Basic Formula of Number System:
1. Sum of all the first n natural numbers =
For example: 1+ 2 +3 +…..+105=
2. Sum of first n odd numbers =
For example 1+3+5+7==16(as there are four odd numbers)
3. Sum of first n even numbers = n (n+1)
For example : 2+4+6+8+….+100 (or 50th even number) = 50×(50+1)= 2550
4. Sum of squares of first n natural numbers =
5. Sum of cubes of first n naturals numbers =
(1) What is the total of all the even numbers from 1 to 400?
From 1 to 400, there are 400 numbers. So, there are 400/2= 200 even numbers.
Hence, sum = 200(200+1) = 40200 (From Rule III)
(2) What is the total of all the even numbers from 1 to 361?
From 1 to 361, there are 361, there are 361 numbers; so there are even numbers. Thus, sum = 180(180+1)=32580
(3) What is the total of all the odd numbers from 1 to 180?
Therefore are 180/2 = 90 odd numbers between the given range. So, the sum =
(4) What is the total of all the odd numbers from 1 to 51?
There are odd numbers between the given range. So, the sum =
(5) Find the of all the odd numbers from 20 to 101.
The required sum = Sum of all the odd numbers from 1 to 101.
Sum of all the odd numbers from 1 to 20
= Sum of first 51 odd numbers – Sum of first 10 odd numbers
1. In a division sum, we have four quantities – Dividend, Divisor, Quotient, and Remainder. These are connected by the relation.
Dividend = (Divisor × Quotient) + Remainder
2. When the division is exact, the remainder is zero (0). In this case, the above relation becomes
Dividend = Divisor × Quotient
Example: 1: The quotient arising from the divisor of 24446 by certain numbers is 79 and the remainder is 35; what is the divisor?
Divisor × Quotient = Dividend - Remainder
79×Divisor = 24446 -35 =24411
Divisor = 24411 ÷ 79 = 309.
Example: 2: A number when divided by 12 leaves a remainder of 7. What remainder will be obtained by dividing the same number by 7?
We see that in the above example, the first divisor 12 is not a multiple of the second divisor 7. Now, we take the two numbers 139 and 151, which when divided by 12, leave 7 as the remainder. But when we divide the above two numbers by 7, we get the respective remainder as 6 and 4. Thus, we conclude that the question is wrong.
This article tends to be beneficial for the following exams - REET, UPTET, CTET, Super TET, DSSSB, KVS, etc.
Note: All the study notes are available in Hindi as well as English language. Click on A/अ to change the language.
|Serial No.||Book Name||Author Name|
|1.||The Pearson Guide To Quantitative Aptitude For Competitive Examination||Dinesh Khattar|
|2.||Quantitative Aptitude Quantum CAT||Sarvesh K.|
|3.||Teach Yourself Quantitative Aptitude||Arun Sharma|
Commentswrite a comment