Quantitative Aptitude – Geometry – Triangles – Let P be an interior point

January 1st, 2020 by

Quantitative Aptitude - Geometry - Triangles - Let P be an interior point Quantitative Aptitude - Geometry - Triangles Question Let P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB. If the perpendicular distance of P from each of AB, BC, and CA is 4 (√2 - l) cm, then the area, in sq cm, of the triangle ABC is Answer 16 Solution From CAT 2017 - Quantitative Aptitude - Geometry - Triangles, we can see that, PQ = PR = PS = 4(√2-1) CS = PR (PC)^2 = (PS)^2 + (CS)^2 On solving, we get, PC = 4√2(

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Quantitative Aptitude – Geometry – Circles – ABCD is a quadrilateral inscribed

January 1st, 2020 by

Quantitative Aptitude - Geometry - Circles - ABCD is a quadrilateral inscribed Quantitative Aptitude - Geometry - Circles Question ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120 degrees and ∠BAC = 30 degrees, then the value of ∠BCD (in degrees) is Answer 90 Solution From CAT 2017 - Quantitative Aptitude - Geometry - Circles, we can see that, OD = OC (Radius of circle) So, angle (ODC) = angle (OCD) = 30 deg Angle (DOA) = 60 degrees Angle (BAC) = 30 degrees (Given) OA = OD (radius of circle)

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Quantitative Aptitude – Geometry – Coordinate – The points (2, 5) and (6, 3)

January 1st, 2020 by

Quantitative Aptitude - Geometry - Coordinate - The points (2, 5) and (6, 3) Quantitative Aptitude - Geometry - Coordinate Question The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is A) -5 B) -6 C) -7 D) -8 Answer Option (D) Solution From CAT 2017 - Quantitative Aptitude - Geometry - Coordinate, we can see that, The diagonals of a rectangle bisect each other. Mid points of the diagonal are (4,4) These points fall on the line with eq

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Quantitative Aptitude – Geometry – Mensuration – The base of a vertical pillar

January 1st, 2020 by

Quantitative Aptitude - Geometry - Mensuration - The base of a vertical pillar Quantitative Aptitude - Geometry - Mensuration Question The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar is A) 1300 B) 1340 C) 1480 D) 1520 Answer

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Quantitative Aptitude – Geometry – Polygons – Let ABCDEF be a regular hexagon

January 1st, 2020 by

Quantitative Aptitude - Geometry - Polygons - Let ABCDEF be a regular hexagon Quantitative Aptitude - Geometry - Polygons Question Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is A) 3√2 B) 3 C) 4 D) √3 Answer Option (B) Solution From CAT 2017 - Quantitative Aptitude - Geometry - Polygons, we can see that, Angle (ABC) = 120 deg According to the formula, Cos (theta) = (b^2 + c^2 – a^2)/2bc Cos (120) = [(AB)^2 + (BC)^2 – (AC)^2]/2*AB*BC

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Quantitative Aptitude – Geometry – Coordinate – The shortest distance

December 30th, 2019 by

Quantitative Aptitude - Geometry - Coordinate - The shortest distance Quantitative Aptitude - Geometry - Coordinate Question The shortest distance of the point (½, 1) from the curve y = |x -1| + |x + 1| is A) 1 B) 0 C) √2 D) √3/2 Answer Option (A) Solution From CAT 2017 - Quantitative Aptitude - Geometry - Coordinate, we can see that, The graph of y = |x – 1| + |x + 1| is shown above. The shortest distance of (1/2, 1) from the graph is 1. Option (A) Download CAT 2017 Question Paper with answers and detail

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Quantitative Aptitude – Geometry – Triangles – Let ABC be a right-angled triangle

December 30th, 2019 by

Quantitative Aptitude - Geometry - Triangles - Let ABC be a right-angled triangle Quantitative Aptitude - Geometry - Triangles Question Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 km, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour is Answer 24 Solution As per the question from CAT 2017 - Quantitative Aptitude - Geometry - Triangles, BC^2 = AB^2 + AC^2 = 625 BC = 25 Shortest Distance from A to hypotenus

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Quantitative Aptitude – Geometry – Mensuration – A ball of diameter 4 cm

December 30th, 2019 by

Quantitative Aptitude - Geometry - Mensuration - A ball of diameter 4 cm Quantitative Aptitude - Geometry - Mensuration Question A ball of diameter 4 cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is 3 cm, while its volume is 9 π cm^3 . Then the vertical distance, in cm, of the topmost point of the ball from the base of the cylinder is Answer 6 Solution As per the question from CAT 2017 - Quantitative Aptitude - Geometry - Mensuration, The height of the cylinder (h) = 3 The volume = 9π

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Quantitative Aptitude – Geometry – Mensuration – A solid metallic cube

December 30th, 2019 by

Quantitative Aptitude - Geometry - Mensuration - A solid metallic cube Quantitative Aptitude - Geometry - Mensuration Question A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio 1 : 1 : 8: 27: 27. The percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube is nearest to A) 10 B) 50 C) 60 D) 20 Answer Option (B) Solution As per the question from CAT 2017 - Quantitative Aptitude - Geometry - Mensuration, Ratio of volumes of 5 sm

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Quantitative Aptitude – Geometry – Circles – Let ABC be a right-angled isosceles

December 30th, 2019 by

Quantitative Aptitude - Geometry - Circles - Let ABC be a right-angled isosceles Quantitative Aptitude - Geometry - Triangles Question Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC. Let BPC be an arc of a circle centered at A and lying between BC and BQC. If AB has length 6 cm then the area, in sq cm, of the region enclosed by BPC and BQC is A) 9π - 18 B) 18 C) 9π D) 9 Answer Option (B) Solution As per the question from CAT 2017 - Quantitative Ap

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