# Quantitative Aptitude Important Formulas

 Clock - Important Formulas,Tricks and Examples Angle traced by hour hand in 12 hrs = 360°. Angle traced by minute hand in 60 min. = 360°. In every hour, both the hand coincide once. In every 12 hours, the hands of clock coincide 11 times. In a day(24 hours), the hands are coinciding 22 times. In every hour, the two hands are in opposite direction once. In every 12 hours, the hands of clock are in opposite direction 11 times. In every hour, the two hands are at right angles 2 times. In every 12 hours, the hands of clock are at right angles 22 times. In a day(24 hours), the two hands are at right angles 44 times. Clock angle problems The hour hand of a normal 12-hour analogue clock turns 360° in 12 hours (720 minutes) or 0.5° per minute. The minute hand rotates through 360° in 60 minutes or 6° per minute. The angle traced of the hour hand = 0.5 * (60*H + M)° The angle of the minute hand = 6°*M The angle between the hands= |Angle of hour hand - Angle of minute hand| Mirror Image Of Clock If the time is between 1 to 11 o'clock then to find the mirror image, time is subtracted by 11 : 60 If the time is between 11 to 1 then to find the mirror image, time is subtracted by 23 : 60 Post/View Answer Post comment Cancel Thanks for your comment.! Write a comment(Click here) ...
 Numbers - Important Formulas,Tricks and Examples The common number system is decimal number system. The Decimal number system used base (or radix) as 10 . This means that the system has ten symbols or numerals to represent any quantity. These symbols are called Digits and they are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Types of Numbers Natural Numbers:The numbers that are used for counting called Natural Numbers.These are infinite and start from the number 1 . Ex : 1, 2, 3, 4, 5, 6 ........ Whole numbers:The whole numbers are just all the natural numbers plus zero. Ex : 0, 1, 2, 3, 4, 5 ............. Integers: Integers incorporate all positive and negative numbers with zero. Ex : .... –3, –2, –1, 0, 1, 2, 3 ..... Even Numbers: An even number is one that can be divided evenly by two leaving no remainder, such as 2, 4, 6, and 8. Odd Numbers: An odd number is one that does not divide evenly by two, such as 1, 3, 5, and 7. Rational Numbers: All numbers of the form p/q where p and q are integers (q ≠ 0) called Rational numbers. Ex : 4, 3/4, 0, …. Irrational Numbers: Irrational numbers are the opposite of rational numbers. An irrational number cannot be written as a fraction as p/q where a and b are integers. the decimal values for irrational numbers never end and do not have a repeating pattern in them.please note ‘pi’ has never ending decimal places, is irrational. Ex : pi, 2^1/2 , 3^1/2, 5^1/2 , 7^1/2 .......... Real numbers: Real numbers include counting numbers, whole numbers, integers, rational numbers and irrational numbers. Ex : 8, 6, 2, (3)^1/2 , 3/5 etc. Prime Number: A prime number is a number which can be divided only by 1 and itself. The prime number has only two factors, 1 and itself. Ex : 2, 3, 7, 11, 13, 17, …. are prime numbers. Composite Number: A Composite Number is a number which can be divided evenly. Any composite number has additional factors than 1 and itself. Ex : 4, 6, 8, 9, 10 ….. Co-primes or Relatively prime numbers: A pair of numbers not having any common factors other than 1 or –1. (Or alternatively their greatest common factor is 1 or –1) Ex : 15 and 28 are co-prime, because the factors of 15 (1,3,5,15) , and the factors of 28 (1,2,4,7,14,28) are not in common (except for 1) . Twin Primes: A pair of prime numbers is said to be twin primes if they differ by 2. Ex : (3,5) , (5,7) , (11,13) , … Algebra (a+b)2 = a2 + 2ab + b2 (a-b)2 = a2 - 2ab + b2 (a+b)2 - (a-b)2 = 4ab (a+b)2 + (a-b)2 = 2 (a2 + b2) a2-b2 = (a-b)(a+b) (a+b)3 = a3+b3+3ab(a+b) = a3+b3+3a2b+3ab2 (a-b)3 = a3-b3-3ab(a-b) = a3-b3-3a2b+3ab2 a3+b3 =(a+b)3-3ab(a+b) = (a+b)(a2-ab+b2) a3-b3 =(a-b)3+3ab(a-b) = (a-b)(a2+ab+b2) Test of Divisibility Divisibility By 2 : A number is divisible by 2, if its unit's digit is zero or even (2, 4, 6, 8..). Divisibility By 3 : A number is divisible by 3, if the sum of its digits is divisible by 3. Divisibility By 4 : A number is divisible by 4, if the number formed by the last two digits is divisible by 4. Divisibility By 5 : A number is divisible by 5, if its unit's digit is either 0 or 5. Divisibility By 6 : A number is divisible by 6, if it is divisible by both 2 and 3. Divisibility By 8 : A number is divisible by 8, if the number formed by the last three digits of the given number is divisible by 8. Divisibility By 9 : A number is divisible by 9, if the sum of its digits is divisible by 9. Divisibility By 10 : A number is divisible by 10, if it ends with 0. Divisibility By 11 : A number is divisible by 11, if the difference of the sum of its digits at odd places and the sum of its digits at even places, is either 0 or a number divisible by 11. Divisibility By 12: A number is divisible By 12 if the number is divisible By both 4 and 3. Divisibility By 13: A number is divisible By 13 if its unit’s place digit is multiplied By 4 and added to the remaining digits and the number obtained is divisible By 13. Divisibility By 14: A number is divisible By 14 if the number is divisible By both 2 and 7. Divisibility By 15: A number is divisible By 15 if the number is divisible By both 3 and 5. Divisibility By 16: A number is divisible By 16 if its last 4 digits is divisible By 16 or if the last four digits are zeros. Divisibility By 17: A number is divisible By 17 if its unit’s place digit is multiplied By 5 and subtracted from the remaining digits and the number obtained is divisible By 17. Divisibility By 18: A number is divisible By 18 if the number is divisible By both 2 and 9. Divisibility By 19: A number is divisible By 19 if its unit’s place digit is multiplied By 2 and added to the remaining digits and the number obtained is divisible By 19. Divisibility By 20: A number is divisible by 20 if it is divisible by 10 and the tens digit is even.