Cat Quant Cheat Sheet

Quantitative Ability Formula Sheet The smart way to learn online CAT and Management Entrance Tests http://www.snapwiz.co.in Arithmetic Fundamentals Table of Squares Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 20 25 Square 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 400 625 Table of Cubes Number 2 3 4 5 10` 20 100 Cube 8 27 64 125 1000 8000 1000000 Commonly used Decimal, Percent and Fractions(Less than 1) Percent 10% 20% 25% 30% 33% 40% 50% 60% 66% 75% 80% 90% 100% 1 2 1 3 1 2 1 3 2 3 4 9 Fractions 1 10 10 4 10 3 5 2 5 3 4 5 10 Decimals 0.1 0.2 0.25 0.3 0.33 0.4 0.5 0.6 0.66 0.75 0.8 0.9 1 Commonly used Decimal, Percent and Fractions (Greater than 1) Percent 100% 125% 133.33% 150% 200% 5 4 3 Fractions 1 2 4 3 2 Decimals 1 1.25 1.33 1.5 2.0 Visit http://www.snapwiz.co.in for free mock CAT tests Page 1

Quantitative Ability Formula Sheet The smart way to learn online CAT and Management Entrance Tests http://www.snapwiz.co.in Divisibility Rule Number Rule Example 2 If last digit is 0,2,4,6, or 8 22, 30, 50, 68, 1024 3 If sum of digits is divisible by 3 123 is divisible by 3 since 1 + 2 + 3 = 6 (and 6 is divisible by 3) 4 If number created by the last 2 864 is divisible by 4 since 64 is divisible by 4 digits is divisible by 4 5 If last digit is 0 or 5 5, 10, 15, 20, 25, 30, 35, 2335 6 If divisible by 2 & 3 522 is divisible by 6 since it is divisible by 2 & 3 9 If sum of digits is divisible by 9 621 is divisible by 9 since 6 + 2 + 1 = 9 (and 9 is divisible by 9) 10 If last digit is 0 10, 20, 30, 40, 50, 5550 Operations Involving Exponents Special Exponents Multiplication �� × �� = ��(��+��) Reciprocal �� Division �� ÷ �� = ��(��−��) �� = ��−�� Power (�� )�� = ��×�� Power 0 �� = �� Roots �� = �� = ( ��)�� Power 1 �� = �� Logarithms Definition: �� = �� → �� = �� Properties Example: �� = �� → �� = �� = �� = �� = �� = �� = �� × �� = �� + �� = �� − �� Visit http://www.snapwiz.co.in for free mock CAT tests Page 2

Quantitative Ability Formula Sheet The smart way to learn online CAT and Management Entrance Tests http://www.snapwiz.co.in Progressions Arithmetic Progression: �� term of an Geometric Progression: �� term of a Arithmetic Progression Geometric Progression �� = �� + �� − �� = �� −�� Sum of n terms of an arithmetic expression Sum of n terms of a geometric progression: �� + �� + �� − �� (��+�� − ��) �� = = �� = �� − �� The first term is ��1 , the common difference The first term is ��1 , the common ratio is ��, and is ��, and the number of terms is ��. the number of terms is ��. Infinite Geometric Progression �� Sum of all terms in an infinite geometric series = �� − �� < �� < �� (��−��) Roots of a Quadratic Equation A quadratic equation of type �� + �� + �� has two solutions, called roots. These two solutions −b± b 2 −4ac may or may not be distinct. The roots are given by the quadratic formula: where 2a –b− b 2 −4ac –b+ b 2 −4ac the ± sign indicates that both and are solutions 2a 2a Common Factoring Formulas 1. �� − �� = �� − �� × �� + �� 2. �� + �� + �� = (�� + ��)�� 3. �� − �� + �� = (�� − ��)�� 4. �� + �� + �� + �� = (�� + ��)�� 5. �� − �� + �� − �� = (�� − ��)�� Binomial Theorem The coefficient of �� (��−��) �� in (�� + ��)�� is: �� ! �� = ��! (�� − ��)! Applies for any real or complex numbers x and y, and any non-negative integer n. Visit http://www.snapwiz.co.in for free mock CAT tests Page 3

Quantitative Ability Formula Sheet The smart way to learn online CAT and Management Entrance Tests http://www.snapwiz.co.in Summary of counting methods Order matters Order doesn’t matter With Replacement If �� objects are taken from a set of �� N/A objects, in a specific order with replacement, how many different samples are possible? �� Without Permutation Rule: If �� objects are Combination Rule: If �� objects are Replacement taken from a set of �� objects without taken from a set of �� objects without replacement, in a specific order, how replacement and disregarding order, many different samples are how many different samples are possible? possible? �� ! �� = (�� − ��)! �� ! �� = ��!(��−��)! Probability The probability of an event A, �� is defined as �� = �� Independent Events: If A and B are independent events, then the probability of A happening and the probability of B happening is: �� = ��(��) × ��(��) Dependent Events: If A and B are dependent events, then the probability of A happening and the probability of B happening, given A, is: �� = ��(��) × ��(�� | ��) Conditional Probability: The probability of an event occurring given that another event has already occurred e.g. what is the probability that B will occur after A ��(�� ) �� = ��(��) Visit http://www.snapwiz.co.in for free mock CAT tests Page 4

Quantitative Ability Formula Sheet The smart way to learn online CAT and Management Entrance Tests http://www.snapwiz.co.in Geometry Fundamentals The sum of angles around a point will always Vertical angles are equal to each other. be 360 degrees. In the adjacent figure �� = �� and In the adjacent figure �� = �� + �� + �� + �� = ��° The sum of angles on a straight line is 180˚. When a line intersects a pair of parallel lines, the corresponding angles are formed are equal to each other In the adjacent figure sum of angles and b is In the figure above 180 i.e. �� + �� = �� = �� ° When a line intersects a pair of parallel lines, Any point on the perpendicular bisector of a the alternate interior and exterior angles line is equidistant from both ends of the line. formed are equal to each other In the adjacent figure alternate In the figure, k interior angles is the a=b and perpendicular alternate exterior bisector of angles c=d segment AB and c=d, e=f Visit http://www.snapwiz.co.in for free mock CAT tests Page 5

Quantitative Ability Formula Sheet The smart way to learn online CAT and Management Entrance Tests http://www.snapwiz.co.in Triangle Properties 1. Sum of all internal angles of a triangle is 180 degrees i.e. �� + �� + �� = ��° 2. Sum of any two sides of a triangle is greater than the third i.e. �� + �� > �� or �� + �� > �� or �� + �� > �� 3. The largest interior angle is opposite the largest side; the smallest interior angle is opposite the smallest side i.e. if �� > �� → �� > �� 4. The exterior angle is supplemental to the adjoining interior angle i.e. �� + �� = ��°. Since �� + �� + �� = ��° it follows that �� = �� + �� 5. The internal bisector of an angle bisects the opposite side in the ratio of the other two sides. In the BD AB adjoining figure DC = BC Pythagoras Theorem Commonly Used Pythagorean Triples Height, Base Hypotenuse 3,4 or 4,3 5 6,8 or 8,6 10 �� = �� + �� 5, 12 or 12,5 13 7, 24 or 24,7 25 Visit http://www.snapwiz.co.in for free mock CAT tests Page 6

Quantitative Ability Formula Sheet The smart way to learn online CAT and Management Entrance Tests http://www.snapwiz.co.in Special Right Triangles The lengths of the The lengths of the sides sides of a 45 45- - of a 30 60 90 - - 90 triangle are in triangle are in the ratio the ratio of ��: ��: �� of ��: ��: �� Test of Acute and Obtuse Triangles If �� < �� + �� then it is an acute-angled If �� > �� + �� then it is an obtuse-angled triangle, i.e. the angle facing side c is an acute triangle, i.e. the angle facing side c is an angle. obtuse angle. Polygons Sum of interior angles of a quadrilateral is 360˚ �� + �� + �� + �� = 360° Sum of interior angles of a pentagon is 540˚ �� + �� + �� + �� + �� = 540° If n is the number of sides of the polygon then, sum of interior angles = (n - 2)180° Visit http://www.snapwiz.co.in for free mock CAT tests Page 7

Quantitative Ability Formula Sheet The smart way to learn online CAT and Management Entrance Tests http://www.snapwiz.co.in Properties of a Circle The angle at the centre of a circle is twice any Every angle subtended at the circumference angle at the circumference subtended by the by the diameter of a circle is a right angle same arc. (90˚). In the adjacent figure angle �� = �� In a cyclic quadrilateral, the opposite angles are The angles at the circumference subtended supplementary i.e. they add up to 180˚. by the same arc are equal. In the figure In the above angle adjacent �� + �� = figure angle ��° and �� = �� + �� = ��° A chord is a straight line joining 2 points on the A radius that circumference of a circle. is perpendicular to a chord bisects the chord into two equal parts and vice versa. In the adjacent figure PW=PZ Visit http://www.snapwiz.co.in for free mock CAT tests Page 8

Quantitative Ability Formula Sheet The smart way to learn online CAT and Management Entrance Tests http://www.snapwiz.co.in Area and Perimeter of Common Geometrical Figures Rectangle Square Triangle Area �� = �� × �� Area �� = �� Area �� = �� × �� × �� Perimeter �� = �� × (�� + ��) Perimeter �� = �� Circle Equilateral Triangle Trapezoid Area �� = �� Perimeter �� = �� Area �� = �� × �� Perimeter �� = �� Area �� = �� (�� + �� ) �� Altitude �� = �� Parallelogram Ring Sector �� in degrees Area �� = �� × �� Area �� = ��(�� − �� ) �� Area �� = �� × �� Perimeter �� = �� × (�� + ��) �� Length of Arc �� = �� × �� Perimeter �� = �� + �� Visit http://www.snapwiz.co.in for free mock CAT tests Page 9

Quantitative Ability Formula Sheet The smart way to learn online CAT and Management Entrance Tests http://www.snapwiz.co.in Volume and Surface Area of 3 Dimensional Figures Cube Sphere Right Circular Cylinder �� Volume �� = �� Volume �� = �� Surface Area �� = �� Volume �� = �� × �� × �� Surface Area �� = �� Surface Area �� = ��(�� + �� + ��) Pyramid Right Circular Cone Frustum �� Volume �� = �� Surface Area = �� = �� + �� Volume B is the area of the base Volume �� = �� is the slant height �� = �� (�� + �� + �� ) Surface Area �� = ��(�� + ��) Coordinate Geometry �� −�� Line: Equation of a line �� = �� + �� Slope of a line �� = ��−�� In the adjoining figure, c is the intercept of the line on Y-axis i.e. c=2, m is the slope Visit http://www.snapwiz.co.in for free mock CAT tests Page 10

Quantitative Ability Formula Sheet The smart way to learn online CAT and Management Entrance Tests http://www.snapwiz.co.in The slopes of parallel lines are equal The slopes of perpendicular lines are opposite reciprocals of one another. In the adjoining In the figure, the two adjoining the lines are two lines are parallel to perpendicular each other i.e. to each other �� = �� −�� i.e. �� = �� Midpoint between two points (�� , �� ) and Distance between two points (�� , �� ) and (�� , �� ) in a x-y plane: (�� , �� ) in a x-y plane: �� − �� − �� = (�� − �� )�� + (�� − �� )�� , �� = , �� Horizontal and Vertical line Equation of a circle with center (h,k) and radius r Equation of line parallel to x-axis (line p) with intercept on y-axis at (0, b) is �� = ��. Equation of line parallel to y-axis (line q) with intercept on x-axis at (a,0) is �� = �� (�� − ��)�� + (�� − ��)�� = �� Visit http://www.snapwiz.co.in for free mock CAT tests Page 11

Quantitative Ability Formula Sheet The smart way to learn online CAT and Management Entrance Tests http://www.snapwiz.co.in Trigonometry Basics Definition: Right Triangle definition for angle θ Pythagorean Relationships Tan and Cot such that 0 < θ < 90° ��2 �� + �� 2 �� = 1 �� = , �� 2 �� + 1 = �� 2 �� 2 2 �� = �� + 1 = �� Half Angle Formulas Even/Odd 1 sin −�� = −�� 1 ��2 �� = (1 − cos 2�� ) 2 �� = , �� = cos −�� = �� 1 �� 2 �� = 1 + cos 2�� 1 2 tan −�� = −�� = , �� = �� (1 − cos 2�� ) ��2 �� = �� 1 (1 + cos 2�� ) �� = , �� = �� sin 2�� = 2��, cos 2�� = �� 2 �� − ��2 �� Periodic Formula: Where n is an integer 0° 30° 45° 60° 90° sin �� + 2�� = sin �� → sin �� + 180° = �� Sin 0 1 1 3 1 2 2 2 cos⁡ + 2��) = cos �� → cos⁡ + 180°) = �� (�� (θ Cos 1 3 1 1 0 tan �� + �� = tan �� → tan θ + 90° = tanθ 2 2 2 Tan 0 1 1 3 ∞ 3 Visit http://www.snapwiz.co.in for free mock CAT tests Page 12

Cat Quant Cheat Sheet

by versabit technologies on Oct 07, 2009

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