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Old 7th August 2014, 09:47 AM
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Join Date: Apr 2013
Default Re: Tricks to solve aptitude questions easily and quickly

As you want to get the details of tricks to solve aptitude questions easily and quicklyso here it is for you:

Addition of numbers close to multiples of ten (e.g. 19, 29, 38, 59 etc.)
This technique is useful for Mental calculations

116 + 39 (Here we can write this 39 as 40-1)
= 116 + (40 - 1)
= 116 + 40 - 1
= 156 - 1 (Instead of adding 39 to 116, we just add 40 to 116 (because we can do this without using pen and paper) and later we subtract one from it)
= 155
Try this.. This is very useful tip while doing calculations.

Now lets try another example.
116 + 97
= 116 + (100 - 3)
= 116 + 100 - 3 (Here, instead of adding 97 to 116, we are just adding a 100 to 116 and then subtracting 3 from it

Addition of decimals
12.5 + 6.25
= (12 + 0.5) + (6 + 0.25)
= 12 + 6 + 0.5 + 0.25 (Here we just added the rounded numbers first and later we added the decimal numbers
= 18 + 0.5 + 0.25
= 18.75

Subtractions Shortcuts :
250 - 96
= 250 - (100 - 4) (here, instead of subtracting 96 from 250, we are just subtracting 100 from 250 and then adding 4)
= 250 - 100 + 4 (Why adding? because the actual amount we have to subtract from 250 is 96. but we are subtracting 100. That means, we are subtracting 4 numbers more than we actually deserve. so our 250 will feel bad. so we should add that 4 to it
= 150 + 4
= 154

250 - 196
= 250 - (200 - 4)

Lets see,

216 - 61 (Here i found it difficult to subtract 61 from 216)
= 216 - (100 - 39) (So i just decided to subtract 100 to it and later will subtract the extra 39)
= 216 - 100 + 39 (Hey, see here. How about writing this 39 as 40 -1 ?)
= 116 + (40 - 1) (dont be confused. just practice this method and you will come to know how easy and efficient method it is
= 156 - 1
= 155

Subtraction of decimals
47 - 9.9 (How about dividing this 9.9 as 9 + 0.9 ??)
= 47 - (9 + 0.9) we can write this as...
= 47 - 9 - 0.9
= 38 - 0.9
= 37.1

18.3 - 0.8
= 18 + 0.3 - 0.8
= (18 - 0.8) + 0.3
= 17.2 + 0.3
= 17.5

Shortcuts in Multiplications:

Multiplication using multiples
Assume that we should find out the result of 12X15.
12 x 15 (Here we can write this 15 as 5x3)
= 12 x 5 x 3 (now 12x5 becomes 60)
= 60 x 3 (For this you just calculate 3x6, that is 18 and add one Zero to it. that is 180)
= 180 (see, how simple it is?)

Multiplication by distribution
Assume that we should find out the result of 12x17
12 x 17 (Here we can divide this 17 as 10+7. here, multiplying 12 with 17 is same as multiplying 12 with 10 and 7 separately and then adding the results)
so, we can write it as
= (12 x 10) + (12 x 7)

Multiplication by "giving and taking"
12 x 47 (Here its little difficult for us to calculate the multiplication of 12 and 47 mentally. so just check for the ROUNDED number nearer to 47. Yes it is 50. so.....

= 12 x (50 - 3)
= (12 x 50) - (12 x 3) (we have discussed this rule earlier)
= 600 - 36
= 564

Multiplication by 5
* If we have to multiply a number with 5, just divide the number with 2 and then multiply the result with 10. Confused? Its very simple step actually....
428 x 5 (Now just divide the number with 2)
= 428 x 1/2 = 214 (Now multiply it with 10. I mean just add a zero at the end :P)
= 214 x 10
= 2140 (This is our result)

Whats the logic behind this step?
Very simple.
* Lets say the number is X.
* Now we are dividing the number with 2. so here X becomes X/2.
* And then we are multiplying it with 10. So it will become 10x / 2
* Now cancel it with 2. so it becomes 10x / 2 = 5X = 5 multiplied by X. Thats it

Multiplication by 10 ------------ just move the decimal point one place to the right
16 x 10
= 160
5.9 = 159
169.93 = 169.3 (Need an explnation for this too??? :P)

Multiplication by 50 ------ divide with 2 and then multiply by 100
Well, this is also same process as we did for 5. Here we should add an extra zero. Thats it
18 x 50
= (18/2) = 9
= 9 x 100
= 900

Multiplication by 100 -------- move the decimal point two places to the right
45 x 100
= 4500

Multiplication by 500-------- divide with two and multiply with 1000
21 x 500
= 21/2 x 1000
= 10.5 x 1000
= 10500

Multiplication by 25 ---------- use the analogy Rs 1 = 4 x 25 Paise
25 x 14 (just divide the 14 as 10+4)
= (25 x 10) + (25 x 4)
= 250 + 100 ---> Rs2.50 + Rs1
= 350

Hey one more thing. Here you can use another technique too. Which we have used for multiplication with 5.

Multiplication by 25 ----------- Divide by 4 and multiply by 100
36 x 25
= (36/4) x 100
= 9 x 100
= 900

Multiplication by 11 (if sum of digits is less than 10)
72 x 11
= 7+2 =9, it is Less than 10. so,
= place this term 9 between 7 &2

Shortcuts in Division:
There are so many types of divisions are there. Lets have a look.

Division by parts --> Imagine you have Rs.874 . You have to give that to your two children.
874/2 [We can write this 874 as 800+74 (for our convenience)
= 800/2 + 74/2

Division using the factors of the divisor: "this is also called as Double Division"
70/14
= (70/7)/2 (Because 7 and 2 are the factors of 14)
= 10/2
= 5

Division using Fractions:
132/2
= (100/2 + 32/2) ( here we've broken the given fraction into two separate fractions)
= (50 + 16)
= 66

Division by 5 :
Note: if you have to divide any number with 5, then divide it by 100 and then just multiply by 20
1400/5
= (1400/100) x 20
= 14 x 20
= 280

Division by 10 (Its very simple, just move the decimal point one place to the left)
0.5/10
= 0.05

Division by 50 ( Just divide with 100 then multiply by 2)
2100/50
= (2100/100) x 2
= 21 x 2
= 42

700/50
= (700/100) x 2
= 7 x 2
= 14

Division by 100 (just move the decimal point two places to the left)
25/100
= 0.25

Division by 500 (just divide with 100 and then multiply with 0.2)
17/500
= (17/100) x 0.2
= 0.17 x 0.2
= 0.034

Division by 25 (just divide by 100 and then multiply by 4 )
500/25
= (500/100) x 4
= 5 x 4
= 20

750/25
= (750/100) x 4
= 7.5 x 2 x 2
= 30
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