# Shortcuts

## Aptitude – Shortcuts for Addition and Subtraction

Addition is one of the four basic operations of arithmetic, with the others being subtraction, multiplication and division. The addition of two whole numbers is the total amount of those quantities combined. SHORTCUTS IN ADDITION: Addition of numbers close to multiples of ten (e.g. 19, 29, 89, 99 etc.) 116 + 39 = 116 + …

## Aptitude – Shortcuts for Multiplication

Multiplication of whole numbers is equivalent to a repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the multiplicand, as the value of the other one, the multiplier. Normally, the multiplier is written first and multiplicand second, though this can vary, as the distinction is not …

## Shortcut of Combination and Probability

Shortcut 99:    nCr=n!/[r!(n-r)!] Question: In how many ways 2 shirts and 3 pants can be selected from 5 shirts and 7 pants? Answer: Selecting 2 shirts out of 5 = 5C2 = 5!/[2!(5 – 2)!] = 10 Selecting 3 shirts out of 7 = 7C3 = 7!/[3!(7 – 3)!] = 35 Since the two …

## Shortcut of Permutation-2

Shortcut 95: Repeated elements      n!/(a!*b!) Question: In how many ways the letters of the word “ENVIRONMENT” can be arranged? Answer: n = 11 Let, a = 2 (E is repeated twice) Let, b = 3 (N is repeated thrice) Number of arrangements = 11!/(2! x 3!) Shortcut 96: Circular arrangement   (n-1)! Question: In …

## Shortcut of Permutation-1

Shortcut 91: Events   Dependent=multiplication   Independent =addition Question: There 3 busses from city A to city B and there are 5 busses from city B to city C. In how many ways a person can travel from city A to C through B? Answer: Choosing a bus from city B depends on choosing a …

## Shortcut of Calendar and Clocks

Shortcut 87:                              Using the odd days Question: Find the day of birth of MS Dhoni (7 July, 1981), if 31 Dec 1999 is Friday Answer: Days after 7/7/1981 in 1981 = 177 Odd days by normal years from 1982 to 1999 = 14 Odd days by leap years = 4 x 2 = 8 …

## Shortcut of Heights and Distances

Shortcut 85: Using tanƟ Ɵ                                tan 0                                    0 30                            $1/\sqrt3$ 45                                  1 60                             $\sqrt3$ 90                              $\infty$ Question: A man on a boat saw a tower of height 100m at an angle of 60o. What is the distance between the man and …

## Shortcut of LCM and HCF

Shortcut 82: Maximum number of items per group     Take HCF Question: There are 40, 45 and 50 balls in three different colors. They have to be arranged in boxes such that all the boxes will have equal number of balls and same colored balls. What is the maximum number of balls that can be …

## Shortcut of Number system

Shortcut 77: Divisibility test Divisibleby                                    Rule 2                            Last digit of a number should be 0,2,4,6, or 8 3                            Sum of the digit should be divisible by 3 4                            Last two digits of a number should be divisible by 4 5                            Last digit of a number should be 0 or 5 6                             Number should be divisible …

## Shortcut of Simple and Compound Interest

Shortcut 75: Simple interest $SI=\frac{PNR}{100}$ P = Principle amount invested or borrowed R = Rate of interest per term N = Number of terms Term = duration for which interest is calculated Question: A man invested Rs. 10000 at 4% per annum simple interest. What is the interest he will get at the end of …

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