Short Cut Methods 6c202h

Take 15 x 13 for an example.  Always place the larger number of the two on top in your mind.  Then draw the shape of Africa mentally so it covers the 15 and the 3 from the 13 below. Those covered numbers are all you need.  First add 15 + 3 = 18  Add a zero behind it (or multiply by 10) to get 180.  Multiply the covered lower 3 x the single digit above it the "5" (3x5= 15)  Add 180 + 15 = 195. 

15 X 13 = 195 MULTIPLICATION SHORT CUT METHODS UP 100 X 100 To multiply two numbers (of two or more digits), split each number into two parts. If the first number is a1 + b1 and the second number is a2 + b2, then the product of the two numbers is: (a1 x a2) + (a1 x b2 + b1 x a2) + (b1 x b2)

The solution comprises three parts (as shown by the boxes and arrows above): the head, the middle, and the tail.

1. The digits on the right are multiplied vertically to get the tail part: b1 x b2 (excess carried over) 2. All digits are multipled crosswise and added together to get the middle part: a1 x b2 + b1 x a2 (excess carried over) 3. The digits on the left are multiplied vertically to get the head part: a1 x a2 Here is a simple example to illustrate this technique.  23 x 41 = 943

The steps are: 1. 3 x 1 = 3 2. 2 x 1 + 3 x 4 = 14, put down 4 and carry over 1 3. 2 x 4 = 8, plus the 1 carried over, is 9 The speed gain using this technique (over the conventional method of multi-line long multiplication) becomes more apparent when handling larger numbers. Here is another example involving excess carryover at each stage.  108 x 64 = 6912

Long Multiplication technique example The steps are: 1. 8 x 4 = 32, put down 2 and carry over 3 2. 10 x 4 + 8 x 6 = 88, plus the 3 carried over, is 91; put down 1 and carry over 9 3. 10 x 6 = 60, plus the 9 carried over, is 69

1 A B C D E F G H I J E 5

11 21 K U L V MW N X O Y P Z Q R S T J O T Y 10 15 20 25

OPPOSITE LETTERS ( SUM IS 27 ) UF BY LOVE SHIRT GAZ PK MN JQ CX DW

Although such question are very simple, yet by doing them in a systematic manner you can save some extra seconds. We suggest that you perform recalculation .In this method, 1) Subtract the numbers if both the direction are same 2) Add the numbers if the directions are opposite

For

example:

1)

ABCDEFGHIJKLMNOPQRSTUVWXYZ

Which letter would be the seventh to the right of the eleventh letter from? The right end 1)K 2) W 3) J 4) U 5) none of these Since both directions are same (right, right) we request we subtract 7 From 11.Hence the answer would be the 4th from the right that is, W Some more examples are given below. 3) Which letter is seventh to the right of the thirteen letters from the left? a) S b) T c) U d) V e) none of these sol: Since we want the seventh letter to the right of the thirteen letter from the left -directions are opposite -hence

we add 7+13=20 .Hence the answer is 20th from the left . Now 20th from the left means 26-20+1=7th from right (note this step). Hence answer is T. You must have understood the method of pre-calculation by now .The trick is to calculate the actual position of the required letter before going to search for it .Now there may be some variations to the above type of problem. Some variations are presented below. See how we precalculate the position of the required letter. Ex: 3If the above alphabet is written in reverse order, which will be the eighth letter to the right of O? a) F b) G c) V d) W e) none of these Sol: The letter which is eighth to the right of O when the alphabet is , reversed must be presently eighth to the left of O. Hence it is G . Ex:4 If the first half of the alphabet is written in reverse order which letter would be the nineteenth letter from the right ? a)F b) G c) E d) H e) none of these sol: Since the second half is not reversed the first 13 letters would be the same when counting is done from right .But next letters after 13th will be actually from the left end( the 14th letter would be A) Hence the Some more rules on English alphabet series a)Question based on dropping or deleting of letters in the english alphabet at regular intervals Ex- every third letter from left to right of the English alphabet is dropped. Find the 7th letter from the left of the new series obtained. sol: In the English alphabet ,every third letter is dropped from the left (given) ,Hence the new series will be like , AB C DE F GH I JK L MN O PQ R ST U VW X YZ That is ; A B D E G H J K M N P Q S T V W Y Z Clearly, 7th letter from the left in the new series is J Quicker method:

Above discussed method is lengthy and time consuming. Therefore you need a quicker method to solve such kind of problems. Question says that every 3rd letter is dropped in the original series that is we are left with two letters after every dropping of letters. Here 2 is the key figure .We have to seek a digit which is just les than 7 but divisible by 2. In this case the required digit is 6. Now we do the following operations to get the required answer. 7th letter from the left in the new series = 7+6/2=10th letter from the left in the original series=J Similarly, you can find any letter at a particular position in the new series. Question based on reversed English alphabet series. The English alphabet series can be reversed in many ways. Some of them are discussed below 1) The whole English Alphabet is reversed 2) First half of the series is reversed 3) Second half of the series is reversed 4) Many sections of the English alphabet series are reversed To solve the questions of the Reversed English alphabet series, you should the basic rule, that is: Mth element counting from left to right of a series of N characters is equal to the (N +1-M)th element counting from right to left of that series. let us take a example : Let us take the english alphabet series as given below: ABCDEFGHIJKLMNOPQRSTUVWXYZ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Suppose we have to find the position of L in the above series counting from right to left. We know that the English alphabet has 26 characters. Hence N =26

Position of L in English alphabet starting from A (left to right) is 12. Hence M=12 Hence Position of L in the above series is from right to left is (26+1-12)=15 Let us take a typical example: Suppose first five letters, then next six letters, then next 7 letters and then after last 8 letters of the following English alphabet series are reversed. ABCDEFGHIJKLMNOPQRSTUVWXYZ Then you are asked to find I) 4th II) 20th elements from the left of the new series .How will you proceed to get the answer? Let us see. According the question, first 5, then next 6,7,8 letters of the English alphabet are reversed. Hence we obtain a new series as given below EDCBA / KJIHGF / RQPONML / ZYXWVUTS 1 2 3 4 We have to find i) 4th letter from the new series, 4th letter falls into group 1 Hence fourth letter in group 1= (5+1-4)=2nd letter from the left in the Original series.(refer to the basic rule ) II) 20th letter from the left of the new series falls into the group 4.There are 8 characters in-group 4.We have to find second letter of the group 4 (Since 5 letters of group 1, 6 letters of group 2 and 7 letters of group 3 Does not effect the position of letter that falls into the group 4 that is 20=5+6+7+2) 2nd letter in the group 4 =18+(8+1-2)=25th letter from the Left in the original series=Ys : - If we want to go back 3 places back from c then answer will be z. similarly if we want to go back 5 places back from the alphabet e then answer will be z. C-3 = Z E-5 = Z C- 5 = X (26+3-5=24 which is the position of x)