": 10, + "Options": "['a ) 15 metres', 'b ) 12 metres', 'c ) 10 metres', 'd ) 9 metres', 'e ) none of these']", + "Correct": "c", + "Explanation": "in a triangle , area = 1 \u2044 2 \u00d7 length of perpendicular \u00d7 base or 615 = 1 \u2044 2 \u00d7 length of perpendicular \u00d7 123 \u2234 length of perpendicular = 615 \u00d7 2 / 123 = 10 m answer c" + }, + { + "Answer": 21, + "Options": "a ) 32 , b ) 64 , c ) 42 , d ) 21 , e ) none of these", + "Correct": "d", + "Explanation": "\"544 = 25 + 171 = ( 2 ) 0 + ( 2 ) 1 + ( 2 ) 2 + ( 2 ) 3 + ( 2 ) 4 + ( 2 ) 5 x ( 17 ) 0 + ( 17 ) 1 . here 20 = 1 = 11 a perfect square , 22 and 24 = 16 = 44 are perfect squares , hence , 1 + 4 + 16 = 21 . correct answer is : d\"" + }, + { + "Answer": 60, + "Options": "a ) 158 , b ) 60 , c ) 150 , d ) 123 , e ) 117", + "Correct": "b", + "Explanation": "\"1 / 2 * 10 * 12 = 60 answer : b\"" + }, + { + "Answer": 3298.6722862692827, + "Options": "a ) 1100 , b ) 2200 , c ) 3300 , d ) 4400 , e ) 5500", + "Correct": "c", + "Explanation": "\"cone curved surface area = \u00ef \u20ac rl 22 / 7 \u00e3 \u2014 35 \u00e3 \u2014 30 = 110 \u00e3 \u2014 30 = 3300 m ( power 2 ) answer is c .\"" + }, + { + "Answer": 8.485281374238571, + "Options": "['a ) 5', 'b ) 6', 'c ) 7', 'd ) 8.485', 'e ) 8']", + "Correct": "d", + "Explanation": "side of triangle is a then perimeter = a + a + a . sqrt 2 ( right angle and pythagorus ) = 2 a + a . sqrt 2 = 12 + 12 sqrt 2 or , a . ( 2 + sqrt 2 ) = 12 ( 1 + sqrt 2 ) , a = 12 * ( 1 + sqrt 2 ) / 2 + sqrt 2 = 12 * 2.414 / 3.414 = then hypotenuse = 8.485 d" + }, + { + "Answer": 6000, + "Options": "a ) rs . 962 , b ) rs . 6000 , c ) rs . 546 , d ) rs . 876 , e ) none of these", + "Correct": "b", + "Explanation": "\"explanation : surface area of a cube = 6 x 20 ^ 2 = 2400 sq . ft quantity of paint required = ( 2400 / 20 ) = 120 kg cost of painting = 50 x 120 = rs . 6000 answer : b\"" + }, + { + "Answer": 8, + "Options": "['a ) 12', 'b ) 9 \u221a 3', 'c ) 9', 'd ) 8', 'e ) 3 \u221a 3']", + "Correct": "d", + "Explanation": "so , bc = bd = cd = ba = ad = 2 the parallelogram has 4 equal sides bc = cd = ba = ad = 2 so the perimeter of the parallelogram will be 2 * 4 = 8 hence answer will be ( d ) 2" + }, + { + "Answer": 4.5, + "Options": "a ) 16 , b ) 4.5 , c ) 4 , d ) 2 , e ) 1", + "Correct": "b", + "Explanation": "\"x be radius of circle x y be radius of circle y given : pi * x ^ 2 = pi * y ^ 2 also , 2 * pi * x = 18 * pi x = 9 thus y = 9 y / 2 = 4.5 ans : b\"" + }, + { + "Answer": 28.2051282051282, + "Options": "a ) 14 % , b ) 15 % , c ) 28 % , d ) 30 % , e ) 35 %", + "Correct": "c", + "Explanation": "\"sol . required change = ( 22 * 100 ) / ( 100 - 22 ) = 28.2 % c\"" + }, + { + "Answer": 13, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 13", + "Correct": "e", + "Explanation": "\"let t be the number of trees . then the length required for trees on the sidewalk will be 1 * t = t to maximize the number of trees , the number of 12 feet spaces between trees should be 1 less than total number of trees . for example , if there are 3 trees , then there should be 2 spaces between them . so the number of 12 feet spaces will be t - 1 . then , the length of sidewalk required for 12 feet spaces will be 12 * ( t - 1 ) it is given that total lenght of sidewalk is 157 feet . or 12 ( t - 1 ) + t = 157 or 12 t - 12 + t = 157 or 13 t = 169 or t = 13 answer : - e\"" + }, + { + "Answer": 105, + "Options": "a ) 128 cm 2 , b ) 36.0 cm 2 , c ) 105 cm 2 , d ) 25 cm 2 , e ) 135 cm 2", + "Correct": "c", + "Explanation": "\"area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 5.0 * 42 / 2 = 105 cm 2 answer : c\"" + }, + { + "Answer": 17, + "Options": "['a ) 19 m', 'b ) 17 m', 'c ) 10 m', 'd ) 12 m', 'e ) 18 m']", + "Correct": "b", + "Explanation": "answer : option b explanation : let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 867 3 b 2 = 867 b 2 = 289 = 172 ( b > 0 ) b = 17 m . answer : option b" + }, + { + "Answer": 36, + "Options": "['a ) 18', 'b ) 56', 'c ) 40', 'd ) 36', 'e ) 64']", + "Correct": "d", + "Explanation": "you can also solve this via using the given numbers in the answer choices ! of course you need to be aware of the basic properties as outlined by the other posts above ( a = x ^ 2 and p = 4 x ) starting with b you will notice that x = 14 is way too big for your area ( 14 ^ 2 ) and will not satisfy : 5 a = 10 p + 45 or a = 2 p + 9 - - > eliminate b and e now pick d ( its either too big , then its a , or too small then you know its c or it is b itsself ) and picking d indeed solves the problem ! ( 36 / 4 - - > 9 ; a = 9 ^ 2 = 81 and 81 = 2 x 36 + 9 )" + }, + { + "Answer": 13.653333333333334, + "Options": "a ) 6 cm , b ) 8.25 cm , c ) 13.65 cm , d ) 15.12 cm , e ) 20.62 cm", + "Correct": "c", + "Explanation": "\"increase in volume = volume of the cube = 16 * 16 * 16 cm ^ 3 rise in water level = volume / area = 16 * 16 * 16 / 20 * 15 = 13.65 cm answer is c\"" + }, + { + "Answer": 136, + "Options": "a ) 124 m 2 , b ) 126 m 2 , c ) 136 m 2 , d ) 158 m 2 , e ) none of these", + "Correct": "c", + "Explanation": "\"area of the outer rectangle = 22 \u00e3 \u2014 16 = 352 m 2 area of the inner rectangle = 18 \u00e3 \u2014 12 = 216 m 2 required area = ( 352 \u00e2 \u20ac \u201c 216 ) = 136 m 2 answer c\"" + }, + { + "Answer": 84, + "Options": "['a ) 72 %', 'b ) 96 %', 'c ) 94 %', 'd ) 84 %', 'e ) 82 %']", + "Correct": "d", + "Explanation": "r = 4 \u00ef \u20ac r 2 = 16 r = 10 \u00ef \u20ac r 2 = 100 100 \u00ef \u20ac \u00e2 \u20ac \u201c 84 \u00ef \u20ac 100 - - - - ? = > 84 % . answer : d" + }, + { + "Answer": 4, + "Options": "['a ) 3 x', 'b ) 4 x', 'c ) 9 x', 'd ) 12 x', 'e ) 27 x']", + "Correct": "b", + "Explanation": "original perimeter = x hence original side = x / 4 new side = 4 x / 4 new perimeter = 4 * 4 x / 4 = 4 x correct option : b" + }, + { + "Answer": 28, + "Options": "a ) 28 . , b ) 40 . , c ) 42 . , d ) 44 . , e ) 46 .", + "Correct": "a", + "Explanation": "\"answer is a : 28 let w be the width , so length is 3 w . therefore : w * 3 w = 588 , solving for , w = 14 , so 3 w - w = 2 w = 2 * 14 = 28\"" + }, + { + "Answer": 200, + "Options": "['a ) 10 \u221a 2 m', 'b ) 100 m', 'c ) 100 \u221a 2 m', 'd ) 200 m', 'e ) none']", + "Correct": "d", + "Explanation": "solution let the altitude of the triangle be h \u00ef and base of each be b . then , ( \u00bd \u00d7 b \u00d7 h 1 ) where h 2 = 100 m . = h 1 = 2 h 2 = ( 2 x 100 ) m = 200 m . answer d" + }, + { + "Answer": 4032, + "Options": "a ) 54 , b ) 4032 , c ) 2,160 , d ) 2,916 , e ) 148,824", + "Correct": "b", + "Explanation": "we have the rectangle with dimensions 9 * 8 ( 9 horizontal dots and 8 vertical ) . ab is parallel to y - axis and ac is parallel to x - axis . choose the ( x , y ) coordinates for vertex a : 9 c 1 * 8 c 1 ; choose the x coordinate for vertex c ( as y coordinate is fixed by a ) : 8 c 1 , ( 9 - 1 = 8 as 1 horizontal dot is already occupied by a ) ; choose the y coordinate for vertex b ( as x coordinate is fixed by a ) : 7 c 1 , ( 8 - 1 = 7 as 1 vertical dot is already occupied by a ) . 9 c 1 * 8 c * 8 c 1 * 7 c 1 = 4032 . answer : b ." + }, + { + "Answer": 10, + "Options": "['a ) 10', 'b ) 88', 'c ) 26', 'd ) 27', 'e ) 28']", + "Correct": "a", + "Explanation": "explanation : we have , a \u03b1 1 / b 2 a * b 2 = k ( constant ) when b = 12 , a = 40 \u2026 . . given k = 40 * ( 12 ) 2 = 5760 now , b = 24 . hence , a = 5760 / 576 = 10 answer : a" + }, + { + "Answer": 3624, + "Options": "a ) 4000 , b ) 3624 , c ) 5673 , d ) 4530 , e ) 4566", + "Correct": "b", + "Explanation": "\"area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 4 = rs . 3624 answer : option b\"" + }, + { + "Answer": 35, + "Options": "['a ) 35 sq . units', 'b ) 45 sq . units', 'c ) 55 sq . units', 'd ) 50 sq . units', 'e ) 40 sq . units']", + "Correct": "a", + "Explanation": "given that the area of the square = 784 sq . units = > side of square = \u00e2 \u02c6 \u0161 784 = 28 units the radius of the circle = side of the square = 28 units length of the rectangle = 1 / 4 * 28 = 7 units given that breadth = 5 units area of the rectangle = lb = 7 * 5 = 35 sq . units answer : a" + }, + { + "Answer": 140, + "Options": "['a ) 100', 'b ) 140', 'c ) 998', 'd ) 729', 'e ) 2879']", + "Correct": "b", + "Explanation": "140 % answer : b" + }, + { + "Answer": 3.2, + "Options": "a ) 1.2 cm , b ) 2.4 cm , c ) 4.8 cm , d ) 2.16 cm , e ) 3.2 cm", + "Correct": "e", + "Explanation": "\"look at the diagram below : now , in case when qy is perpendicular to pr , two right triangles pqr and pqy are similar : qy : qp = qr : pr - - > qy : 4 = 8 : 10 - - > qy = 3.2 . answer : e\"" + }, + { + "Answer": 29.975864606614373, + "Options": "['a ) 65 cm 2', 'b ) 30 cm 2', 'c ) 76 cm 2', 'd ) 68 cm 2', 'e ) 46 cm 2']", + "Correct": "b", + "Explanation": "the circumference of the circle is equal to the permeter of the rectangle . let l = 6 x and b = 5 x 2 ( 6 x + 5 x ) = 2 * 22 / 7 * 3.5 = > x = 1 therefore l = 6 cm and b = 5 cm area of the rectangle = 6 * 5 = 30 cm 2 answer : b" + }, + { + "Answer": 60, + "Options": "a ) 30 , b ) 45 , c ) 60 , d ) 75 , e ) 90", + "Correct": "c", + "Explanation": "\"c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be q = 60 . c\"" + }, + { + "Answer": 20, + "Options": "['a ) 22', 'b ) 20', 'c ) 9', 'd ) 8', 'e ) 1']", + "Correct": "b", + "Explanation": "let the radius of the pool be r . then area of the wall and pool = \u03c0 ( r + 4 ) 2 \u03c0 ( r + 4 ) 2 area of the pool = \u03c0 ( r ) 2 \u03c0 ( r ) 2 area of the wall = \u03c0 ( r + 4 ) 2 \u2212 \u03c0 ( r ) 2 \u03c0 ( r + 4 ) 2 \u2212 \u03c0 ( r ) 2 given \u03c0 ( r + 4 ) 2 \u2212 \u03c0 ( r ) 2 \u03c0 ( r + 4 ) 2 \u2212 \u03c0 ( r ) 2 = 1125 ( \u03c0 r 2 ) 1125 ( \u03c0 r 2 ) r 2 + 8 r + 16 \u2212 r 2 = 1125 r 2 r 2 + 8 r + 16 \u2212 r 2 = 1125 r 2 11 r 2 \u2212 200 r \u2212 400 = 011 r 2 \u2212 200 r \u2212 400 = 0 solving r = 20 answer : b" + }, + { + "Answer": 308, + "Options": "a ) 298 cm 2 , b ) 384 cm 2 , c ) 308 cm 2 , d ) 286 cm 2 , e ) 276 cm 2", + "Correct": "c", + "Explanation": "\"area of a parallelogram = base * height = 22 * 14 = 308 cm 2 answer : c\"" + }, + { + "Answer": 16, + "Options": "a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 16", + "Correct": "e", + "Explanation": "\"let t be the number of trees . then the length required for trees on the sidewalk will be 1 * t = t to maximize the number of trees , the number of 14 feet spaces between trees should be 1 less than total number of trees . for example , if there are 3 trees , then there should be 2 spaces between them . so the number of 9 feet spaces will be t - 1 . then , the length of sidewalk required for 9 feet spaces will be 9 * ( t - 1 ) it is given that total lenght of sidewalk is 151 feet . or 9 ( t - 1 ) + t = 151 or 9 t - 9 + t = 151 or 10 t = 160 or t = 16 answer : - e\"" + }, + { + "Answer": 1539.3804002589986, + "Options": "['a ) 4150', 'b ) 1780', 'c ) 1540', 'd ) 1500', 'e ) 6100']", + "Correct": "c", + "Explanation": "\u03c0 * 14 * 35 = 1540 answer : c" + }, + { + "Answer": 36, + "Options": "a ) 6 : 1 , b ) 12 : 1 , c ) 24 : 1 , d ) 36 : 1 , e ) 72 : 1", + "Correct": "d", + "Explanation": "\"let x be the length of the small cube ' s side . the total surface area of the small cube is 6 x ^ 2 . the total surface area of the large cube is 6 ( 6 x ) ^ 2 = 216 x ^ 2 . the ratio of surface areas is 36 : 1 . the answer is d .\"" + }, + { + "Answer": 485.99999999999983, + "Options": "['a ) 486 sq . cm', 'b ) 456 sq . cm', 'c ) 446 sq . cm', 'd ) 476 sq . cm', 'e ) none of these']", + "Correct": "a", + "Explanation": "explanation : a 3 = 729 ; a = 9 surface area = ( 6 x 9 x 9 ) = 486 cm 2 answer : a" + }, + { + "Answer": 5600, + "Options": "a ) 1940 , b ) 4800 , c ) 5600 , d ) 5200 , e ) 5000", + "Correct": "c", + "Explanation": "\"area of the rhombus = 1 / 2 d 1 d 2 = ( 1 / 2 \u00e3 \u2014 70 \u00e3 \u2014 160 ) cm ( power ) 2 = 70 \u00e3 \u2014 80 = 5600 cm ( power ) 2 answer is c .\"" + }, + { + "Answer": 72, + "Options": "a ) 56 , b ) 72 , c ) 112 , d ) 116 , e ) 120", + "Correct": "b", + "Explanation": "\"ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 8 + 8 = 16 length of 2 nd diagonal = 4.5 + 4.5 = 9 area = 1 / 2 * 16 * 9 = 72 b is the answer\"" + }, + { + "Answer": 201.06192982974676, + "Options": "a ) 154 cm 2 , b ) 308 m 2 , c ) 201 m 2 , d ) 205 m 2 , e ) none of these", + "Correct": "c", + "Explanation": "\"area of the shaded portion = 1 \u2044 4 \u00d7 \u03c0 \u00d7 ( 16 ) 2 = 201 m 2 answer c\"" + }, + { + "Answer": 2601, + "Options": "['a ) 2400', 'b ) 2601', 'c ) 1987', 'd ) 2000', 'e ) can not be determined']", + "Correct": "b", + "Explanation": "explanatory answer the shape of the area used for growing broccoli has remained a square in both the years . let the side of the square area used for growing broccoli this year be x ft . therefore , the area of the ground used for cultivation this year = x 2 sq . ft . let the side of the square area used for growing broccoli last year be y ft . therefore , the area of the ground used for cultivation last year = y 2 sq . ft . as the number of broccoli grown has increased by 101 , the area would have increased by 101 sq ft because each broccoli takes 1 sq ft space . hence , x 2 - y 2 = 101 ( x + y ) ( x - y ) = 101 . 101 is a prime number and hence it will have only two factors . i . e . , 101 and 1 . therefore , 101 can be expressed as product of 2 numbers in only way = 101 * 1 i . e . , ( x + y ) ( x - y ) = 101 * 1 so , ( x + y ) should be 101 and ( x - y ) should be 1 . solving the two equations we get x = 51 and y = 50 . therefore , number of broccoli produced this year = x 2 = 512 = 2601 . alternative approach : use answer choices the area in both the years are squares of two numbers . that rules out choice a , c and d . as 2400,1987 and 2000 are not the square of any number . check choice b : if this year ' s produce is 2601 , last year ' s produce would have been 2601 - 101 = 2500 2500 is the square of 50 . so , 2601 is the answer . choice b" + }, + { + "Answer": 96, + "Options": "['a ) 96', 'b ) 86', 'c ) 108', 'd ) 144', 'e ) 118']", + "Correct": "a", + "Explanation": "this question is an example of a ' punch out ' question - we have to find the area of everything , then ' punch out ' the part that we do n ' t want . we ' re told that a wall photo 2 inches wide is placed around a rectangular paper with dimensions 8 inches by 12 inches . we ' re asked for the area of the wall photo , in square inches . area of a rectangle = ( length ) ( width ) so the area of the wall photo is . . . ( 8 ) ( 12 ) = 96 the wall photo ' adds ' 2 inches to the top , bottom , left and right ' sides ' of the picture , so the area of everything is . . . ( 8 + 2 + 2 ) ( 12 + 2 + 2 ) = ( 12 ) ( 16 ) = 196 when we ' punch out ' the area of the paper , we ' ll be left with the area of the wall photo : 192 - 96 = 96 final answer : a" + }, + { + "Answer": 45, + "Options": "a ) a ) 72 , b ) b ) 45 , c ) c ) 729 , d ) d ) 34 , e ) e ) 35", + "Correct": "b", + "Explanation": "\"explanation : area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 36 / 2 = 45 cm 2 answer : option b\"" + }, + { + "Answer": 14, + "Options": "['a ) 2', 'b ) 5', 'c ) 6', 'd ) 7', 'e ) 14']", + "Correct": "e", + "Explanation": "solution : this problem is testing us on the rule that when we express a perfect square by its unique prime factors , every prime factor ' s exponent is an even number . let \u2019 s start by prime factorizing 3,150 . 3,150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2 3,150 = 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 ( notice that the exponents of both 2 and 7 are not even numbers . this tells us that 3,150 itself is not a perfect square . ) we also are given that 3,150 multiplied by d is the square of an integer . we can write this as : 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 x d = square of an integer according to our rule , we need all unique prime factors ' exponents to be even numbers . thus , we need one more 2 and one more 7 . therefore , d = 7 x 2 = 14 answer is e ." + }, + { + "Answer": 150, + "Options": "a ) 158 , b ) 129 , c ) 150 , d ) 123 , e ) 117", + "Correct": "c", + "Explanation": "\"1 / 2 * 15 * 20 = 150 answer : c\"" + }, + { + "Answer": 5941.9251828093165, + "Options": "a ) 4457 , b ) 4567 , c ) 5943 , d ) 4547 , e ) 4675", + "Correct": "c", + "Explanation": "\"explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . \u03c0 r 2 = 175600 \u21d4 ( r ) 2 = ( 175600 x ( 7 / 22 ) ) \u21d4 r = 236.37 m . circumference = 2 \u03c0 r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 4 ) = rs . 5943 . answer : option c\"" + }, + { + "Answer": 840, + "Options": "['a ) 120', 'b ) 240', 'c ) 360', 'd ) 380', 'e ) 840']", + "Correct": "e", + "Explanation": "let the side of the square plot be a ft . a 2 = 196 = > a = 14 length of the fence = perimeter of the plot = 4 a = 56 ft . cost of building the fence = 56 * 15 = rs . 840 . answer : e" + }, + { + "Answer": 180, + "Options": "a ) 120 , b ) 772 , c ) 180 , d ) 266 , e ) 2848", + "Correct": "c", + "Explanation": "\"the triangle with sides 26 cm , 24 cm and 15 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 24 * 15 = 180 cm 2 answer : c\"" + }, + { + "Answer": 225, + "Options": "['a ) 60 .', 'b ) 85 .', 'c ) 125 .', 'd ) 225 .', 'e ) it can not be determined from the information given']", + "Correct": "d", + "Explanation": "length of one side = 15 ( 20 - 5 ) since , its a square , the area will be a = 15 ^ 2 = 225 d is the answer" + }, + { + "Answer": 50, + "Options": "a ) 87 cm 2 , b ) 28 cm 2 , c ) 98 cm 2 , d ) 26 cm 2 , e ) 50 cm 2", + "Correct": "e", + "Explanation": "\"area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 40 / 2 = 50 cm 2 answer : e\"" + }, + { + "Answer": 5, + "Options": "a ) 5 % increase , b ) 7 % increase , c ) 6 % increase , d ) 4 % increase , e ) 3 % increase", + "Correct": "a", + "Explanation": "\"let l and b be 100 each 100 * 100 = 10000 l increase by 40 % = 140 b decrease by 25 % = 75 140 * 75 = 10500 5 % increase answer : a\"" + }, + { + "Answer": 3.0004166666666667, + "Options": "['a ) 2 min', 'b ) 3 min', 'c ) 4 min', 'd ) 5 min', 'e ) 6 min']", + "Correct": "b", + "Explanation": "area of a square field = 7201 sq m let the side of square = a a ^ 2 = 7201 = > a = 84.86 diagonal = ( 2 ) ^ ( 1 / 2 ) * a = 1.414 * 84.86 = 120 speed of lady = 2.4 km / hour = 2400 m / hour = 40 m / min time taken by lady to cross the field diagonally = 120 / 40 = 3 min answer b" + }, + { + "Answer": 6334.72526658735, + "Options": "a ) 2399 , b ) 6336 , c ) 2999 , d ) 5808 , e ) 2888", + "Correct": "b", + "Explanation": "\"explanation : area = ( 13.86 x 10000 ) sq . m = 138600 sq . m circumference = cost of fencing = rs . ( 1320 x 4.80 ) = rs . 6336 . answer : b ) 6336\"" + }, + { + "Answer": 500, + "Options": "a ) 450 , b ) 600 , c ) 500 , d ) 2400 , e ) 3200", + "Correct": "c", + "Explanation": "\"answer a ) 4800 yards need 1200 lbs 1 yard will need 1200 / 8400 = 1 / 7 lbs 3600 yards will need 1 / 7 * 3500 yards = 500 lbs c\"" + }, + { + "Answer": 1600, + "Options": "['a ) 1600', 'b ) 1500', 'c ) 1650', 'd ) 1700', 'e ) can not be determined']", + "Correct": "a", + "Explanation": "explanatory answer the shape of the area used for growing broccoli has remained a square in both the years . let the side of the square area used for growing broccoli this year be x ft . therefore , the area of the ground used for cultivation this year = x 2 sq . ft . let the side of the square area used for growing broccoli last year be y ft . therefore , the area of the ground used for cultivation last year = y 2 sq . ft . as the number of broccoli grown has increased by 79 , the area would have increased by 79 sq ft because each broccoli takes 1 sq ft space . hence , x 2 - y 2 = 79 ( x + y ) ( x - y ) = 79 . 79 is a prime number and hence it will have only two factors . i . e . , 79 and 1 . therefore , 79 can be expressed as product of 2 numbers in only way = 79 * 1 i . e . , ( x + y ) ( x - y ) = 79 * 1 so , ( x + y ) should be 79 and ( x - y ) should be 1 . solving the two equations we get x = 40 and y = 39 . therefore , number of broccoli produced this year = x 2 = 402 = 1600 . alternative approach : use answer choices the area in both the years are squares of two numbers . that rules out choice b , c and d . as 1500,1650 and 1700 are not the square of any number . check choice a : if this year ' s produce is 1600 , last year ' s produce would have been 1600 - 79 = 1521 1521 is the square of 39 . so , 1600 is the answer . choice a" + }, + { + "Answer": 30.000000000000004, + "Options": "['a ) 25 %', 'b ) 30 %', 'c ) 50 %', 'd ) 65 %', 'e ) 70 %']", + "Correct": "b", + "Explanation": "the original area is l * w the new area is 1.4 l * 0.5 w = 0.7 * l * w = l * w - 0.3 * l * w the area decreased by 30 % . the answer is b ." + }, + { + "Answer": 135, + "Options": "['a ) 135', 'b ) 125', 'c ) 145', 'd ) 115', 'e ) 155']", + "Correct": "a", + "Explanation": "( cylinder volume ) / ( cone volume ) ( \u03c0 r ( power 2 ) h ) / ( 1 / 3 \u03c0 r ( power 2 ) h ) = ( \u03c0 \u00d7 12 \u00d7 12 \u00d7 10 ) / ( 1 / 3 \u03c0 \u00d7 4 \u00d7 4 \u00d7 2 ) = 135 answer is a ." + }, + { + "Answer": 6, + "Options": "a ) 3 cm , b ) 4 cm , c ) 6 cm , d ) 8 cm , e ) none", + "Correct": "c", + "Explanation": "\"solution 4 \u03c0 r 2 = 2 \u03c0 6 x 12 \u21d2 r 2 = ( 6 x 12 / 2 ) \u21d2 36 \u21d2 r = 6 cm . answer c\"" + }, + { + "Answer": 6, + "Options": "a ) 6 m , b ) 7 m , c ) 60 m , d ) 13 m , e ) none", + "Correct": "a", + "Explanation": "b * h = 72 . h * 12 = 72 = > h = 6 m . answer : ( a )" + }, + { + "Answer": 40, + "Options": "['a ) 27', 'b ) 35', 'c ) 40', 'd ) 49', 'e ) 38']", + "Correct": "c", + "Explanation": "let length = x meters and breadth = y meters . then , ( x + 1 ) ( y + 1 ) - xy = 21 x + y = 20 \u00e3 \u00a2 \u00e2 \u201a \u00ac \u00e2 \u00a6 \u00e3 \u00a2 \u00e2 \u201a \u00ac \u00e2 \u00a6 \u00e3 \u00a2 \u00e2 \u201a \u00ac \u00e2 \u00a6 \u00e3 \u00a2 \u00e2 \u201a \u00ac \u00e2 \u00a6 \u00e3 \u00a2 \u00e2 \u201a \u00ac \u00e2 \u00a6 \u00e3 \u00a2 \u00e2 \u201a \u00ac \u00e2 \u00a6 1 and , xy - [ ( x + 1 ) ( y - 1 ) ] = 5 x - y = 6 \u00e3 \u00a2 \u00e2 \u201a \u00ac \u00e2 \u00a6 \u00e3 \u00a2 \u00e2 \u201a \u00ac \u00e2 \u00a6 \u00e3 \u00a2 \u00e2 \u201a \u00ac \u00e2 \u00a6 \u00e3 \u00a2 \u00e2 \u201a \u00ac \u00e2 \u00a6 \u00e3 \u00a2 \u00e2 \u201a \u00ac \u00e2 \u00a6 \u00e3 \u00a2 \u00e2 \u201a \u00ac \u00e2 \u00a6 . . 2 solving ( i ) and ( ii ) , we get : x = 13 and y = 7 so , length = 13 m and breadth = 7 m . perimeter = [ 2 ( 13 + 7 ) ] m = 40 m . answer : c" + }, + { + "Answer": 198, + "Options": "['a ) a ) 160 degree', 'b ) b ) 198 degree', 'c ) c ) 191 degree', 'd ) d ) 192 degree', 'e ) e ) 204 degree']", + "Correct": "b", + "Explanation": "let the common ratio be x . . so m = 2 x and f = 3 x and total = 5 x 1 / 4 of m = 2 x / 4 and 3 / 4 of f = 9 / 4 x . . total preferring that carrer = x / 2 + 9 x / 4 = 11 x / 4 now 5 x = 360 , so x = 360 / 5 = 72 . . so 72 * 11 / 4 = 198 ans 198 b" + }, + { + "Answer": 4, + "Options": "a ) 4 , b ) 4 , c ) 6 , d ) 8 , e ) 10", + "Correct": "b", + "Explanation": "\"ans is ` ` b ' ' . for max volume of cylinder ( pi * r ^ 2 * h ) we need to max out r ^ 2 * h . we do n ' t know what the dimensions of the crate refer to . . therefore for max vol base should be 8 x 10 i . e . of radius 8 / 2 = 4 b\"" + }, + { + "Answer": 75, + "Options": "['a ) 50 %', 'b ) 60 %', 'c ) 75 %', 'd ) 80 %', 'e ) 89 %']", + "Correct": "c", + "Explanation": "let the volume of sphere pp be 64 parts . therefore volume of sphere qq = 64 \u2212 3764 % = 64 \u2212 3764 % of 6464 = 64 \u2212 37 = 27 = 64 \u2212 37 = 27 parts . the volume of rr = 27 \u2212 1927 \u00d7 27 = 27 \u2212 1927 \u00d7 27 = 27 \u2212 19 = 8 = 27 \u2212 19 = 8 parts . volume ratio : = p : q : r = 64 : 27 : 8 = p : q : r = 64 : 27 : 8 radius ratio : = p : q : r = 4 : 3 : 2 = p : q : r = 4 : 3 : 2 the surface area will be 16 : 9 : 516 : 9 : 5 surface area of rr is less than the surface area of sphere pp 16 k \u2212 4 k = 12 k 16 k \u2212 4 k = 12 k now , = 12 k 16 k \u00d7 100 = 12 k 16 k \u00d7 100 = 75 % = 75 % thus surface area of sphere rr is less than the surface area of sphere p by 75 % c" + }, + { + "Answer": 3440, + "Options": "['a ) rs . 3430', 'b ) rs . 3440', 'c ) rs . 3450', 'd ) rs . 3460', 'e ) rs . 3490']", + "Correct": "b", + "Explanation": "explanation : in this question , we are having perimeter . we know perimeter = 2 ( l + b ) , right so , 2 ( l + b ) = 340 as we have to make 1 meter boundary around this , so area of boundary = ( ( l + 2 ) + ( b + 2 ) - lb ) = 2 ( l + b ) + 4 = 340 + 4 = 344 so required cost will be = 344 * 10 = 3440 answer : option b" + }, + { + "Answer": 276, + "Options": "a ) 200 , b ) 276 , c ) 230 , d ) 240 , e ) 250", + "Correct": "b", + "Explanation": "let no of sits in vip enclosure is x then x * 45 + 20 ( 320 - x ) = 7500 or 25 x = 7500 - 6400 , x = 1100 / 25 = 44 vip = 44 general 320 - 44 = 276 b" + }, + { + "Answer": 50, + "Options": "['a ) 40', 'b ) 50', 'c ) 60', 'd ) 70', 'e ) 80']", + "Correct": "b", + "Explanation": "alternate approach backsolving ( using answer options to reach the correct answer ) can work wonders here if one is fast in calculations . given perimeter is 150 so , 2 ( l + b ) = 150 or , l + b = 75 now use the answer options ( given length ; breath will be half the length ) ( a ) 40 l = 40 ; b = 20 l + b = 60 ( b ) 50 l = 50 ; b = 25 l + b = 75 ( c ) 60 l = 60 ; b = 30 l + b = 90 ( d ) 70 l = 70 ; b = 35 l + b = 105 ( e ) 80 l = 80 ; b = 40 l + b = 120 thus you see no , need of any calculations , u can reach the correct option only by checking options ; correct answer will be ( b )" + }, + { + "Answer": 60, + "Options": "a ) 30 , b ) 45 , c ) 60 , d ) 75 , e ) 90", + "Correct": "c", + "Explanation": "\"c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be 60 . c\"" + }, + { + "Answer": 9.18, + "Options": "a ) 9.18 , b ) 9.25 , c ) 9.5 , d ) 8.98 , e ) 8.88", + "Correct": "a", + "Explanation": "\"100 * 100 = 10000 103 * 106 = 10918 - - - - - - - - - - - 918 10000 - - - - - - - 918 100 - - - - - - - - - - 9.18 ans a\"" + }, + { + "Answer": 54, + "Options": "a ) 88 m 2 , b ) 10 m 2 , c ) 66 m 2 , d ) 54 m 2 , e ) 31 m 2", + "Correct": "d", + "Explanation": "\"1 / 2 * 18 * 6 = 54 m 2 answer : d\"" + }, + { + "Answer": 12, + "Options": "a ) 12 , b ) 9 , c ) 7 , d ) 6 , e ) 5", + "Correct": "a", + "Explanation": "\"2 x * x = 288 = > x = 12 answer : a\"" + }, + { + "Answer": 0.1111111111111111, + "Options": "a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 5 , e ) 1 / 3", + "Correct": "a", + "Explanation": "\"if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 8,12 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives q = 1 / 9 . a\"" + }, + { + "Answer": 4.5, + "Options": "['a ) decrease by 12.5 %', 'b ) increase by 12.5 %', 'c ) increase by 4.5 %', 'd ) increase by 25 %', 'e ) none of these']", + "Correct": "c", + "Explanation": "explanation : let the initial height be 100 and the base be 200 units . \u00e2 \u02c6 \u00b4 area = 1 / 2 x 100 x 200 = 10000 sq units now , height = 95 units and base = 220 units \u00e2 \u02c6 \u00b4 new area = 1 / 2 x 95 x 220 = 10450 \u00e2 \u02c6 \u00b4 area is increased by ( 10450 - 10000 ) / 10000 x 10 = 4.5 % answer : option c" + }, + { + "Answer": 100, + "Options": "a ) 100 feet , b ) 120 feet , c ) 150 feet , d ) 180 feet , e ) 186 feet", + "Correct": "a", + "Explanation": "\"explanation : we are given with length and area , so we can find the breadth . as length * breadth = area = > 20 * breadth = 800 = > breadth = 40 feet area to be fenced = 2 b + l = 2 * 40 + 20 = 100 feet answer : option a\"" + }, + { + "Answer": 50, + "Options": "a ) 43 % , b ) 47 % , c ) 50 % , d ) 65 % , e ) 68 %", + "Correct": "c", + "Explanation": "\"let original length = x and original breadth = y . original area = xy . new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c\"" + }, + { + "Answer": 10, + "Options": "a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 10", + "Correct": "e", + "Explanation": "\"if the width is w , then length and height would be w / 2 . so , w * w / 2 * w / 2 = 128 = > w ^ 3 = ( 2 ^ 3 ) * 64 = ( 2 ^ 3 ) * ( 4 ^ 3 ) = > w = 2 * 4 = 8 in . along the width of the cuboid , 8 cubes do n ' t touch the tin foil . so the actual width will be non - touching cubes + touching cubes = 8 + 2 = y = 10 ans e .\"" + }, + { + "Answer": 507, + "Options": "a ) 507 sq m , b ) 356 sq m , c ) 452 sq m , d ) 428 sq m , e ) 525 sq m", + "Correct": "a", + "Explanation": "\"2 ( 3 x + x ) = 104 l = 39 b = 13 lb = 39 * 13 = 507 answer : a\"" + }, + { + "Answer": 74, + "Options": "a ) 74 ft , b ) 88 ft , c ) 22 ft , d ) 11 ft , e ) 66 ft", + "Correct": "a", + "Explanation": "\"given that length and area , so we can find the breadth . length x breadth = area 34 x breadth = 680 breadth = 20 feet area to be fenced = 2 b + l = 2 ( 20 ) + 34 = 88 feet answer : a ) 74 ft\"" + }, + { + "Answer": 301.59289474462014, + "Options": "a ) 32 m 3 , b ) 36 m 3 , c ) 40 m 3 , d ) 44 m 3 , e ) 301.6", + "Correct": "e", + "Explanation": "\"solution volume = \u03c0 r 2 h \u2039 = \u203a ( 22 / 7 \u00d7 2 \u00d7 2 \u00d7 24 ) m 3 \u2039 = \u203a 301.6 m 3 . answer e\"" + }, + { + "Answer": 96, + "Options": "['a ) 72', 'b ) 84', 'c ) 96', 'd ) 108', 'e ) 120']", + "Correct": "c", + "Explanation": "each side of the cube has 6 x 6 = 36 cubelets . only the interior cubelets are painted one colour . on each side , 4 x 4 = 16 cubelets are painted one colour . since the cube has six sides , the number of cubes with one colour is 6 * 16 = 96 the answer is c ." + }, + { + "Answer": 46, + "Options": "['a ) 44 cm', 'b ) 42 cm', 'c ) 46 cm', 'd ) 49 cm', 'e ) 41 cm']", + "Correct": "c", + "Explanation": "second side = \u221a 17 power 2 - 8 power 2 = \u221a 289 - 64 = 15 cm perimeter = 2 ( l + b ) = 2 ( 8 + 5 ) cm = 2 ( 23 ) = 46 cm answer is c ." + }, + { + "Answer": 149.248115565993, + "Options": "a ) 100 , b ) 120 , c ) 150 , d ) 148.5 , e ) none", + "Correct": "d", + "Explanation": "\"solution other side = \u221a ( 18 ) 2 - ( 15 ) 2 = \u221a 324 - 225 = \u221a 99 = 9.9 m . \u2234 area = ( 15 x 9.9 ) m 2 = 148.5 m 2 . answer d\"" + }, + { + "Answer": 10, + "Options": "['a ) 6', 'b ) 40', 'c ) 15', 'd ) 10', 'e ) 22']", + "Correct": "d", + "Explanation": "volume of the block = 15 * 30 * 75 = 33750 cm ^ 3 side of the largest cube = h . c . f of 15 , 30,75 = 15 cm volume of the cube = 15 * 15 * 15 = 3375 cm ^ 3 number of cubes = 33750 / 3375 = 10 answer is d" + }, + { + "Answer": 12, + "Options": "a ) 11 m 2 , b ) 10 m 2 , c ) 18 m 2 , d ) 19 m 2 , e ) 12 m 2", + "Correct": "e", + "Explanation": "\"1 / 2 * 4 * 6 = 12 m 2 answer : e\"" + }, + { + "Answer": 18, + "Options": "['a ) 18 cm', 'b ) 19 cm', 'c ) 20 cm', 'd ) 21 cm', 'e ) none']", + "Correct": "a", + "Explanation": "solution : if the side of the square is 12 cm , then its perimetre will be 48 cm . we build the rectangle from the same wire , so it will have the same perimetre . its width is 6 cm , so its length will be ( 48 - 12 ) \u00f7 2 = 36 \u00f7 2 = 18 cm answer a" + }, + { + "Answer": 60, + "Options": "a ) 107 , b ) 60 , c ) 70 , d ) 89 , e ) 78", + "Correct": "b", + "Explanation": "\"number of cubes required = volume of box / volume of cube = 8 * 15 * 5 / 10 = 60 cubes answer : b\"" + }, + { + "Answer": 75, + "Options": "['a ) 45 %', 'b ) 56 %', 'c ) 67 %', 'd ) 75 %', 'e ) none of these']", + "Correct": "d", + "Explanation": "explanation : we will first subtract the cone volume from wood volume to get the wood wasted . then we can calculate its percentage . sphere volume = 4 / 3 \u03c0 r 3 cone volume = 1 / 3 \u03c0 r 2 h volume of wood wasted = ( 4 / 3 \u03c0 \u2217 9 \u2217 9 \u2217 9 ) \u2212 ( 1 / 3 \u03c0 \u2217 9 \u2217 9 \u2217 9 ) = \u03c0 \u2217 9 \u2217 9 \u2217 9 cm 3 required percentage = \u03c0 \u2217 9 \u2217 9 \u2217 9 / 4 / 3 \u03c0 \u2217 9 \u2217 9 \u2217 9 \u2217 100 % = 3 / 4 \u2217 100 % = 75 % option d" + }, + { + "Answer": 1680, + "Options": "a ) 1276 , b ) 1680 , c ) 2832 , d ) 1299 , e ) 1236", + "Correct": "b", + "Explanation": "\"explanation : l * 30 = 1200 \u00e8 l = 40 40 + 30 + 50 = 120 120 * 14 = 1680 answer : option b\"" + }, + { + "Answer": 1687.5, + "Options": "a ) 975.5 , b ) 1250.5 , c ) 1465.5 , d ) 1687.5 , e ) 1824.5", + "Correct": "d", + "Explanation": "\"2 hl + 2 hw = 2 lw h = lw / ( l + w ) volume = lwh = ( lw ) ^ 2 / ( l + w ) = 1687.5 the answer is d .\"" + }, + { + "Answer": 314, + "Options": "a ) 152 m 2 , b ) 162 m 2 , c ) 180 m 2 , d ) 300 m 2 , e ) 314 m 2", + "Correct": "e", + "Explanation": "\"surface area of a cuboid = 2 ( lb + bh + lh ) = 2 ( 9 * 8 + 8 * 5 + 9 * 5 ) = 2 ( 72 + 40 + 45 ) = 2 * 157 = 314 m 2 answer : e\"" + }, + { + "Answer": 0.03703703703703703, + "Options": "['a ) 1 / 4', 'b ) 1 / 5', 'c ) 1 / 6', 'd ) 1 / 27', 'e ) 1 / 9']", + "Correct": "d", + "Explanation": "the length of cube q = 1 ; the length of cube p = 3 ; the ratio of the volume of cube q to the volume of cube p = 1 ^ 3 / 3 ^ 3 = 1 / 27 answer : d" + }, + { + "Answer": 43.99999999999999, + "Options": "a ) 33 % , b ) 44 % , c ) 55 % , d ) 56 % , e ) 73 %", + "Correct": "b", + "Explanation": "\"the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 20 % increase a surface = 6 * ( ( 1.2 a ) ^ 2 ) = 6 * 1.44 * a ^ 2 the increase in the surface area = ( 6 * 1.44 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 1.44 - 1 ) ) / ( 6 * a ^ 2 ) = 1.44 - 1 = 0.44 = 44 % answer : b\"" + }, + { + "Answer": 161.9601685880785, + "Options": "['a ) 162', 'b ) 766', 'c ) 298', 'd ) 277', 'e ) 198']", + "Correct": "a", + "Explanation": "explanation : perimeter of window = { \\ color { blue } \\ pi } r + 2 r = [ { ( 22 / 7 ) * ( 63 / 2 ) } + 63 ] = 99 + 63 = 162 cm answer : a ) 162" + }, + { + "Answer": 231, + "Options": "a ) 231 cm 2 , b ) 384 cm 2 , c ) 672 cm 2 , d ) 267 cm 2 , e ) 286 cm 2", + "Correct": "a", + "Explanation": "\"area of a parallelogram = base * height = 21 * 11 = 231 cm 2 answer : a\"" + }, + { + "Answer": 60, + "Options": "a ) 60 , b ) 70 , c ) 80 , d ) 90 , e ) 100", + "Correct": "a", + "Explanation": "\"alternate approach backsolving ( using answer options to reach the correct answer ) can work wonders here if one is fast in calculations . given perimeter is 180 so , 2 ( l + b ) = 180 or , l + b = 90 now use the answer options ( given length ; breath will be half the length ) ( a ) 60 l = 60 ; b = 30 l + b = 90 ( b ) 70 l = 70 ; b = 35 l + b = 105 ( c ) 80 l = 80 ; b = 40 l + b = 120 ( d ) 90 l = 90 ; b = 45 l + b = 135 ( e ) 100 l = 100 ; b = 50 l + b = 150 thus you see no , need of any calculations , u can reach the correct option only by checking options ; correct answer will be ( a )\"" + }, + { + "Answer": 2016, + "Options": "['a ) 3008', 'b ) 2002', 'c ) 1008', 'd ) 2016', 'e ) 3000']", + "Correct": "d", + "Explanation": "note that trapezoids axy d and bxy c are congruent , so the area of axy d is always 4032 / 2 = 2016 . correct answer d" + }, + { + "Answer": 0.36, + "Options": "['a ) 3 / 6', 'b ) 8 / 24', 'c ) 14 / 16', 'd ) 9 / 25', 'e ) 2 / 3']", + "Correct": "d", + "Explanation": "the questions asks us to find the surface which is not covered by the inner circle i . e . , area of the surface not covered . where as circumference is the length along the edge of the circle , 2 * pi * r implies the length of the curve pi * r ^ 2 implies area enclosed by that curve . . hence area of the circle is considered for this problem area of the inner circle = pi * r ^ 2 , where r = 12 = > pi * 144 area of the outer circle = pi * 225 surface not covered by the inner circle = pi * 225 - pi * 144 = pi * 81 fraction of outer circle ' s surface is not covered by the inner circle = pi * 81 / total area of the outer circle = > pi * 81 / pi * 225 = 9 / 25 answer is d" + }, + { + "Answer": 4012, + "Options": "a ) 3944 , b ) 920 , c ) 7290 , d ) 6928 , e ) 4012", + "Correct": "e", + "Explanation": "\"explanation : let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 59 = rs . 4012 . answer : option e\"" + }, + { + "Answer": 16, + "Options": "a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) none of the above", + "Correct": "d", + "Explanation": "\"d it takes 3 distinct points to define a circle . only 2 are given here . the two points essentially identify a single chord of the circle c . since no other information is provided , however , the radius of the circle can essentially be anything . all this information tell us is that the radius isgreater 16 d\"" + }, + { + "Answer": 0.375, + "Options": "['a ) 5 / 12', 'b ) 3 / 5', 'c ) 1 / 2', 'd ) 3 / 8', 'e ) 5 / 6']", + "Correct": "d", + "Explanation": "so we are looking for the area of the cloth over the area of the table area of the cloth = ( pi ) ( r ) ^ 2 which is about ( 3 ) ( 9 ) ( 9 ) area of the table = ( 24 ) ( 24 ) so the quick way to estimate is looking at the fraction like this : ( 3 / 24 ) ( 81 / 24 ) i hope this is easy to follow , so with some simplification i get ( 1 / 8 ) ( 3 ) = ( 3 / 8 ) answer is d" + }, + { + "Answer": 24, + "Options": "a ) 18 square meters , b ) 20 square meters , c ) 24 square meters , d ) 28 square meters , e ) 30 square meters", + "Correct": "c", + "Explanation": "\"total = rug 1 + rug 2 + rug 3 - { overlap of exactly 2 rugs } - 2 * { overlap of exactly 3 rugs } 140 = 212 - 24 - 2 * { overlap of exactly 2 rugs } - - > { overlap of exactly 3 rugs } = 24 . answer : c .\"" + }, + { + "Answer": 675, + "Options": "a ) 432 sq m , b ) 356 sq m , c ) 452 sq m , d ) 428 sq m , e ) 675 sq m", + "Correct": "e", + "Explanation": "\"2 ( 3 x + x ) = 120 l = 45 b = 15 lb = 45 * 15 = 675 answer : e\"" + }, + { + "Answer": 2638.9378290154264, + "Options": "['a ) 260 cm 2', 'b ) 2610 cm 2', 'c ) 2600 cm 2', 'd ) 2640 cm 2', 'e ) 264 cm 2']", + "Correct": "d", + "Explanation": "volume = pier 2 h = pie x 72 x 60 = 9240 cm 3 curved surface area = 2 pierh = ( 2 x 3.14 x 7 x 60 ) cm 2 = 2640 cm 2 answer : d" + }, + { + "Answer": 50, + "Options": "a ) 11 , b ) 10 , c ) 50 , d ) 122 , e ) 12", + "Correct": "c", + "Explanation": "\"1 / 2 * 10 * 10 = 50 m 2 answer : c\"" + }, + { + "Answer": 279, + "Options": "a ) 144 , b ) 131 , c ) 279 , d ) 90 , e ) 45", + "Correct": "c", + "Explanation": "\"there are 18 business exec and in each handshake 2 business execs are involved . hence 18 c 2 = 153 also , each of 18 exec will shake hand with every 7 other chairmen for total of 126 handshake . total = 153 + 126 = 279 ans : c\"" + }, + { + "Answer": 63, + "Options": "['a ) 63 cm', 'b ) 53 cm', 'c ) 56 cm', 'd ) 66 cm', 'e ) none of these']", + "Correct": "a", + "Explanation": "volume of the bucket = volume of the sand emptied volume of sand = \u03c0 ( 21 ) 2 \u00d7 36 let r be the radius of the conical heap . then , 1 \u2044 3 \u03c0 r 2 \u00d7 12 = \u03c0 ( 21 ) 2 \u00d7 36 or r 2 = ( 21 ) 2 \u00d7 9 or r = 21 \u00d7 3 = 63 answer a" + }, + { + "Answer": 162, + "Options": "a ) 120 cm 2 , b ) 112 cm 2 , c ) 162 cm 2 , d ) 666 cm 2 , e ) 886 cm 2", + "Correct": "c", + "Explanation": "\"the triangle with sides 32 cm , 27 cm and 12 cm is right angled , where the hypotenuse is 32 cm . area of the triangle = 1 / 2 * 27 * 12 = 162 cm 2 answer : c\"" + }, + { + "Answer": 36, + "Options": "a ) 36 , b ) 4 , c ) 16 , d ) 38 , e ) 40", + "Correct": "a", + "Explanation": "\"pythogoras will help here ! let the sides be x and diagonal be d then d ^ 2 = 2 x ^ 2 and area = x ^ 2 now plug in the given diagonal values to find x values and then subtract the areas ans will be 19 ^ 2 / 2 - 17 ^ 2 / 2 = 72 / 2 = 36 ans a .\"" + }, + { + "Answer": 27, + "Options": "a ) 27 , b ) 36 , c ) 42 , d ) 64 , e ) 147", + "Correct": "a", + "Explanation": "\"112 ounces of a substance has a volume of 48 cubic inches 63 ounces of a substance has a volume of ( 48 / 112 ) * 63 = 27 cubic inches answer a alternatively , we can use estimation 112 ounces of a substance has a volume of 48 cubic inches 56 ounces of a substance has a volume of 24 cubic inches therefore , 63 will have a volume a little more than 24 , that is 27 answer : a\"" + }, + { + "Answer": 4290, + "Options": "a ) 4290 , b ) 2535 , c ) 2530 , d ) 2515 , e ) 2520", + "Correct": "a", + "Explanation": "\"length = breadth + 23 . therefore , 4 \u00d7 breadth + 2 \u00d7 23 = 266 m \u21d2 breadth = 55 m length = 55 + 23 = 78 m area = 78 \u00d7 55 = 4290 m 2 answer is a .\"" + }, + { + "Answer": 384, + "Options": "['a ) 354', 'b ) 384', 'c ) 324', 'd ) 344', 'e ) 364']", + "Correct": "b", + "Explanation": "\u221a 3 . a = 8 \u221a 3 = > a = 8 volume = a ( power ) 3 = > ( 8 \u00d7 8 \u00d7 8 ) cm ( power ) 3 = > 512 cm ( power ) 3 surface area = > 6 a ( power ) 2 = > ( 6 \u00d7 8 \u00d7 8 ) cm ( power ) 2 = > 384 cm ( power ) 2 answer is b ." + }, + { + "Answer": 144, + "Options": "['a ) 128', 'b ) 136', 'c ) 144', 'd ) 152', 'e ) 160']", + "Correct": "c", + "Explanation": "1 / 4 * 2 / 5 + 1 / 2 * 3 / 5 = 2 / 20 + 6 / 20 = 2 / 5 the number of degrees is 2 / 5 * 360 = 144 degrees the answer is c ." + }, + { + "Answer": 4480, + "Options": "a ) 4480 , b ) 5120 , c ) 6420 , d ) 8960 , e ) 7960", + "Correct": "a", + "Explanation": "\"clearly , l = ( 48 - 8 ) m = 40 m , b = ( 36 - 8 ) m = 28 m , h = 8 m . volume of the box = ( 40 x 28 x 4 ) m 3 = 4480 m 3 . answer : option a\"" + }, + { + "Answer": 1008, + "Options": "a ) 3008 , b ) 2002 , c ) 1008 , d ) 2016 , e ) 3000", + "Correct": "c", + "Explanation": "note that trapezoids axy d and bxy c are congruent , so the area of axy d is always 2016 / 2 = 1008 . correct answer c" + }, + { + "Answer": 56, + "Options": "a ) 48 , b ) 56 , c ) 60 , d ) 56 , e ) 192", + "Correct": "d", + "Explanation": "\"say length of garden is l meters . then ( l * 16 ) = 16 * 12 [ given area is same . area = l * b ] therefore l works out to 12 meters . perimeter of garden = 2 * ( 12 + 16 ) = 56 meter . answer is d\"" + }, + { + "Answer": 160, + "Options": "['a ) 289 cm', 'b ) 160 cm', 'c ) 829 cm', 'd ) 288 cm', 'e ) 289 cm']", + "Correct": "b", + "Explanation": "area of the square = s * s = 5 ( 32 * 10 ) = 1600 = > s = 40 = 40 cm perimeter of the square = 4 * 40 = 160 cm . answer : b" + }, + { + "Answer": 140, + "Options": "['a ) 140 sq . units', 'b ) 149', 'c ) 148', 'd ) 17', 'e ) 143']", + "Correct": "a", + "Explanation": "given that the area of the square = 1225 sq . units = > side of square = \u221a 1225 = 35 units the radius of the circle = side of the square = 35 units length of the rectangle = 2 / 5 * 35 = 14 units given that breadth = 10 units area of the rectangle = lb = 14 * 10 = 140 sq . units answer : option a" + }, + { + "Answer": 12.25, + "Options": "a ) 15.25 sq cm , b ) 18.25 sq cm , c ) 12.25 sq cm , d ) 21.25 sq cm , e ) 25.25 sq cm", + "Correct": "c", + "Explanation": "\"though there might be some technicalities concerning the termnearest ( as 3.5 is equidistant from both 3 and 4 ) the answer still should be : 3.5 ^ 2 = 12.25 . answer : c\"" + }, + { + "Answer": 4080, + "Options": "a ) s . 3944 , b ) s . 3948 , c ) s . 4080 , d ) s . 3965 , e ) s . 3929", + "Correct": "c", + "Explanation": "\"let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 60 = rs . 4080 . answer : c\"" + }, + { + "Answer": 12, + "Options": "['a ) 10', 'b ) 11', 'c ) 12', 'd ) 13', 'e ) 14']", + "Correct": "c", + "Explanation": "area = l * w = 3 w ^ 2 = 432 w ^ 2 = 144 w = 12 the answer is c ." + }, + { + "Answer": 8, + "Options": "a ) 5 , b ) 6 , c ) 8 , d ) 13 , e ) 28", + "Correct": "c", + "Explanation": "\"suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 96 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , number of tiles = ( r - 2 ) * ( c + 4 ) = 96 comparing both of them we get c * r = ( r - 2 ) * ( c + 4 ) = > 4 r - 2 c = 8 c = 2 r - 4 putting it in c * r = 96 ( 2 r - 4 ) * r = 96 2 r ^ 2 - 4 r - 96 = 0 r can not be negative so r = 8 and c = 12 so , answer will be c\"" + }, + { + "Answer": 576, + "Options": "a ) 122 cm 2 , b ) 576 cm 2 , c ) 246 cm 2 , d ) 42 cm 2 , e ) 39 cm 2", + "Correct": "b", + "Explanation": "\"area of a parallelogram = base * height = 12 * 48 = 576 cm 2 answer : b\"" + }, + { + "Answer": 2, + "Options": "['a ) 5', 'b ) 4', 'c ) 7', 'd ) 2', 'e ) 1']", + "Correct": "d", + "Explanation": "let the sides of the rectangle be l and b respectively . from the given data , ( \u221a l 2 + b 2 ) = ( 1 + 108 1 / 3 % ) lb = > l 2 + b 2 = ( 1 + 325 / 3 * 1 / 100 ) lb = ( 1 + 13 / 12 ) lb = 25 / 12 lb = > ( l 2 + b 2 ) / lb = 25 / 12 12 ( l 2 + b 2 ) = 25 lb adding 24 lb on both sides 12 l 2 + 12 b 2 + 24 lb = 49 lb 12 ( l 2 + b 2 + 2 lb ) = 49 lb but 2 ( l + b ) = 28 = > l + b = 14 12 ( l + b ) 2 = 49 lb = > 12 ( 14 ) 2 = 49 lb = > lb = 48 since l + b = 14 , l = 8 and b = 6 l - b = 8 - 6 = 2 m . answer : d" + }, + { + "Answer": 9409, + "Options": "a ) 8,208 , b ) 9,409 , c ) 11,424 , d ) 12,586 , e ) can not be determined", + "Correct": "b", + "Explanation": "\"let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 193 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 193 ( x + y ) ( x - y ) = 193 193 is a prime number and thus it will be ( 97 + 96 ) * ( 97 - 96 ) . thus x = 97 and y = 96 x ^ 2 = 97 ^ 2 = 9409 the answer is b .\"" + }, + { + "Answer": 14, + "Options": "a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 14", + "Correct": "e", + "Explanation": "solution : this problem is testing us on the rule that when we express a perfect square by its unique prime factors , every prime factor ' s exponent is an even number . let \u2019 s start by prime factorizing 3150 . 3150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2 3150 = 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 ( notice that the exponents of both 2 and 7 are not even numbers . this tells us that 3150 itself is not a perfect square . ) we also are given that 3150 multiplied by d is the square of an integer . we can write this as : 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 x d = square of an integer according to our rule , we need all unique prime factors ' exponents to be even numbers . thus , we need one more 2 and one more 7 . therefore , d = 7 x 2 = 14 answer is e ." + }, + { + "Answer": 194, + "Options": "['a ) 194', 'b ) 195', 'c ) 196', 'd ) 197', 'e ) 198']", + "Correct": "a", + "Explanation": "volume of cube of dimensions 7 7 6 is 7 * 7 * 6 = 294 if it were to look hollow the imaginary inside cube volume is to be deducted which is ( 7 - 2 ) * ( 7 - 2 ) * ( 6 - 2 ) = 100 ( here 2 is deducted because the inside cube which has to be hollow is 2 cubes more on every dimension ) so minimum number of cubes required to make hollow cube is 294 - 100 = 194 cubes answer : a" + }, + { + "Answer": 6500, + "Options": "a ) 6500 , b ) 2779 , c ) 2779 , d ) 3900 , e ) 2781", + "Correct": "a", + "Explanation": "\"area = ( l + b \u00e2 \u20ac \u201c d ) d ( 80 + 60 \u00e2 \u20ac \u201c 10 ) 10 = > 1300 m 2 1300 * 5 = rs . 6500 answer : a\"" + }, + { + "Answer": 18, + "Options": "['a ) 18', 'b ) 28', 'c ) 38', 'd ) 48', 'e ) 58']", + "Correct": "a", + "Explanation": "explanation : l 2 + b 2 = 41 also , lb = 20 ( l + b ) 2 = l 2 + b 2 + 2 lb = 41 + 40 = 81 ( l + b ) = 9 perimeter = 2 ( l + b ) = 18 cm . answer : a" + }, + { + "Answer": 37.69911184307752, + "Options": "['a ) 75.4', 'b ) 31.42', 'c ) 36', 'd ) 18.85', 'e ) 37.7']", + "Correct": "e", + "Explanation": "circumference of a circle = c = 2 \u00ef \u20ac r square is 12 wide , so circle ' s diameter would be 12 , and radius would be 6 c = 2 \u00ef \u20ac 6 which is approximately 37.7 answer is e" + }, + { + "Answer": 36, + "Options": "a ) 5 square inches , b ) 36 square inches , c ) 15 square inches , d ) 25 square inches , e ) 350 square inches", + "Correct": "b", + "Explanation": "\"in the first case each can buy one pizza of $ 10 and one pizza of $ 20 . in square inches that would be ( 12 * 12 = 144 ) for the small pizza and ( 18 * 18 = 324 ) for the large pizza . in total sq inches that would be ( 144 + 324 ) * 2 = 936 sq inches . in the second case if they pool their money together they can buy 3 large pizzas . in terms of square inches that would be 3 * 324 = 972 sq inches . hence , the difference is 36 square inches more ( 972 - 936 ) . the correct answer is b\"" + }, + { + "Answer": 5, + "Options": "['a ) 2.5', 'b ) 5', 'c ) 10', 'd ) 15', 'e ) 20']", + "Correct": "b", + "Explanation": "longest chord of a circle is the diameter of the circle diameter = 2 * radius if diameter of the circle is given as 10 = 2 * 5 so radius of the circle = 5 correct answer - b" + }, + { + "Answer": 0.036, + "Options": "a ) 0.036 , b ) 0.36 , c ) 0.6 , d ) 6 , e ) 3.6", + "Correct": "a", + "Explanation": "\"the volume of oil pumped to the tank = the volume of oil taken away from stationary cylinder . pi * 36 * 10 = pi * h * 100 * 100 ( h is distance that the oil level dropped ) h = 360 / 10,000 = 36 / 1000 = 0.036 ft the answer is a .\"" + }, + { + "Answer": 43, + "Options": "a ) 43 square meters , b ) 36 square meters , c ) 42 square meters , d ) 83.3 square meters , e ) 120 square meters", + "Correct": "a", + "Explanation": "\"300 - 180 = 120 sq m of the wallpaper overlaps ( in either two layers or three layers ) if 36 sq m has two layers , 120 - 34 = 86 sq m of the wallpaper overlaps in three layers . 86 sq m makes two extra layers hence the area over which it makes two extra layers is 43 sq m . answer ( a ) .\"" + }, + { + "Answer": 12, + "Options": "['a ) 12', 'b ) 15', 'c ) 10', 'd ) 8', 'e ) 14']", + "Correct": "a", + "Explanation": "think of a pringles can . if you took off the bottom and top and cut a slit down the length , it would flatten to a rectangle . the dimensions of the rectangle are the height of the can and the circumference of the circle . since you know both , one side and thehypothenuse use pythagoreans theorem or properties of 3 - 4 - 5 triangles to solve for the other side , 12 . correct answer a" + }, + { + "Answer": 3.3333333333333335, + "Options": "a ) 3.33 , b ) 3.34 , c ) 3.53 , d ) 5.32 , e ) 3.92", + "Correct": "a", + "Explanation": "\"300 kg - 1 cubic meter ; 300,000 g - 1 cubic meter ; 300,000 g - 1 , 000,000 cubic centimeters ; 1 g - 1 , 000,000 / 300,000 = 10 / 3 = 3.33 cubic centimeters . answer : a .\"" + }, + { + "Answer": 18, + "Options": "a ) 10 feet , b ) 12 feet , c ) 13 feet , d ) 15 feet , e ) 18 feet", + "Correct": "e", + "Explanation": "\"total circuit = 18 / 3 = 6 total feet squirrel travels = 6 * 3 = 18 feet answer : e\"" + }, + { + "Answer": 1.875, + "Options": "['a ) 15 ohms', 'b ) 15 / 8 ohms', 'c ) 1 / 8 ohms', 'd ) 8 / 15 ohms', 'e ) 8 ohms']", + "Correct": "b", + "Explanation": "the wording is a bit confusing , though basically we are told that 1 / r = 1 / 3 + 1 / 5 , from which it follows that r = 15 / 8 ohms . answer : b ." + }, + { + "Answer": 40, + "Options": "a ) 40 , b ) 33 , c ) 50 , d ) 51 , e ) 52", + "Correct": "a", + "Explanation": "\"yes , ensure that you understand the relation thoroughly ! cost per liter = k * fraction of spirit 40 cents is the cost of 2 liters of solution ( 1 part water , 1 part spirit ) . so cost per liter is 20 cents . fraction of spirit is 1 / 2 . 20 = k * ( 1 / 2 ) k = 40 cost per liter = 40 * ( 1 / 3 ) ( 1 part spirit , 2 parts water ) cost for 3 liters = 40 * ( 1 / 3 ) * 3 = 40 cents a . 40 cents\"" + }, + { + "Answer": 9, + "Options": "a ) 2.5 , b ) 9 , c ) 10 , d ) 15 , e ) 20", + "Correct": "b", + "Explanation": "\"longest chord of a circle is the diameter of the circle diameter = 2 * radius if diameter of the circle is given as 18 = 2 * 9 so radius of the circle = 9 correct answer - b\"" + }, + { + "Answer": 20, + "Options": "a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25", + "Correct": "d", + "Explanation": "\"l * w = 500 : area , l is the length and w is the width . 2 l + 2 w = 90 : perimeter l = 45 - w : solve for l ( 45 - w ) * w = 500 : substitute in the area equation w = 20 and l = 25 correct answer d\"" + }, + { + "Answer": 80, + "Options": "a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 100", + "Correct": "d", + "Explanation": "\"a quick note on doubling . when you double a length you have 2 * l 1 . when you double all lengths of a rectangle you have ( 2 * l 1 ) ( 2 * l 2 ) = a . an increase of 2 ^ 2 or 4 . when you double all lengths of a rectangular prism you have ( 2 * l 1 ) ( 2 * l 2 ) ( 2 * l 3 ) = v . an increase of 2 ^ 3 or 8 . this leads to the basic relationship : line : 2 * original size rectangle : 4 * original size rectangular prism : 8 * original size answer is d\"" + }, + { + "Answer": 150, + "Options": "a ) 200 , b ) 350 , c ) 100 , d ) 150 , e ) 120", + "Correct": "d", + "Explanation": "\"the 5 inch side should be aligned to the 15 inch side ( 3 layer ) 2 inch side should be aligned to the 20 inch side . ( 10 layer ) 7 inch side should be aligned to the 35 inch side . ( 5 layer ) maximum number of rectangles = 3 * 10 * 5 = 150 answer is d\"" + }, + { + "Answer": 288, + "Options": "a ) 297 cm 2 , b ) 384 cm 2 , c ) 672 cm 2 , d ) 267 cm 2 , e ) 288 cm 2", + "Correct": "e", + "Explanation": "\"area of a parallelogram = base * height = 24 * 12 = 288 cm 2 answer : e\"" + }, + { + "Answer": 24, + "Options": "['a ) 19', 'b ) 23', 'c ) 24', 'd ) 16', 'e ) 17']", + "Correct": "c", + "Explanation": "4 x * x = 2304 = > x = 24 answer : c" + }, + { + "Answer": 0.88, + "Options": "a ) 0.11 % , b ) 0.7 % , c ) 0.4 % , d ) 0.6 % , e ) 0.88 %", + "Correct": "e", + "Explanation": "\"let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 26 / 25 ) x ( 32 / 33 ) y = ( 344 / 341 ) ( xy ) error in measurement = ( 344 / 341 ) xy - xy = ( 3 / 341 ) xy error percentage = [ ( 3 / 341 ) xy ( 1 / xy ) 100 ] % = ( 22 / 25 ) % = 0.88 % . answer is e .\"" + }, + { + "Answer": 100, + "Options": "a ) 50 % , b ) 87 % , c ) 100 % , d ) 187 % , e ) 200 %", + "Correct": "c", + "Explanation": "\"let ' s just look at the dimensions ( no calculation needed ) . with dimension 11 the same , the other dimension 15 is twice 7.5 then the area will be double which means 100 % greater . the answer is c .\"" + }, + { + "Answer": 30, + "Options": "a ) 13 , b ) 30 , c ) 50 , d ) 51 , e ) 52", + "Correct": "b", + "Explanation": "\"yes , ensure that you understand the relation thoroughly ! cost per liter = k * fraction of spirit 30 cents is the cost of 2 liters of solution ( 1 part water , 1 part spirit ) . so cost per liter is 15 cents . fraction of spirit is 1 / 2 . 15 = k * ( 1 / 2 ) k = 30 cost per liter = 30 * ( 1 / 3 ) ( 1 part spirit , 2 parts water ) cost for 3 liters = 30 * ( 1 / 3 ) * 3 = 50 cents b . 30 cents\"" + }, + { + "Answer": 420, + "Options": "['a ) there is no empty capacity', 'b ) 100 gallons', 'c ) 300 gallons', 'd ) 420 gallons', 'e ) 840 gallons']", + "Correct": "d", + "Explanation": "radius of first cylinder = r , diameter = 2 r , height = h radius of second cylinder = 2 r , diamter = 2 d and height = 2 h volume of first cylinder = pie ( r ^ 2 ) * h = 60 volume of second cylinder = pie ( 2 r ^ 2 ) 2 h put the value of pie ( r ^ 2 ) * h = 60 in the second cylinder , volume = pie ( r ^ 2 ) * 4 * 2 = 60 * 8 = 480 gallons empty capacity = 420 gallons answer d" + }, + { + "Answer": 999.9999999999994, + "Options": "a ) 24 , b ) 48 , c ) 64 , d ) 80 , e ) 1000", + "Correct": "e", + "Explanation": "\"volume = 125 = side ^ 3 i . e . side of cube = 5 new cube has dimensions 10 , 10 , and 10 as all sides are twice of teh side of first cube volume = 10 * 10 * 10 = 1000 square feet answer : option e\"" + }, + { + "Answer": 254.46900494077323, + "Options": "a ) 154 cm 2 , b ) 308 m 2 , c ) 254 m 2 , d ) 260 m 2 , e ) none of these", + "Correct": "c", + "Explanation": "\"area of the shaded portion = 1 \u2044 4 \u00d7 \u03c0 \u00d7 ( 18 ) 2 = 254 m 2 answer c\"" + }, + { + "Answer": 32, + "Options": "a ) t = 16 , b ) t = 32 , c ) t = 64 , d ) 128 , e ) 512", + "Correct": "b", + "Explanation": "\"weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )\"" + }, + { + "Answer": 3, + "Options": "['a ) 0 feet', 'b ) 1 feet', 'c ) 2 feet', 'd ) 3 feet', 'e ) 4 feet']", + "Correct": "d", + "Explanation": "36 pie cubic feet of water and its filled to half tank ' s capacity . . . volume of tank = 72 pie cubic feet height of tank = 4 * 2 = 8 feet ( since tank is placed upright on its circular base on level ground , the height of water in the tank is 4 feet . ) 72 pie = pie * r 2 * 8 r 2 = 9 r = 3 feet answer : d" + }, + { + "Answer": 5, + "Options": "['a ) a ) 4 inches', 'b ) b ) 6 inches', 'c ) c ) 5 inches', 'd ) d ) 8 inches', 'e ) e ) 10 inches']", + "Correct": "c", + "Explanation": "you need to divide the width and length of the rectangular to equal pieces where l = w you can solve this using gcf 35 = 5 * 7 45 = 3 * 3 * 5 gcf = 5 p . s you can make squares with side of 5 answer : c" + }, + { + "Answer": 90.25, + "Options": "a ) 96.25 sq cm , b ) 98.25 sq cm , c ) 92.25 sq cm , d ) 100.25 sq cm , e ) 90.25 sq cm", + "Correct": "e", + "Explanation": "\"though there might be some technicalities concerning the termnearest ( as 9.5 is equidistant from both 9 and 10 ) the answer still should be : 9.5 ^ 2 = 90.25 . answer : e\"" + }, + { + "Answer": 5.000000000000001, + "Options": "a ) 1.5 , b ) 2 , c ) 3 , d ) 4 , e ) 5", + "Correct": "e", + "Explanation": "\"let x be the side length of square a . then the area of square a is x ^ 2 . the area of square b is ( sqrt ( 5 ) x ) ^ 2 = 5 x ^ 2 . the answer is e .\"" + }, + { + "Answer": 4, + "Options": "a ) 3.6 cm , b ) 2.4 cm , c ) 4.0 cm , d ) 2.16 cm , e ) 3.2 cm", + "Correct": "c", + "Explanation": "\"look at the diagram below : now , in case when qy is perpendicular to pr , two right triangles pqr and pqy are similar : qy : qp = qr : pr - - > qy : 5 = 8 : 10 - - > qy = 4.0 . answer : c .\"" + }, + { + "Answer": 75, + "Options": "a ) 10 % decrease , b ) 20 % decrease , c ) 75 % decrease , d ) 40 % decrease , e ) 50 % decrease", + "Correct": "c", + "Explanation": "\"area of square = pi * radius ^ 2 new radius = 0.5 * old radius so new area = ( 0.5 ) ^ 2 old area = > 0.25 of old area = > 25 % old area ans : c\"" + }, + { + "Answer": 500, + "Options": "a ) 100 cm 2 , b ) 150 cm 2 , c ) 200 cm 2 , d ) 250 cm 2 , e ) 500 cm 2", + "Correct": "e", + "Explanation": "\"1 / 2 * 50 ( 15 + 5 ) = 500 cm 2 answer : e\"" + }, + { + "Answer": 89.79719001510823, + "Options": "['a ) 80 cc', 'b ) 90 cc', 'c ) 110 cc', 'd ) 105 cc', 'e ) 100 cc']", + "Correct": "b", + "Explanation": "edge of the cube = 3 \u221a 334 = 7 cm \u2234 radius of cone = 3.5 cm height = 7 cm volume of cone = 1 \u2044 3 \u03c0 r 2 h 1 \u2044 3 \u03c0 r 2 h = 1 \u2044 3 \u00d7 22 \u2044 7 \u00d7 ( 3.5 ) 2 \u00d7 7 = 1 \u2044 3 \u00d7 22 \u00d7 12.25 \u2248 90 sec answer b" + }, + { + "Answer": 12.5, + "Options": "['a ) 10', 'b ) 12.5', 'c ) 15', 'd ) 16', 'e ) 17.5']", + "Correct": "b", + "Explanation": "area of rectangle = 20 x 10 = 200 cm \u00e2 \u00b2 let ' l ' the length of other diagonal = 0.5 x 32 xl = 200 which gives x = 12.5 cm answer : b" + }, + { + "Answer": 1200, + "Options": "['a ) 2400 m ^ 2', 'b ) 1500 m ^ 2', 'c ) 2520 m ^ 2', 'd ) 1200 m ^ 2', 'e ) 2580 m ^ 2']", + "Correct": "d", + "Explanation": "solving the two equations , we get : l = 30 and b = 40 . area = ( l x b ) = ( 30 x 40 ) m 2 = 1200 m ^ 2 d" + }, + { + "Answer": 21, + "Options": "a ) 34 , b ) 40 , c ) 68 , d ) 21 , e ) 78", + "Correct": "d", + "Explanation": "\"we have : l = 20 ft and lb = 10 sq . ft . so , b = 0.5 ft . length of fencing = ( l + 2 b ) = ( 20 + 1 ) ft = 21 ft . answer : d\"" + }, + { + "Answer": 8, + "Options": "a ) 3 : 6 , b ) 3 : 3 , c ) 3 : 8 , d ) 8 : 1 , e ) 3 : 2", + "Correct": "d", + "Explanation": "\"d = 8 d d = d a \u221a 2 = 8 d a \u221a 2 = d a = 8 d / \u221a 2 a = d / \u221a 2 = > 8 : 1 answer : d\"" + }, + { + "Answer": 9216, + "Options": "a ) 7,251 , b ) 8406 , c ) 9216 , d ) 10,348 , e ) can not be determined", + "Correct": "c", + "Explanation": "\"let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 191 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 191 ( x + y ) ( x - y ) = 191 191 is a prime number and thus it will be ( 96 + 95 ) * ( 96 - 95 ) . thus x = 96 and y = 95 x ^ 2 = 96 ^ 2 = 9216 the answer is c .\"" + }, + { + "Answer": 54, + "Options": "['a ) 18 \u00b0', 'b ) 36 \u00b0', 'c ) 54 \u00b0', 'd ) 72 \u00b0', 'e ) 90 \u00b0']", + "Correct": "c", + "Explanation": "the percent of the budget for transportation is 100 - ( 61 + 10 + 6 + 5 + 3 ) = 15 % 100 % of the circle is 360 degrees . then ( 15 % / 100 % ) * 360 = 54 degrees the answer is c ." + }, + { + "Answer": 35, + "Options": "a ) 875 , b ) 35 , c ) 1425 , d ) 2025 , e ) 2500", + "Correct": "b", + "Explanation": "\"there ' s a direct formula for this . number of diagonals in a regular polygon = [ n * ( n - 3 ) ] / 2 , n = number of sides of the regular polygon . here , n = 10 . plugging it in , we get 35 diagonals ! answer ( b ) .\"" + }, + { + "Answer": 93, + "Options": "a ) $ 1.60 , b ) $ 16.00 , c ) $ 93.00 , d ) $ 108.00 , e ) $ 196.00", + "Correct": "c", + "Explanation": "\"total surface area = 6 a ^ 2 = 6 * 10 * 10 = 600 each quart covers 20 sqr ft thus total number of quarts = 600 / 20 = 30 cost will be 30 * 3.1 = $ 93 ans : c\"" + }, + { + "Answer": 14, + "Options": "['a ) 12', 'b ) 13', 'c ) 14', 'd ) 15', 'e ) 16']", + "Correct": "c", + "Explanation": "the square of an odd number is an odd number : 10 < odd < 1,000 10 < odd ^ 2 < 1,000 3 . something < odd < 31 . something ( by taking the square root ) . so , that odd number could be any odd number from 5 to 31 , inclusive : 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19 , 21 , 23 , 25 , 27 , 29 , and 31 . 14 numbers . answer : c ." + }, + { + "Answer": 6, + "Options": "['a ) 1 cm', 'b ) 3 cm', 'c ) 6 cm', 'd ) 4 cm', 'e ) 2 cm']", + "Correct": "c", + "Explanation": "let base = x cm height = 2 x cm area = x \u00e3 \u2014 2 x = 2 x ^ 2 area = x \u00e3 \u2014 2 x = 2 x ^ 2 area is given as 72 cm ^ 2 2 x ^ 2 = 72 x ^ 2 = 36 x = 6 cm answer : c" + }, + { + "Answer": 343, + "Options": "a ) 8 cc , b ) 9 cc , c ) 2 cc , d ) 343 cc , e ) 6 cc", + "Correct": "d", + "Explanation": "\"6 a 2 = 294 = 6 * 49 a = 7 = > a 3 = 343 cc answer : d\"" + }, + { + "Answer": 592, + "Options": "['a ) 576', 'b ) 566', 'c ) 596', 'd ) 556', 'e ) 586']", + "Correct": "c", + "Explanation": "total surface area of cuboid = 2 ( lb + bh + lh ) = 2 ( 120 + 80 + 96 ) = 2 ( 296 ) = > 596 m ( power 2 ) answer is c ." + }, + { + "Answer": 45, + "Options": "a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60", + "Correct": "b", + "Explanation": "the number of males is 170 - 110 = 60 . the number of males with advanced degrees is 60 - 25 = 35 . the number of females with advanced degrees is 80 - 35 = 45 . the answer is b ." + }, + { + "Answer": 36, + "Options": "['a ) 288', 'b ) 48', 'c ) 36', 'd ) 864', 'e ) 964']", + "Correct": "c", + "Explanation": "d = 6 , r = 2 ; volume of the largest sphere = 4 / 3 \u03c0 r 3 = 4 / 3 * \u03c0 * 3 * 3 * 3 = 36 \u03c0 cm 3 answer : c" + }, + { + "Answer": 550, + "Options": "['a ) 660 sq . units', 'b ) 440 sq . units', 'c ) 770 sq . units', 'd ) 550 sq . units', 'e ) 220 sq . units']", + "Correct": "d", + "Explanation": "given that the area of the square = 5929 sq . units = > side of square = \u00e2 \u02c6 \u0161 5929 = 77 units the radius of the circle = side of the square = 77 units length of the rectangle = 2 / 7 * 77 = 22 units given that breadth = 25 units area of the rectangle = lb = 22 * 25 = 550 sq . units answer : d" + }, + { + "Answer": 4, + "Options": "['a ) 4 / 3 cm', 'b ) 3 / 4 cm', 'c ) 3 cm', 'd ) 4 cm', 'e ) 5 cm']", + "Correct": "d", + "Explanation": "explanation : \u00e2 \u02c6 \u0161 3 / 4 a 2 = 4 \u00e2 \u02c6 \u0161 3 - > a = 4 answer is d" + }, + { + "Answer": 56.25, + "Options": "a ) 54.25 % , b ) 56.25 $ , c ) 53.25 % , d ) 55.25 % , e ) 58.25 %", + "Correct": "b", + "Explanation": "\"if sides are a and b , after increase sides would be 1.25 a and 1.25 b . percentage increase in area = ( 1.25 a * 1.25 b - ab ) * 100 / ab = 56.25 % answer : b\"" + }, + { + "Answer": 16, + "Options": "['a ) 16', 'b ) 24', 'c ) 32', 'd ) 40', 'e ) 48']", + "Correct": "a", + "Explanation": "let x and y be the width and length of the photograph . ( x + 2 ) ( y + 2 ) = m and so ( 1 ) xy + 2 x + 2 y + 4 = m ( x + 6 ) ( y + 6 ) = m and so ( 2 ) xy + 6 x + 6 y + 36 = m + 64 let ' s subtract equation ( 1 ) from equation ( 2 ) . 4 x + 4 y + 32 = 64 2 x + 2 y = 16 , which is the perimeter of the photograph . the answer is a ." + }, + { + "Answer": 6, + "Options": "a ) 6 , b ) 16 , c ) 8 , d ) 36 , e ) none", + "Correct": "a", + "Explanation": "\"2 x * x = 72 = > x = 6 answer : a\"" + }, + { + "Answer": 2.5, + "Options": "a ) 1.5 , b ) 2.5 , c ) 3.5 , d ) 4.5 , e ) 5.5", + "Correct": "b", + "Explanation": "\"400 kg - 1 cubic meter ; 400,000 g - 1 cubic meter ; 400,000 g - 1 , 000,000 cubic centimeters ; 1 g - 1 , 000,000 / 400,000 = 10 / 4 = 2.5 cubic centimeters . answer : b .\"" + }, + { + "Answer": 480, + "Options": "a ) 480 cm 2 , b ) 765 cm 2 , c ) 216 cm 2 , d ) 197 cm 2 , e ) 275 cm 2", + "Correct": "a", + "Explanation": "\"the triangle with sides 52 cm , 48 cm and 20 cm is right angled , where the hypotenuse is 52 cm . area of the triangle = 1 / 2 * 48 * 20 = 480 cm 2 answer : a\"" + }, + { + "Answer": 50, + "Options": "['a ) 13', 'b ) 33', 'c ) 56', 'd ) 50', 'e ) 52']", + "Correct": "d", + "Explanation": "c . 50 cents yes , ensure that you understand the relation thoroughly ! cost per liter = k * fraction of spirit 50 cents is the cost of 2 liters of solution ( 1 part water , 1 part spirit ) . so cost per liter is 25 cents . fraction of spirit is 1 / 2 . 25 = k * ( 1 / 2 ) k = 50 cost per liter = 50 * ( 1 / 4 ) ( 1 part spirit , 3 parts water ) cost for 4 liters = 50 * ( 1 / 4 ) * 4 = 50 cents d . 50 cents" + }, + { + "Answer": 1200, + "Options": "a ) 2387 , b ) 1298 , c ) 1128 , d ) 1237 , e ) 1200", + "Correct": "e", + "Explanation": "\"l * 30 = 1200 l = 40 40 + 30 + 50 = 120 120 * 10 = 1200 e\"" + }, + { + "Answer": 32, + "Options": "a ) 30 square inches , b ) 75 square inches , c ) 68 square inches , d ) 89 square inches , e ) 32 square inches", + "Correct": "e", + "Explanation": "\"if the width is 4 in and the length is 2 times the width , then the length is 2 * 4 = 8 in the area is given by 4 * 8 = 32 square inches correct answer e\"" + }, + { + "Answer": 9600, + "Options": "['a ) 9.6 m 3', 'b ) 96 m 3', 'c ) 960 m 3', 'd ) 9600 m 3', 'e ) 96000 m 3']", + "Correct": "d", + "Explanation": "let the height be h 2 ( 30 + 24 ) x h \u2013 2 ( 30 - 24 ) h = ( 2 ( 30 x 24 ) ) / ( 2 ( 30 + 24 ) ) = ( 30 x 24 ) / 54 = 40 / 3 m volume = 30 x 24 x 40 / 3 = 9600 m 3 answer : d" + }, + { + "Answer": 2970.9625914046583, + "Options": "a ) 2972 , b ) 4567 , c ) 4235 , d ) 4547 , e ) 4675", + "Correct": "a", + "Explanation": "\"explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . \u03c0 r 2 = 175600 \u21d4 ( r ) 2 = ( 175600 x ( 7 / 22 ) ) \u21d4 r = 236.37 m . circumference = 2 \u03c0 r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 2 ) = rs . 2972 . answer : option a\"" + }, + { + "Answer": 4608, + "Options": "a ) 4830 , b ) 5120 , c ) 4608 , d ) 7500 , e ) 8960", + "Correct": "c", + "Explanation": "\"l = ( 48 - 16 ) m = 32 m , b = ( 34 - 16 ) m = 18 m , h = 8 m . volume of the box = ( 32 x 18 x 8 ) m 3 = 4608 m 3 . answer : option c\"" + }, + { + "Answer": 9, + "Options": "['a ) 6 / \u03c0', 'b ) 9 / \u03c0', 'c ) 6', 'd ) 9', 'e ) 12']", + "Correct": "d", + "Explanation": "given area of the base of a hemisphere is 3 = pi * r ^ 2 thus r = sqrt ( 3 / pi ) . surface area of whole sphere = 4 * pi * r ^ 2 . = 4 * pi * 3 / pi = 12 . since the hemisphere is half of a sphere the surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . but the total surface area = 6 + area of the base of a hemisphere . = 6 + 3 = 9 . answer is d ! !" + }, + { + "Answer": 0.6342592592592593, + "Options": "['a ) 137 / 216', 'b ) 137 / 218', 'c ) 137 / 217', 'd ) 136 / 216', 'e ) 138 / 216']", + "Correct": "a", + "Explanation": "sandra score can be like 1,4 , 9,16 , 25,36 eric score less then 1 - - > 0 eric score less then 4 = ( 1,1 ) , ( 1,2 ) ( 2,1 ) - - > 3 eric score less then 9 are ( 1,1 ) ( 1,2 ) ( 1,3 ) ( 1,4 ) ( 1,5 ) ( 1,6 ) ( 2,1 ) ( 2,2 ) ( 2,3 ) ( 2,4 ) ( 2,5 ) ( 2,6 ) ( 3,1 ) ( 3,2 ) ( 3,3 ) ( 3,4 ) ( 3,5 ) ( 4,1 ) ( 4,2 ) ( 4,3 ) ( 4,4 ) ( 5,1 ) ( 5,2 ) ( 5,3 ) ( 6,1 ) ( 6,2 ) - - > 26 eric score will always be less then 16 - - - > 36 eric score will always be less then 25 - - - > 36 eric score will always be less then 36 - - - > 36 total favorable outcomes = 3 + 26 + 36 + 36 + 36 = 137 total possible outcomes = 216 ( 36 * 6 ) probability = 137 / 216 answer : a" + }, + { + "Answer": 868, + "Options": "['a ) 878 cm ^ 2', 'b ) 858 cm ^ 2', 'c ) 838 cm ^ 2', 'd ) 868 cm ^ 2', 'e ) none of them']", + "Correct": "d", + "Explanation": "volume = ( 16 x 14 x 7 ) m ^ 3 = 1568 m ^ 3 . surface area = [ 2 ( 16 x 14 + 14 x 7 + 16 x 7 ) ] cm ^ 2 = ( 2 x 434 ) cm ^ 2 = 868 cm ^ 2 . answer is d" + }, + { + "Answer": 55, + "Options": "a ) 38 cm 2 , b ) 55 cm 2 , c ) 65 cm 2 , d ) 45 cm 2 , e ) 35 cm 2", + "Correct": "b", + "Explanation": "\"area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 44 / 2 = 55 cm 2 answer : b\"" + }, + { + "Answer": 60, + "Options": "a ) 30 , b ) 45 , c ) 60 , d ) 75 , e ) 90", + "Correct": "c", + "Explanation": "\"c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be x = 60 . c\"" + }, + { + "Answer": 90, + "Options": "a ) 18 \u00b0 , b ) 36 \u00b0 , c ) 54 \u00b0 , d ) 72 \u00b0 , e ) 90 \u00b0", + "Correct": "e", + "Explanation": "\"the percent of the budget for transportation is 100 - ( 55 + 9 + 5 + 4 + 2 ) = 25 % 100 % of the circle is 360 degrees . then ( 25 % / 100 % ) * 360 = 90 degrees the answer is e .\"" + }, + { + "Answer": 4.8, + "Options": "['a ) 4.8 cm', 'b ) 4.4 cm', 'c ) 4.9 cm', 'd ) 5.0 cm', 'e ) 5.2 cm']", + "Correct": "a", + "Explanation": "area of triangle is 1 / 2 * 12 * 8 = 48 side of square = x the entire triangle split into two right angled triangle and one square with dimensions as follows i ) square with side x ii ) right angled triangle with perpendicular sides x and 12 - x iii ) right angled triangle with perpendicular sides 8 - x and x sum of area of all three = 48 = x 2 + 1 / 2 * x * ( 12 - x ) + 1 / 2 * x * ( 8 - x ) = 48 = x = 4.8 cm answer : a" + }, + { + "Answer": 6, + "Options": "['a ) 6 cm', 'b ) 10 cm', 'c ) 8 cm', 'd ) data inadequate', 'e ) none of these']", + "Correct": "a", + "Explanation": "diagonal 2 = 64 + b 2 or , 10 ( 2 ) = 64 + 6 ( 2 ) answer a" + }, + { + "Answer": 6, + "Options": "a ) 4 , b ) 6 , c ) 9 , d ) 10 , e ) 12", + "Correct": "b", + "Explanation": "the top and the bottom are each single faces formed by three equilateral triangles joining , as in the diagram on the left , to make an isosceles trapezoid . top = 1 face , and bottom = 1 face . this is a four - sided figure , so there are four rectangles extending from the bottom of this prism to the congruent figure at the top . notice , in particular , the larger vertical face in the \u201c back \u201d of the diagram to the right is formed by two faces of the original triangular prisms lying next to each other and smoothly joining . total = 1 top + 1 bottom + 4 sides = 6 faces . answer = b ." + }, + { + "Answer": 42, + "Options": "a ) 17 , b ) 42 , c ) 54 , d ) 108 , e ) 864", + "Correct": "b", + "Explanation": "\"least number of cubes will be required when the cubes that could fit in are biggest . 7 is the biggest number that could divide all three , 49 , 21 and 14 . thus side of cube must be 7 , and total number of cubes = 49 / 7 * 21 / 7 * 14 / 7 = 42 ans b it is .\"" + }, + { + "Answer": 1856, + "Options": "a ) 3944 , b ) 2882 , c ) 2999 , d ) 1856 , e ) 2121", + "Correct": "d", + "Explanation": "\"let the side of the square plot be a ft . a 2 = 64 = > a = 8 length of the fence = perimeter of the plot = 4 a = 32 ft . cost of building the fence = 32 * 58 = rs . 1856 . answer : d\"" + }, + { + "Answer": 324, + "Options": "a ) 225 sq m , b ) 186 sq m , c ) 586 sq m , d ) 324 sq m , e ) 296 sq m", + "Correct": "d", + "Explanation": "\"18 * 18 = 324 sq m answer : d\"" + }, + { + "Answer": 120, + "Options": "a ) 120 , b ) 147 , c ) 251 , d ) 451 , e ) 258", + "Correct": "a", + "Explanation": "\"other side = ( ( 17 ) 2 - ( 15 ) 2 ) ( 1 / 2 ) = ( 289 - 225 ) ( 1 / 2 ) = ( 64 ) ( 1 / 2 ) = 8 m . area = ( 15 x 8 ) m 2 = 120 m 2 . ans : a\"" + }, + { + "Answer": 32, + "Options": "a ) 5 square meters , b ) 32 square meters , c ) 42 square meters , d ) 83.3 square meters , e ) 120 square meters", + "Correct": "b", + "Explanation": "\"280 - 180 = 100 sq m of the wallpaper overlaps ( in either two layers or three layers ) if 36 sq m has two layers , 100 - 36 = 64 sq m of the wallpaper overlaps in three layers . 64 sq m makes two extra layers hence the area over which it makes two extra layers is 32 sq m . answer ( b ) .\"" + }, + { + "Answer": 200, + "Options": "['a ) 290 cm 2', 'b ) 380 cm 2', 'c ) 270 cm 2', 'd ) 280 cm 2', 'e ) 200 cm 2']", + "Correct": "e", + "Explanation": "area of a parallelogram = base * height = 20 * 10 = 200 cm 2 answer : e" + }, + { + "Answer": 127.99999999999996, + "Options": "a ) 34 , b ) 65 , c ) 88 , d ) 90 , e ) 128", + "Correct": "e", + "Explanation": "\"lets suppose length = l , breadth = b , depth = d front face area = l * w = 1 / 2 w * d ( l = 1 / 2 d or d = 2 l ) top face area = w * d side face area = w * d = 1.5 d * l ( w = 1.5 l ) volume = l * w * d = 1536 l * 1.5 l * 2 l = 1536 l = 8 side face area = l * d = l * 2 l = 8 * 2 * 8 = 128 e is the answer\"" + }, + { + "Answer": 50, + "Options": "['a ) 50', 'b ) 30', 'c ) 20', 'd ) 40', 'e ) 10']", + "Correct": "a", + "Explanation": "let length = 2 x meters and breadth = 3 x meter . now , area = ( 1 / 6 ) x 1000 m 2 = 5000 / 3 m 2 so , 2 x * 3 x = 5000 / 3 < = > x 2 = 2500 / 9 < = > x = 50 / 3 therefore length = 2 x = ( 100 / 3 ) m = 33 ( 1 / 3 ) m and breadth = 3 x = 3 ( 50 / 3 ) m = 50 m . answer is a" + }, + { + "Answer": 80, + "Options": "a ) 75 , b ) 80 , c ) 85 , d ) 90 , e ) 95", + "Correct": "b", + "Explanation": "\"in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 \u00b0 ) . given : x + ( x + 20 ) = 180 - - > x = 80 . answer : b .\"" + }, + { + "Answer": 243, + "Options": "a ) 432 , b ) 212 , c ) 243 , d ) 992 , e ) 212", + "Correct": "c", + "Explanation": "\"2 ( 3 x + x ) = 72 l = 27 b = 9 lb = 27 * 9 = 243 answer : c\"" + }, + { + "Answer": 54967, + "Options": "['a ) 55522 feet', 'b ) 45522 feet', 'c ) 35522 feet', 'd ) 25522 feet', 'e ) none']", + "Correct": "a", + "Explanation": "solution : first , model the pressure ( p ) in terms of depth ( d ) with a linear equation . we will find the equation p = md + b use ( 0 , 15 ) and ( 33 , 30 ) to find m m = 30 - 15 / 33 - 0 m = 15 / 33 = 0.45 p = 0.45 d + b use ( 0 , 15 ) to find b 15 = 0.45 \u00d7 0 + b 15 = b p = 0.45 d + 15 25000 = 0.45 d + 15 25000 - 15 = 0.45 d + 15 - 15 24985 = 0.45 d d = 24985 / 0.45 = 55522 feet answer a" + }, + { + "Answer": 312, + "Options": "a ) 281 , b ) 284 , c ) 288 , d ) 255 , e ) 312", + "Correct": "e", + "Explanation": "\"area of a parallelogram = base * height = 26 * 12 = 312 cm 2 answer : e\"" + }, + { + "Answer": 88, + "Options": "a ) 34 , b ) 40 , c ) 68 , d ) 88 , e ) 98", + "Correct": "d", + "Explanation": "\"explanation : we have : l = 20 ft and lb = 680 sq . ft . so , b = 34 ft . length of fencing = ( l + 2 b ) = ( 20 + 68 ) ft = 88 ft . answer : d\"" + }, + { + "Answer": 0.1111111111111111, + "Options": "a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 5 , e ) 1 / 3", + "Correct": "a", + "Explanation": "if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 812 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives c = 1 / 9 . a" + }, + { + "Answer": 20, + "Options": "a ) 16 , b ) 20 , c ) 24 , d ) 25 , e ) 30", + "Correct": "b", + "Explanation": "\"length of side 1 = 4 + 1 = 5 length of side 2 = 3 + 1 = 4 area of rectangle = 5 * 4 = 20 b is the answer\"" + }, + { + "Answer": 8, + "Options": "['a ) 8 .', 'b ) 2', 'c ) 6', 'd ) 4', 'e ) 10']", + "Correct": "a", + "Explanation": "let the radius be r and the the height be h . new radius = 2 r and height = 2 h . area ( new ) : area ( old ) = pi \u2217 ( 2 r ) ^ 2 \u2217 2 h / pi \u2217 r ^ 2 \u2217 h = 8 : 1 . hence the answer is a ." + }, + { + "Answer": 461.8141200776996, + "Options": "['a ) 462 cm \u00b2', 'b ) 530 cm \u00b2', 'c ) 1345 cm \u00b2', 'd ) 1788 cm \u00b2', 'e ) none']", + "Correct": "a", + "Explanation": "sol . total surface area = 3 \u220f r \u00b2 = [ 3 * 22 / 7 * 7 * 7 ] cm \u00b2 = 462 cm \u00b2 answer a" + }, + { + "Answer": 55, + "Options": "a ) 76 , b ) 88 , c ) 66 , d ) 55 , e ) 35", + "Correct": "d", + "Explanation": "\"area of a triangle = r * s where r is the in radius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 44 / 2 = 55 cm 2 answer : d\"" + }, + { + "Answer": 11, + "Options": "a ) 4 , b ) 8 , c ) 11 , d ) 16 , e ) 18", + "Correct": "c", + "Explanation": "\"let length of rectangle = l 11 ^ 2 = l * 11 = > l = 121 / 11 = 11 answer c\"" + }, + { + "Answer": 12, + "Options": "['a ) 12', 'b ) 8', 'c ) 6', 'd ) 10', 'e ) 16']", + "Correct": "a", + "Explanation": "the mini - cubes with 2 painted sides are all on the edge of the cube , in the ` ` middle ' ' of the edge . there are 4 in front , 4 in back and 4 more on the ` ` strip ' ' that runs around the left / top / right / bottom of the cube . 4 + 4 + 4 = 12 . answer a" + }, + { + "Answer": 480, + "Options": "a ) 480 cm 2 , b ) 580 cm 2 , c ) 380 cm 2 , d ) 180 cm 2 , e ) 280 cm 2", + "Correct": "a", + "Explanation": "\"the triangle with sides 52 cm , 48 cm and 20 cm is right angled , where the hypotenuse is 52 cm . area of the triangle = 1 / 2 * 48 * 20 = 480 cm 2 answer : a\"" + }, + { + "Answer": 8, + "Options": "['a ) 8', 'b ) 4 \u03c0', 'c ) 4', 'd ) 6', 'e ) 5']", + "Correct": "a", + "Explanation": "circumference = 2 * pi * r = 2 * pi * 4 / pi = > 8 a" + }, + { + "Answer": 217.5, + "Options": "a ) 220.75 cm 2 , b ) 258 cm 2 , c ) 225.50 cm 2 , d ) 222.25 cm 2 , e ) 217.5 cm 2", + "Correct": "e", + "Explanation": "\"the triangle with sides 31 cm , 29 cm and 15 cm is right angled , where the hypotenuse is 31 cm . area of the triangle = 1 / 2 * 29 * 15 = 217.5 cm 2 answer : e\"" + }, + { + "Answer": 76.96902001294993, + "Options": "['a ) 154 sq metres', 'b ) 77 sq metres', 'c ) 308 sq metres', 'd ) 22 sq metres', 'e ) none of these']", + "Correct": "b", + "Explanation": "area of semicircle = \u00bd \u03c0 r 2 = \u00bd \u00d7 22 \u2044 7 \u00d7 7 \u00d7 7 = 77 m 2 answer b" + }, + { + "Answer": 1013.9999999999997, + "Options": "a ) 864 , b ) 1014 , c ) 1299 , d ) 1268 , e ) 1191", + "Correct": "b", + "Explanation": "a 3 = 2197 = > a = 13 6 a 2 = 6 * 13 * 13 = 1014 answer : b" + }, + { + "Answer": 150, + "Options": "a ) 150 , b ) 131 , c ) 115 , d ) 90 , e ) 45", + "Correct": "a", + "Explanation": "\"there are 15 business exec and in each handshake 2 business execs are involved . hence 15 c 2 = 105 also , each of 15 exec will shake hand with every 3 other chairmen for total of 45 handshake . total = 45 + 105 = 150 ans : a\"" + }, + { + "Answer": 16.5, + "Options": "a ) 11 m 2 , b ) 16.5 m 2 , c ) 18.5 m 2 , d ) 19.5 m 2 , e ) 12 m 2", + "Correct": "b", + "Explanation": "\"1 / 2 * 5.5 * 6 = 16.5 m 2 answer : b\"" + }, + { + "Answer": 5100, + "Options": "a ) s . 5100 , b ) s . 3900 , c ) s . 3228 , d ) s . 3922 , e ) s . 3928", + "Correct": "a", + "Explanation": "\"area = ( l + b \u2013 d ) d ( 120 + 60 \u2013 10 ) 10 = > 1700 m 2 1700 * 3 = rs . 5100 answer : a\"" + }, + { + "Answer": 10800, + "Options": "a ) 10800 , b ) 1299 , c ) 1000 , d ) 10000 , e ) 2887", + "Correct": "a", + "Explanation": "\"100 * 100 = 10000 135 * 80 = 10800 answer : a\"" + }, + { + "Answer": 450, + "Options": "['a ) 430 sq . m', 'b ) 425 sq . m', 'c ) 450 sq . m', 'd ) 475 sq . m', 'e ) 350 sq . m']", + "Correct": "c", + "Explanation": "distance covered in ( 9 \u00d7 1000 ) / ( 3600 ) \u00d7 12 = 30 m diagonal of squarre field = 30 m . area of square field = 30 ( power ) 2 / 2 = 900 / 2 = 450 sq . m answer is c ." + }, + { + "Answer": 50, + "Options": "a ) a ) 72 , b ) b ) 828 , c ) c ) 50 , d ) d ) 34 , e ) e ) 35", + "Correct": "c", + "Explanation": "\"explanation : area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 40 / 2 = 50 cm 2 answer : option c\"" + }, + { + "Answer": 21, + "Options": "a ) 11 , b ) 17 , c ) 18 , d ) 21 , e ) 1322", + "Correct": "d", + "Explanation": "\"let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 1323 3 b 2 = 1323 b 2 = 441 = 21 ( b > 0 ) b = 21 m . answer : d\"" + }, + { + "Answer": 11.25, + "Options": "a ) 45 \u00b0 , b ) 30 \u00b0 , c ) 22.5 \u00b0 , d ) 18 \u00b0 , e ) 11.25 \u00b0", + "Correct": "e", + "Explanation": "thecomplementof angle a is the angle which , when added to angle a , gives 90 degrees . the two acute angles of a right triangle are complements , for example . the original angle is x , so the complement is 7 x , and together , these add up to 90 degrees . x + 7 x = 90 8 x = 90 x = 11.25 \u00b0 answer = ( e )" + }, + { + "Answer": 5, + "Options": "a ) 11 , b ) 10 , c ) 787 , d ) 122 , e ) 5", + "Correct": "e", + "Explanation": "\"1 / 2 * 2 * 5 = 5 m 2 answer : e\"" + }, + { + "Answer": 25, + "Options": "['a ) 25 / \u221a \u03c0', 'b ) 30 / \u221a \u03c0', 'c ) 20', 'd ) 25', 'e ) 30']", + "Correct": "d", + "Explanation": "60 / 360 = 1 / 6 1 / 6 of total area = 5 5 / 6 of total area = 5 * 5 = 25 answer : d" + }, + { + "Answer": 198, + "Options": "['a ) 277', 'b ) 266', 'c ) 198', 'd ) 288', 'e ) 212']", + "Correct": "c", + "Explanation": "1 / 2 * 18 * 22 = 198 answer : c" + }, + { + "Answer": 45.6, + "Options": "a ) 45.6 , b ) 40 , c ) 68 , d ) 88 , e ) 92", + "Correct": "a", + "Explanation": "\"given that length and area , so we can find the breadth . length x breadth = area 20 x breadth = 256 breadth = 12.8 feet area to be fenced = 2 b + l = 2 ( 12.8 ) + 20 = 45.6 feet answer : a\"" + }, + { + "Answer": 36, + "Options": "['a ) 36', 'b ) 14', 'c ) 12', 'd ) 15', 'e ) 11']", + "Correct": "a", + "Explanation": "the 4 inch side should be aligned to the 16 inch side ( 4 layer ) 6 inch side should be aligned to the 18 inch side . ( 3 layer ) and 10 inch side should be aligned to the 30 inch side . ( 3 layer ) maximum number of rectangles = 4 * 3 * 3 = 36 answer is a" + }, + { + "Answer": 1300, + "Options": "a ) s . 1350 , b ) s . 1300 , c ) s . 1328 , d ) s . 1397 , e ) s . 1927", + "Correct": "b", + "Explanation": "\"area = ( l + b + 2 d ) 2 d = ( 70 + 55 + 2.5 * 2 ) 2 * 2.5 = > 650 650 * 2 = rs . 1300 answer : b\"" + }, + { + "Answer": 270, + "Options": "a ) 570 cm 2 , b ) 370 cm 2 , c ) 170 cm 2 , d ) 271 cm 2 , e ) 270 cm 2", + "Correct": "e", + "Explanation": "\"the triangle with sides 39 cm , 36 cm and 15 is right angled , where the hypotenuse is 39 cm . area of the triangle = 1 / 2 * 36 * 15 = 270 cm 2 answer : e\"" + }, + { + "Answer": 260, + "Options": "a ) 126 , b ) 156 , c ) 190 , d ) 321 , e ) 260", + "Correct": "e", + "Explanation": "\"sol . let width = x , length = ( 10 + x ) perimeter = 2 ( x + ( 10 + x ) ) = 2 ( 2 x = 10 ) & 2 ( 2 x + 10 ) * 6.5 = 1650 x = 60 required perimeter = 2 ( 60 + 70 ) = 260 e\"" + }, + { + "Answer": 200, + "Options": "a ) 200 sq feet , b ) 300 sq feet , c ) 400 sq feet , d ) 500 sq feet , e ) 600 sq feet", + "Correct": "a", + "Explanation": "first room because area 50 * 50 = 2500 sq feet second room area 100 sq yard in feet 300 sq feet third room area 200 sq feet answer : a" + }, + { + "Answer": 600, + "Options": "a ) 200 cm 2 , b ) 100 cm 2 , c ) 42 cm 2 , d ) 600 cm 2 , e ) 230 cm 2", + "Correct": "d", + "Explanation": "\"area of a parallelogram = base * height = 15 * 40 = 600 cm 2 answer : d\"" + }, + { + "Answer": 13, + "Options": "a ) 16 , b ) 17 , c ) 13 , d ) 19 , e ) 14", + "Correct": "c", + "Explanation": "\"let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 507 3 b 2 = 507 b 2 = 169 b = 13 m . answer : option c\"" + }, + { + "Answer": 1, + "Options": "['a ) 8', 'b ) 1', 'c ) 3', 'd ) 4', 'e ) 6']", + "Correct": "b", + "Explanation": "perimeter of rectangular yard = 2 ( l + b ) = 12 - - > l + b = 6 area = l * b = 9 b = 6 - l l ( 6 - l ) = 9 6 l - l ^ 2 = 9 l ^ 2 - 6 l + 9 = 0 upon simplifying we get l = 3 . answer : b" + }, + { + "Answer": 275, + "Options": "a ) 160 , b ) 275 , c ) 360 , d ) 440 , e ) 560", + "Correct": "b", + "Explanation": "\"the number of jumbo tiles = x . the number of regular tiles = 2 x . assume the ratio of the dimensions of a regular tile is a : a - - > area = a ^ 2 . the dimensions of a jumbo tile is 3 a : 3 a - - > area = 9 a ^ 2 . the area of regular tiles = 2 x * a ^ 2 = 50 . the area of jumbo tiles = x * 9 a ^ 2 = 4.5 ( 2 x * a ^ 2 ) = 4.5 * 50 = 225 . total area = 50 + 225 = 275 . answer : b .\"" + }, + { + "Answer": 8912.887774213974, + "Options": "a ) 4457 , b ) 4567 , c ) 4235 , d ) 4547 , e ) 8915", + "Correct": "e", + "Explanation": "\"explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . \u03c0 r 2 = 175600 \u21d4 ( r ) 2 = ( 175600 x ( 7 / 22 ) ) \u21d4 r = 236.37 m . circumference = 2 \u03c0 r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 6 ) = rs . 8915 . answer : option e\"" + }, + { + "Answer": 113.09733552923255, + "Options": "a ) 154 cm 2 , b ) 113 m 2 , c ) 123 m 2 , d ) 115 m 2 , e ) none of these", + "Correct": "b", + "Explanation": "\"area of the shaded portion = 1 \u2044 4 \u00d7 \u03c0 \u00d7 ( 12 ) 2 = 113 m 2 answer b\"" + }, + { + "Answer": 2520, + "Options": "['a ) 2520', 'b ) 2510', 'c ) 2525', 'd ) 2025', 'e ) 2020']", + "Correct": "a", + "Explanation": "l - b = 23 . . . ( 1 ) perimeter = 206 2 ( l = b ) = 206 l + b = 103 . . . ( 2 ) ( 1 ) + ( 2 ) 2 l = 23 + 103 = 126 l = 126 / 2 = 63 metre substituting the value of l in ( 1 ) , we get 63 - b = 23 b = 63 - 23 = 40 metre area = lb = 63 \u00e3 \u2014 40 = 2520 m 2 answer : a" + }, + { + "Answer": 96, + "Options": "a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92", + "Correct": "d", + "Explanation": "\"the triangle with sides 20 cm , 12 cm and 16 cm is right angled , where the hypotenuse is 20 cm . area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d\"" + }, + { + "Answer": 18, + "Options": "['a ) 18', 'b ) 20', 'c ) 27', 'd ) 32', 'e ) 25']", + "Correct": "a", + "Explanation": "side of square = \u221a 36 = 6 m . length = 6 m and breadth = 3 m area of rectangle = 6 * 3 = 18 sq . m answer a" + }, + { + "Answer": 23.561944901923447, + "Options": "a ) 34 , b ) 35 , c ) 56 , d ) 67 , e ) 23.57", + "Correct": "e", + "Explanation": "\"let the side of the square be a cm . parameter of the rectangle = 2 ( 16 + 14 ) = 60 cm parameter of the square = 60 cm i . e . 4 a = 60 a = 15 diameter of the semicircle = 15 cm circimference of the semicircle = 1 / 2 ( \u220f ) ( 15 ) = 1 / 2 ( 22 / 7 ) ( 15 ) = 330 / 14 = 23.57 cm to two decimal places answer : option e\"" + }, + { + "Answer": 800, + "Options": "a ) 100 cm 2 , b ) 250 cm 2 , c ) 800 cm 2 , d ) 296 cm 2 , e ) 456 cm 2", + "Correct": "c", + "Explanation": "\"area of a parallelogram = base * height = 20 * 40 = 800 cm 2 answer : c\"" + }, + { + "Answer": 1.875, + "Options": "['a ) 15 ohms', 'b ) 15 / 8 ohms', 'c ) 1 / 8 ohms', 'd ) 8 / 15 ohms', 'e ) 8 ohms']", + "Correct": "b", + "Explanation": "the wording is a bit confusing , though basically we are told that 1 / r = 1 / 3 + 1 / 5 , from which it follows that r = 15 / 8 ohms . answer : b ." + }, + { + "Answer": 80, + "Options": "a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 100", + "Correct": "d", + "Explanation": "\"a quick note on doubling . when you double a length you have 2 * l 1 . when you double all lengths of a rectangle you have ( 2 * l 1 ) ( 2 * l 2 ) = a . an increase of 2 ^ 2 or 4 . when you double all lengths of a rectangular prism you have ( 2 * l 1 ) ( 2 * l 2 ) ( 2 * l 3 ) = v . an increase of 2 ^ 3 or 8 . this leads to the basic relationship : line : 2 * original size rectangle : 4 * original size rectangular prism : 8 * original size answer is d\"" + }, + { + "Answer": 150, + "Options": "a ) 200 , b ) 350 , c ) 100 , d ) 150 , e ) 120", + "Correct": "d", + "Explanation": "\"the 5 inch side should be aligned to the 15 inch side ( 3 layer ) 2 inch side should be aligned to the 20 inch side . ( 10 layer ) 7 inch side should be aligned to the 35 inch side . ( 5 layer ) maximum number of rectangles = 3 * 10 * 5 = 150 answer is d\"" + }, + { + "Answer": 24, + "Options": "['a ) 19', 'b ) 23', 'c ) 24', 'd ) 16', 'e ) 17']", + "Correct": "c", + "Explanation": "4 x * x = 2304 = > x = 24 answer : c" + }, + { + "Answer": 420, + "Options": "['a ) there is no empty capacity', 'b ) 100 gallons', 'c ) 300 gallons', 'd ) 420 gallons', 'e ) 840 gallons']", + "Correct": "d", + "Explanation": "radius of first cylinder = r , diameter = 2 r , height = h radius of second cylinder = 2 r , diamter = 2 d and height = 2 h volume of first cylinder = pie ( r ^ 2 ) * h = 60 volume of second cylinder = pie ( 2 r ^ 2 ) 2 h put the value of pie ( r ^ 2 ) * h = 60 in the second cylinder , volume = pie ( r ^ 2 ) * 4 * 2 = 60 * 8 = 480 gallons empty capacity = 420 gallons answer d" + }, + { + "Answer": 32, + "Options": "a ) t = 16 , b ) t = 32 , c ) t = 64 , d ) 128 , e ) 512", + "Correct": "b", + "Explanation": "\"weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )\"" + }, + { + "Answer": 3, + "Options": "['a ) 0 feet', 'b ) 1 feet', 'c ) 2 feet', 'd ) 3 feet', 'e ) 4 feet']", + "Correct": "d", + "Explanation": "36 pie cubic feet of water and its filled to half tank ' s capacity . . . volume of tank = 72 pie cubic feet height of tank = 4 * 2 = 8 feet ( since tank is placed upright on its circular base on level ground , the height of water in the tank is 4 feet . ) 72 pie = pie * r 2 * 8 r 2 = 9 r = 3 feet answer : d" + }, + { + "Answer": 89.79719001510823, + "Options": "['a ) 80 cc', 'b ) 90 cc', 'c ) 110 cc', 'd ) 105 cc', 'e ) 100 cc']", + "Correct": "b", + "Explanation": "edge of the cube = 3 \u221a 334 = 7 cm \u2234 radius of cone = 3.5 cm height = 7 cm volume of cone = 1 \u2044 3 \u03c0 r 2 h 1 \u2044 3 \u03c0 r 2 h = 1 \u2044 3 \u00d7 22 \u2044 7 \u00d7 ( 3.5 ) 2 \u00d7 7 = 1 \u2044 3 \u00d7 22 \u00d7 12.25 \u2248 90 sec answer b" + }, + { + "Answer": 12.5, + "Options": "['a ) 10', 'b ) 12.5', 'c ) 15', 'd ) 16', 'e ) 17.5']", + "Correct": "b", + "Explanation": "area of rectangle = 20 x 10 = 200 cm \u00e2 \u00b2 let ' l ' the length of other diagonal = 0.5 x 32 xl = 200 which gives x = 12.5 cm answer : b" + }, + { + "Answer": 1200, + "Options": "['a ) 2400 m ^ 2', 'b ) 1500 m ^ 2', 'c ) 2520 m ^ 2', 'd ) 1200 m ^ 2', 'e ) 2580 m ^ 2']", + "Correct": "d", + "Explanation": "solving the two equations , we get : l = 30 and b = 40 . area = ( l x b ) = ( 30 x 40 ) m 2 = 1200 m ^ 2 d" + }, + { + "Answer": 6, + "Options": "['a ) 1 cm', 'b ) 3 cm', 'c ) 6 cm', 'd ) 4 cm', 'e ) 2 cm']", + "Correct": "c", + "Explanation": "let base = x cm height = 2 x cm area = x \u00e3 \u2014 2 x = 2 x ^ 2 area = x \u00e3 \u2014 2 x = 2 x ^ 2 area is given as 72 cm ^ 2 2 x ^ 2 = 72 x ^ 2 = 36 x = 6 cm answer : c" + }, + { + "Answer": 592, + "Options": "['a ) 576', 'b ) 566', 'c ) 596', 'd ) 556', 'e ) 586']", + "Correct": "c", + "Explanation": "total surface area of cuboid = 2 ( lb + bh + lh ) = 2 ( 120 + 80 + 96 ) = 2 ( 296 ) = > 596 m ( power 2 ) answer is c ." + }, + { + "Answer": 550, + "Options": "['a ) 660 sq . units', 'b ) 440 sq . units', 'c ) 770 sq . units', 'd ) 550 sq . units', 'e ) 220 sq . units']", + "Correct": "d", + "Explanation": "given that the area of the square = 5929 sq . units = > side of square = \u00e2 \u02c6 \u0161 5929 = 77 units the radius of the circle = side of the square = 77 units length of the rectangle = 2 / 7 * 77 = 22 units given that breadth = 25 units area of the rectangle = lb = 22 * 25 = 550 sq . units answer : d" + }, + { + "Answer": 4, + "Options": "['a ) 4 / 3 cm', 'b ) 3 / 4 cm', 'c ) 3 cm', 'd ) 4 cm', 'e ) 5 cm']", + "Correct": "d", + "Explanation": "explanation : \u00e2 \u02c6 \u0161 3 / 4 a 2 = 4 \u00e2 \u02c6 \u0161 3 - > a = 4 answer is d" + }, + { + "Answer": 9600, + "Options": "['a ) 9.6 m 3', 'b ) 96 m 3', 'c ) 960 m 3', 'd ) 9600 m 3', 'e ) 96000 m 3']", + "Correct": "d", + "Explanation": "let the height be h 2 ( 30 + 24 ) x h \u2013 2 ( 30 - 24 ) h = ( 2 ( 30 x 24 ) ) / ( 2 ( 30 + 24 ) ) = ( 30 x 24 ) / 54 = 40 / 3 m volume = 30 x 24 x 40 / 3 = 9600 m 3 answer : d" + }, + { + "Answer": 9, + "Options": "['a ) 6 / \u03c0', 'b ) 9 / \u03c0', 'c ) 6', 'd ) 9', 'e ) 12']", + "Correct": "d", + "Explanation": "given area of the base of a hemisphere is 3 = pi * r ^ 2 thus r = sqrt ( 3 / pi ) . surface area of whole sphere = 4 * pi * r ^ 2 . = 4 * pi * 3 / pi = 12 . since the hemisphere is half of a sphere the surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . but the total surface area = 6 + area of the base of a hemisphere . = 6 + 3 = 9 . answer is d ! !" + }, + { + "Answer": 0.6342592592592593, + "Options": "['a ) 137 / 216', 'b ) 137 / 218', 'c ) 137 / 217', 'd ) 136 / 216', 'e ) 138 / 216']", + "Correct": "a", + "Explanation": "sandra score can be like 1,4 , 9,16 , 25,36 eric score less then 1 - - > 0 eric score less then 4 = ( 1,1 ) , ( 1,2 ) ( 2,1 ) - - > 3 eric score less then 9 are ( 1,1 ) ( 1,2 ) ( 1,3 ) ( 1,4 ) ( 1,5 ) ( 1,6 ) ( 2,1 ) ( 2,2 ) ( 2,3 ) ( 2,4 ) ( 2,5 ) ( 2,6 ) ( 3,1 ) ( 3,2 ) ( 3,3 ) ( 3,4 ) ( 3,5 ) ( 4,1 ) ( 4,2 ) ( 4,3 ) ( 4,4 ) ( 5,1 ) ( 5,2 ) ( 5,3 ) ( 6,1 ) ( 6,2 ) - - > 26 eric score will always be less then 16 - - - > 36 eric score will always be less then 25 - - - > 36 eric score will always be less then 36 - - - > 36 total favorable outcomes = 3 + 26 + 36 + 36 + 36 = 137 total possible outcomes = 216 ( 36 * 6 ) probability = 137 / 216 answer : a" + }, + { + "Answer": 868, + "Options": "['a ) 878 cm ^ 2', 'b ) 858 cm ^ 2', 'c ) 838 cm ^ 2', 'd ) 868 cm ^ 2', 'e ) none of them']", + "Correct": "d", + "Explanation": "volume = ( 16 x 14 x 7 ) m ^ 3 = 1568 m ^ 3 . surface area = [ 2 ( 16 x 14 + 14 x 7 + 16 x 7 ) ] cm ^ 2 = ( 2 x 434 ) cm ^ 2 = 868 cm ^ 2 . answer is d" + }, + { + "Answer": 60, + "Options": "a ) 30 , b ) 45 , c ) 60 , d ) 75 , e ) 90", + "Correct": "c", + "Explanation": "\"c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be x = 60 . c\"" + }, + { + "Answer": 4.8, + "Options": "['a ) 4.8 cm', 'b ) 4.4 cm', 'c ) 4.9 cm', 'd ) 5.0 cm', 'e ) 5.2 cm']", + "Correct": "a", + "Explanation": "area of triangle is 1 / 2 * 12 * 8 = 48 side of square = x the entire triangle split into two right angled triangle and one square with dimensions as follows i ) square with side x ii ) right angled triangle with perpendicular sides x and 12 - x iii ) right angled triangle with perpendicular sides 8 - x and x sum of area of all three = 48 = x 2 + 1 / 2 * x * ( 12 - x ) + 1 / 2 * x * ( 8 - x ) = 48 = x = 4.8 cm answer : a" + }, + { + "Answer": 6, + "Options": "['a ) 6 cm', 'b ) 10 cm', 'c ) 8 cm', 'd ) data inadequate', 'e ) none of these']", + "Correct": "a", + "Explanation": "diagonal 2 = 64 + b 2 or , 10 ( 2 ) = 64 + 6 ( 2 ) answer a" + }, + { + "Answer": 6, + "Options": "a ) 4 , b ) 6 , c ) 9 , d ) 10 , e ) 12", + "Correct": "b", + "Explanation": "the top and the bottom are each single faces formed by three equilateral triangles joining , as in the diagram on the left , to make an isosceles trapezoid . top = 1 face , and bottom = 1 face . this is a four - sided figure , so there are four rectangles extending from the bottom of this prism to the congruent figure at the top . notice , in particular , the larger vertical face in the \u201c back \u201d of the diagram to the right is formed by two faces of the original triangular prisms lying next to each other and smoothly joining . total = 1 top + 1 bottom + 4 sides = 6 faces . answer = b ." + }, + { + "Answer": 120, + "Options": "a ) 120 , b ) 147 , c ) 251 , d ) 451 , e ) 258", + "Correct": "a", + "Explanation": "\"other side = ( ( 17 ) 2 - ( 15 ) 2 ) ( 1 / 2 ) = ( 289 - 225 ) ( 1 / 2 ) = ( 64 ) ( 1 / 2 ) = 8 m . area = ( 15 x 8 ) m 2 = 120 m 2 . ans : a\"" + }, + { + "Answer": 50, + "Options": "['a ) 50', 'b ) 30', 'c ) 20', 'd ) 40', 'e ) 10']", + "Correct": "a", + "Explanation": "let length = 2 x meters and breadth = 3 x meter . now , area = ( 1 / 6 ) x 1000 m 2 = 5000 / 3 m 2 so , 2 x * 3 x = 5000 / 3 < = > x 2 = 2500 / 9 < = > x = 50 / 3 therefore length = 2 x = ( 100 / 3 ) m = 33 ( 1 / 3 ) m and breadth = 3 x = 3 ( 50 / 3 ) m = 50 m . answer is a" + }, + { + "Answer": 54967, + "Options": "['a ) 55522 feet', 'b ) 45522 feet', 'c ) 35522 feet', 'd ) 25522 feet', 'e ) none']", + "Correct": "a", + "Explanation": "solution : first , model the pressure ( p ) in terms of depth ( d ) with a linear equation . we will find the equation p = md + b use ( 0 , 15 ) and ( 33 , 30 ) to find m m = 30 - 15 / 33 - 0 m = 15 / 33 = 0.45 p = 0.45 d + b use ( 0 , 15 ) to find b 15 = 0.45 \u00d7 0 + b 15 = b p = 0.45 d + 15 25000 = 0.45 d + 15 25000 - 15 = 0.45 d + 15 - 15 24985 = 0.45 d d = 24985 / 0.45 = 55522 feet answer a" + }, + { + "Answer": 8, + "Options": "['a ) 8 .', 'b ) 2', 'c ) 6', 'd ) 4', 'e ) 10']", + "Correct": "a", + "Explanation": "let the radius be r and the the height be h . new radius = 2 r and height = 2 h . area ( new ) : area ( old ) = pi \u2217 ( 2 r ) ^ 2 \u2217 2 h / pi \u2217 r ^ 2 \u2217 h = 8 : 1 . hence the answer is a ." + }, + { + "Answer": 461.8141200776996, + "Options": "['a ) 462 cm \u00b2', 'b ) 530 cm \u00b2', 'c ) 1345 cm \u00b2', 'd ) 1788 cm \u00b2', 'e ) none']", + "Correct": "a", + "Explanation": "sol . total surface area = 3 \u220f r \u00b2 = [ 3 * 22 / 7 * 7 * 7 ] cm \u00b2 = 462 cm \u00b2 answer a" + }, + { + "Answer": 12, + "Options": "['a ) 12', 'b ) 8', 'c ) 6', 'd ) 10', 'e ) 16']", + "Correct": "a", + "Explanation": "the mini - cubes with 2 painted sides are all on the edge of the cube , in the ` ` middle ' ' of the edge . there are 4 in front , 4 in back and 4 more on the ` ` strip ' ' that runs around the left / top / right / bottom of the cube . 4 + 4 + 4 = 12 . answer a" + }, + { + "Answer": 480, + "Options": "a ) 480 cm 2 , b ) 580 cm 2 , c ) 380 cm 2 , d ) 180 cm 2 , e ) 280 cm 2", + "Correct": "a", + "Explanation": "\"the triangle with sides 52 cm , 48 cm and 20 cm is right angled , where the hypotenuse is 52 cm . area of the triangle = 1 / 2 * 48 * 20 = 480 cm 2 answer : a\"" + }, + { + "Answer": 8, + "Options": "['a ) 8', 'b ) 4 \u03c0', 'c ) 4', 'd ) 6', 'e ) 5']", + "Correct": "a", + "Explanation": "circumference = 2 * pi * r = 2 * pi * 4 / pi = > 8 a" + }, + { + "Answer": 76.96902001294993, + "Options": "['a ) 154 sq metres', 'b ) 77 sq metres', 'c ) 308 sq metres', 'd ) 22 sq metres', 'e ) none of these']", + "Correct": "b", + "Explanation": "area of semicircle = \u00bd \u03c0 r 2 = \u00bd \u00d7 22 \u2044 7 \u00d7 7 \u00d7 7 = 77 m 2 answer b" + }, + { + "Answer": 450, + "Options": "['a ) 430 sq . m', 'b ) 425 sq . m', 'c ) 450 sq . m', 'd ) 475 sq . m', 'e ) 350 sq . m']", + "Correct": "c", + "Explanation": "distance covered in ( 9 \u00d7 1000 ) / ( 3600 ) \u00d7 12 = 30 m diagonal of squarre field = 30 m . area of square field = 30 ( power ) 2 / 2 = 900 / 2 = 450 sq . m answer is c ." + }, + { + "Answer": 11.25, + "Options": "a ) 45 \u00b0 , b ) 30 \u00b0 , c ) 22.5 \u00b0 , d ) 18 \u00b0 , e ) 11.25 \u00b0", + "Correct": "e", + "Explanation": "thecomplementof angle a is the angle which , when added to angle a , gives 90 degrees . the two acute angles of a right triangle are complements , for example . the original angle is x , so the complement is 7 x , and together , these add up to 90 degrees . x + 7 x = 90 8 x = 90 x = 11.25 \u00b0 answer = ( e )" + }, + { + "Answer": 25, + "Options": "['a ) 25 / \u221a \u03c0', 'b ) 30 / \u221a \u03c0', 'c ) 20', 'd ) 25', 'e ) 30']", + "Correct": "d", + "Explanation": "60 / 360 = 1 / 6 1 / 6 of total area = 5 5 / 6 of total area = 5 * 5 = 25 answer : d" + }, + { + "Answer": 36, + "Options": "['a ) 36', 'b ) 14', 'c ) 12', 'd ) 15', 'e ) 11']", + "Correct": "a", + "Explanation": "the 4 inch side should be aligned to the 16 inch side ( 4 layer ) 6 inch side should be aligned to the 18 inch side . ( 3 layer ) and 10 inch side should be aligned to the 30 inch side . ( 3 layer ) maximum number of rectangles = 4 * 3 * 3 = 36 answer is a" + }, + { + "Answer": 270, + "Options": "a ) 570 cm 2 , b ) 370 cm 2 , c ) 170 cm 2 , d ) 271 cm 2 , e ) 270 cm 2", + "Correct": "e", + "Explanation": "\"the triangle with sides 39 cm , 36 cm and 15 is right angled , where the hypotenuse is 39 cm . area of the triangle = 1 / 2 * 36 * 15 = 270 cm 2 answer : e\"" + }, + { + "Answer": 18, + "Options": "['a ) 18', 'b ) 20', 'c ) 27', 'd ) 32', 'e ) 25']", + "Correct": "a", + "Explanation": "side of square = \u221a 36 = 6 m . length = 6 m and breadth = 3 m area of rectangle = 6 * 3 = 18 sq . m answer a" + }, + { + "Answer": 23.561944901923447, + "Options": "a ) 34 , b ) 35 , c ) 56 , d ) 67 , e ) 23.57", + "Correct": "e", + "Explanation": "\"let the side of the square be a cm . parameter of the rectangle = 2 ( 16 + 14 ) = 60 cm parameter of the square = 60 cm i . e . 4 a = 60 a = 15 diameter of the semicircle = 15 cm circimference of the semicircle = 1 / 2 ( \u220f ) ( 15 ) = 1 / 2 ( 22 / 7 ) ( 15 ) = 330 / 14 = 23.57 cm to two decimal places answer : option e\"" + } + ] +} \ No newline at end of file