Last Digit / Units Digit 

 

 

 

 

 

To find the units digit of xy we only consider the units digits of the number x.
To calculate units digit of 237234 we only consider the units digit of 237. Hence, we find the units digit of 7234.
To find the units digit of a × b, we only consider the units digits of the numbers a and b.
To calculate units digit of 233 ×  254, we only consider the units digit of 233 and 254 i.e. 3  and 4, respectively. Hence, the units digit of 233 ×  254 = units digit of 3 × 4 i.e 2.

First digit of a Number

Problems for practice

1. Find the unit digit of [ 1020000 / ( 10100 +3) ] where [ x ] is greatest Integer less than or equal to x.
2. Find the unit digit of the product of first 120 primes .
3. What is the unit digit of 1! + 2! + 3! + 4! +….. + 2018! ?
4.  What is the unit digit of (1! + 2! + 3! + 4! +….. + 2018!)2?
5. What is the unit digit of 231001 ?

Some more ‘Gyan’ on numbers :
Nifty Formulae for Natural Numbers
Divisibility Rule of a Number (Divisibility Test)
Remainders theorem 
Divisors of a Number ( Number of Divisors of a number)

Do you know that we have a forum where you can get all your doubts cleared?
Forums

Important Concepts and Formulae

 

Hello CAT takers,

Now that we are just a few days away from CAT, you must be revising everything for one final time before CAT. Here is a compilation of all the important Concepts and formulae for Quant. Whether you need to revise the formulae or you need them while solving problems of different topics, it’s all at one place for your ready reference.

Download it and use it for your benefit. 

Important Concepts for CAT2018

PRIME NUMBERS : The Most Mysterious Figures in Math 

Prime numbers have always fascinated mathematicians. They appear among the integers seemingly at random, and yet not quite: there seems to be some order or pattern, just a little below the surface, just a little out of reach.
—Underwood Dudley

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. For example, 11 is a prime number because it has no positive divisors other than 1 and 11.

Read More

Alphametics The Art of Numbers

As CAT 2018 preparation starts heating up, I am going to flag the race with an oddball topic: Alphametics. What are alphametics or cryptarithms as they are also known?

Alphametics are number puzzles in basic arithmetic operations where digits are represented by alphabets. It is customary that different digits are represented by different alphabets. Why are alphametics relevant? Because they require a good knowledge of the properties of numbers and skill in working with them. Solving alphametics helps you quickly identify the solution to many problems which might otherwise require a good amount of time.

Read More

Some properties of natural numbers :

1•Sum of first n natural numbers : 1 + 2 + 3 +……+ n = n ( n +1)/2

2• Sum of squares of first n natural numbers : 1² + 2² + 3² +……+ n² = n ( n +1) ( 2n +1) /6

3• Sum of cubes of first n natural numbers : 1³ + 2³ + 3³ +……+ n³ = [ n ( n +1)/2]²

4• Sum of first n odd numbers: n²

5• Sum of first n even numbers: n² + n

Read More

Similar Triangles

Similar Triangles

The current article deals with a frequently occurring topic in geometry in CAT- similarity of triangles. Most of you will notice that this topic is coming year after year in CAT and, as geometry questions in CAT are easy compared with other topics, mastering the concept is easier than mastering concepts in Algebra, Permutation, and Combination, or Probability.

Read More

 Divisibility Rules
A. Divisibility by 2, 4, 8, 16, 32.

A number is divisible by 2, 4, 8, 16, 32,.. 2 when the number formed by the last one, two, three, four, five…n digits is divisible by 2, 4, 8, 16, 32,..2 respectively.

Example: 1246384 is divisible by 8 because the number formed by the last three digits i.e. 384 is divisible by 8. The number 89764 is divisible by 4 because the number formed by the last two digits, 64 is divisible by 4.

B. Divisibility by 3 and 9

A number is divisible by 3 or 9 when the sum of the digits of the number is divisible by 3 or 9 respectively.

Read More

LOGARITHM

If a is a positive real number other than 1, and am = x, then we can write: m = logax, and we say that the value of log x to the base a is m.
Examples:

(i) 104 = 10000     log10 10000 = 4.

(ii) 35 = 243     log3 243 = 5.

(iii) (0.1)3 = 0.001     log (0.1) (0.001) = 3.


Properties of Logarithms

Read More