Amazing squares:( APPLICABLE FOR ONLY THESE NOS) Amazing squares: ========================== The square of 11,101,1001,10001..... is 121,10201,1002001,100020001...... respectively. The square of 12,102,1002,10002......is 144,10404,1004004,100040004...... respectively The square of13, 103,1003,10003......is 169,10609,1006009,100060009...... respectively The square of 21,201,2001,20001......is 441,40401,4004001,400040001 ......respectively The square of 22,202,2002,20002......is 484,40804,4008004,400080004.......respectively The square of 31,301,3001,30001......is 961,90601,9006001,900060001...... respectively NOTE: this method does not follow for any other number directly. REMEMBER while doing SQUARE Some points to remember: ( SILLY THING ... BUT HELP ALOT AT SOME TIME)

======================== If the last digit of any number is 0 the square of the number will end with 2 zeroes. If the last digit of any number is 1 then the last digit of the square also be 1. If the last digit of any number is 2 then the last digit of the square will be 4. If the last digit of any number is 3 then the last digit of the square will be 9. If the last digit of any number is 4 then the last digit of the square will be 6. If the last digit of any number is 5 then the last digit of the square will be 5 and last two 25. If the last digit of any number is 6 then the last digit of the square will also be 6. If the last digit of any number is 7 then the last digit of the square will be 9 . If the last digit of any number is 8 then the last digit of the square will be 4. If the last digit of any number is 9 then the last digit of the square will be 1. CATCH THE CUBES =================== If the last digit of any number is 0 the cube of the number will end with 3 zeroes. If the last digit of any number is 1 then the last digit of the cube also be 1. If the last digit of any number is 2 then the last digit of the cube will be 8.

If the last digit of any number is 3 then the last digit of the cube will be 7. If the last digit of any number is 4 then the last digit of the cube will be 4. If the last digit of any number is 5 then the last digit of the cube will be 5. If the last digit of any number is 6 then the last digit of the cube will be 6. If the last digit of any number is 7 then the last digit of the cube will be 3. If the last digit of any number is 8 then the last digit of the cube will be 2. .If the last digit of any number is 9 then the last digit of the cube will be 9. Cube in exam...in any bank exam if you ask to find out cube then in my view you don't need to calculate but to go through options.first you check the last digit and then you visit the nearing zero. CATCH THE CUBES - some examples ============================ Q: 93³= ? 1) 753571 , 2) 250047 , 3) 912673 4) 804357 5)None of these way to solve: First step : Last digit of the number is 3 then the last digit of cube will definitely be 7,it means option number 1 and 3 can not be the answer.

Second step: Now we know that the cube of 9 is 729 and 90 is 729000, it means the cube of 93 must be more than 729000 but less than 1000000( WHICH IS CUBE OF 100) , it also means that option number 2 is incorrect. Now we know that 804357 is answer. None of these will not be an answer (see next example) ================== Q: 76³= ? 1) 97336, 2) 405224, 3) 531441 4) 884736, 5) None of these way to solve: First step : Last digit of the number is 6 then the last digit of the cube will definitely be 6,it means option number 2 and 3 can not be the answer. Second step: Now we know that the cube of 7 is 343 and 70 is 343000, it means the cube of 76 must be more than 343000 but less than 512000(WHICH IS CUBE OF 80 ) , it also means that option number 1 and 4 are incorrect because they are nowhere in between 343000 and 512000. Now is there any problem to say that the answer is none of these . More Shortcuts for Square of (xxxxx.....n)²

=============================== To learn this method you should go through these examples::: example number 1 : (222)² ==================== step 1 : take square of 2 which is 4 step 2 : 4,8,12,8,4 (answer will be right to left and yes please consider carryover also) Note: here we have first multiplied 4 by 1 then 2 and then 3 and then we multiplied 4 by 2 and then 3.(we have started and multiplied the number as many time as the digits are and then we return from there) Answer: 49284 (rightmost to the left) example number 2 : (333)² =========================== step 1 : take square of 3 which is 9 step 2 : 9,18,27,18,9 (answer will be right to left and yes please consider carryover also) Note: here we have first multiplied 9 by 1 then 2 and then 3 and then we multiplied 9 by 2 and then 3.(we have started and multiplied the number as many time as the digits are and then we return from there) Answer: 110889 (rightmost to the left) example number 3 : (2222)²

======================== step 1 : take square of 2 which is 4 step 2 : 4,8,12,16,12,8,4 (answer will be right to left and yes please consider carryover also) Note: here we have first multiplied 4 by 1 then 2 then 3 and then 4 we multiplied 4 by 3,then 2 and then 1.(we have started and multiplied the number as many time as the digits are and then we return from there) Answer: 4937284(rightmost to the left) COMPOUND INTEREST(increasing value method ) COMPOUND INTEREST ========================== We do have a formula for compound interest [ CI = p (1+r/100)^t ] but i think you should adopt the increasing value method which i am elaborating in the next paragraph.... Suppose you have 10000/- as a principal amount and the rate of interest is 10%. And now you are to calculate CI for three years: Then you should do this question step by step First step : 10000 * 10 / 100 = 1000 Second Step : Add these 1000 in principal which is 10000. answer will be 11000 [ after first year this is the total amount we can get on

10000 @ 10%] Third step : 11000 * 10/100 = 1100 Fourth Step : Add these 1100 in 11000. answer will be 12100 [ after second year this is the total amount we can get on 12100 @ 10%] Fifth Step : 12100 * 10/100 = 1210 Sixth Step: Add these 1210 in 12100 . answer will be 13310 [ after third year this is the total amount we can get on 10000 @ 10%] For Answer : 13310 - 10000 = 3310 (this is your answer) ********************************************************** [Note: this method is easy if you find a flow though it looks lengthy primarily ] number (xxx) % 37 = ( x+x+x) = 3x {remainder 0} If a three digit number has all the digits with same face value, it will divided by number 37. the Quotient value is addition of those three digits.. Example ================= 111 % 37 = 3 (remainder zero 0) 444 % 37 = 12

888 % 37 = 24 999 % 37 = 27 MUL:TEN's digt are same & addn of ONE's digt is 10 MUL:TEN's digit are same, and addn of ONE's digit [XY ] multiply by [X(10-Y)] eg 37 mutiply by 33 => 37 x 33 ************************************************* TEN's digit are same, and addition of ONE's digit is 10 Method: 1) Multiply the digits in ONE’s place 2) Mutiply the common digit by the (same digit +1) 3) Arrange in LEFT to RIGHT Eg 37 x 33 = 1221 Step 1 ********** 7 x 3 = 21 Step 2 ********* 3 x (3+1) = 3 x 4 = 12

Step 3 ********** 1221 ( Left to Right ) ..................................................................................... Eg 2: ========= 86 x 84 = 7224 Step 1: 6 x 4 = 24 Step 2: 8 x (8+1) = 8 x 9 = 72 Step 3: Arrange Left to Right Ans = 7224 MULTIPLICATION 37 * 33 take the bas 50

50-37=13 50-33=17_____________________17*13=221 . . 37-17 or 33-13 =20 20/2 (as we take 50 base) 10 ..221 --------- 1221 MULTIPLICATION 97*93 take 100 as base 100-97=3 100-93=7 7*3=21 rhs . . 97-7 or 93-3= 90 ur lhs 9021 Finding - Day of the Week

Day of the Week: =============== January has 31 days. It means that every date in February will be 3 days later than the same date in January(28 is 4 weeks exactly). The below table is calculated in such a way. Remember this table which will help you to calculate. January 0 February 3 March 3 April 6 May 1 June 4 July 6 August 2 September 5 October 0 November 3 December 5 Step1: Ask for the Date. Ex: 23rd June 1986 Step2: Number of the month on the list, June is 4. Step3: Take the date of the month, that is 23

Step4: Take the last 2 digits of the year, that is 86. Step5: Find out the number of leap years. Divide the last 2 digits of the year by 4, 86 divide by 4 is 21. Step6: Now add all the 4 numbers: 4 + 23 + 86 + 21 = 134. Step7: Divide 134 by 7 = 19 remainder 1. The reminder tells you the day. Sunday 0 Monday 1 Tuesday 2 Wednesday 3 Thursday 4 Friday 5 Saturday 6 *************************** Answer: Monday *************************** Finding Remainder of a given Statement Question : ======== Find remainder if following expression is divided by 7

19 X 20 X 22 X 23 X 24 Conventional method is multiplying all numbers then divided by 7 . It takes lot of time , you can do this question mentally .How? First we divide individually all numbers by 7 and take all remainders as a first step . ========= Now multiply all remainders and again divide by 7 and take required remainder . That is our answer 19 X 20 X 22 X 23 X 24 5 X 6 X 1 X 2 X 3 = 180 ( Multiplications of remainders) 180/7 = 25 + remainder 5 so, Answer =5 We make it more easy ===================== Take two remainders multiplication and divide it by 7 ,again take others three remainders multiplication and divide it by 7 (5 X 6) X ( 1 X 2 X 3) = 2 X 6 ( Multiplications of remainders) = 12/ 7 = 1+ remainder 5

hence the answer , Answer (Remainder) = 5

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