January 1st, 2020 by Ravi Handa

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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January 1st, 2020 by Ravi Handa

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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January 1st, 2020 by Ravi Handa

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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January 1st, 2020 by Ravi Handa

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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January 1st, 2020 by Ravi Handa

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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December 30th, 2019 by Ravi Handa

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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December 30th, 2019 by Ravi Handa

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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December 30th, 2019 by Ravi Handa

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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December 30th, 2019 by Ravi Handa

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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December 30th, 2019 by Ravi Handa

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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