# Math Tricks for Competitive exams

### 1. Multiplication of any two numbers, lies between 11 and 19

13*19 = (13+9)*10 + (3*9) = 220 + 27 = 247
Means add first number and last digit of the second number take zero in the third place of this number then add product of last digit of the two numbers in it.

Example : 18*14 = (18+4)*10 + (8*4) = 220 + 32 = 252

### 2. EXCLUSIVE DIVISION RULE FOR 8

If a number is divisible by eight the last three digits are divisible by   8

Example :

4857248
last three digits are 248
248/8 = 31
Then 4857248 is divisible by 8

### 3.  AWESOME DIVISION RULE FOR 11

If a number is divisible by eleven the difference between the sum of the digits in the even places and the  sum of the digits in the odd places is 11 or 0.
23485 is shown to be divisible by 11 because

2 + 4 + 5 = 11
3 + 8 = 11
11 – 11 = 0
and

and 60852 is shown to be divisible by 11 because
6 + 8 + 2 = 16
0 + 5 = 5
16 – 5 = 11

### 4.  Amazing number 4

With number 4 the secret steps in the multiplication tables become a little more intricate.
4*1 = 4 ———————————– 4
4*2 = 8 —————————- 8
4*3 = 12 —————— 1+2 = ——— 3
4*4 = 16 —————— 1+6 = — 7
4*5 = 20 —————— 2+0 = ——— 2
4*6 = 24 —————— 2+4 = — 6
4*7 = 28 —-2+8=10—- 1+0 = ———– 1
4*8 = 32 —————— 3+2 = — 5
4*9 = 36 —————— 3+6 = ——— 9
4*10 = 40 —————– 4+0 = — 4
4*11 = 44 —————– 4+4 = ——— 8
4*12 = 48 —4+8=12 ——- 1+2=– 3
4*13 = 52 —————– 5+2 = ——— 7
4*14 = 56 —5+6=11——– 1+1=– 2
4*15 = 60 —————– 6+0 = ——— 6
4*16 = 64 —6+4=10——– 1+0=– 1

At first the sums of the digits look like a jumble of figure, but choose at random any sequence of numbers and multiply them by 4 and you will see the pattern emerge of two interlinked columns of digits in descending order.

2160*4 = 8640 — 8+6+4+0 = 18 ———– 1+8 = —- 9
2161*4 = 8644 — 8+6+4+4 = 22 ———– 2+2 = 4
2162*4 = 8648 — 8+6+4+8 = 26 ———– 2+6 = —- 8
2163*5 = 8652 — 8+6+5+2 = 21 ———– 2+1 = 3
2164*4 = 8656 — 8+6+5+6 = 25 ———– 2+5 = —- 7
2165*4 = 8660 — 8+6+6+0 = 20 ———– 2+0 = 2
2166*4 = 8664 — 8+6+6+4 = 24 ———– 2+4 = —- 6
2167*4 = 8668 — 8+6+6+8 = 28 — 2+8=10 – 1+0 = 1
2168*4 = 8672 — 8+6+7+2 = 23 ———– 2+3 = —- 5

### 5. The 11 Rule

You likely all know the 10 rule (to multiply by 10, just add a 0 behind the number) but do you know the 11 rule? It is as easy! You should be able to do this one in you head for any two digit number. Practice it on paper first!

To multiply any two digit number by 11:

• For this example we will use 54.
• Separate the two digits in you mind (5__4).
• Notice the hole between them!
• Add the 5 and the 4 together (5+4=9)
• Put the resulting 9 in the hole 594. That’s it! 11 x 54=594

The only thing tricky to remember is that if the result of the addition is greater than 9, you only put the “ones” digit in the hole and carry the “tens” digit from the addition. For example 11 x 57 … 5__7 … 5+7=12 … put the 2 in the hole and add the 1 from the 12 to the 5 in to get 6 for a result of 627 … 11 x 57 = 627

### 6.  Percentage computation

Calculate 65% of 460:
50% of 460 = 230
10% of 460 = 46
5% of 460 = 23 (half 46)
——————————
65% of 460 = 299 (sum)

Example :

Calculate 67.5% of 460:
50% of 460 = 230
10% of 460 = 46
5% of 460 = 23 (half 46)
2.5% of 460 =11.5 (half 23)
——————————
67.5% of 460 = 310.5 (sum )

### 7.  To calculate reminder on dividing the number by 7 11 and 13

Let me explain this rule by taking examples
consider number 34568276, we have to calculate the reminder on diving this number by 7 11 and 13 respectively.
make triplets as written below starting from units place
34………568……….276
now alternate sum = 34+276 = 310 and 568
and difference of these sums = 568-310 = 258
divide it by 7 we get reminder as 6
divide it by 11 we get reminder as 5
divide it by 13 we get reminder as 11
Other Example :

consider the number 4523895099854
triplet pairs are 4…523…895…099…854
alternate sums are 4+895+854=1753 and 523+099=622
difference = 1131
revise the same tripling process
1……131
so difference = 131-1 = 130
divide it by 7 we get reminder as 4
divide it by 11 we get reminder as 9
divide it by 13 we get reminder as 0

### 8. Square a 2 Digit Number Ending in 5

For this example we will use 25

·         Take the “tens” part of the number (the 2 and add 1)=3

·         Multiply the original “tens” part of the number by the new number (2×3)

·         Take the result (2×3=6) and put 25 behind it. Result the answer 625.

Try a few more 75 squared … = 7×8=56 … put 25 behind it is 5625.
55 squared = 5×6=30 … put 25 behind it … is 3025. Another easy one! Practice it on paper first!

### 9.   Square 2 Digit Number: UP-DOWN Method

Square a 2 Digit Number, for this example 37:

·            Look for the nearest 10 boundary

·            In this case up 3 from 37 to 40.

·            Since you went UP 3 to 40 go DOWN 3 from 37 to 34.

·            Now mentally multiply 34×40

·            The way I do it is 34×10=340;

·            Double it mentally to 680

·            Double it again mentally to 1360

·            This 1360 is the FIRST interim answer.

·            37 is “3” away from the 10 boundary 40.

·            Square this “3” distance from 10 boundary.

·            3×3=9 which is the SECOND interim answer.