1. Multiplying by 9, or 99, or 999

Multiplying by 9 is really multiplying by 10-1.

So, 9×9 is just 9x(10-1) which is 9×10-9 which is 90-9 or 81.

Let’s try a harder example: 46×9 = 46×10-46 = 460-46 = 414.

One more example: 68×9 = 680-68 = 612.

To multiply by 99, you multiply by 100-1.

So, 46×99 = 46x(100-1) = 4600-46 = 4554.

Multiplying by 999 is similar to multiplying by 9 and by 99.

38×999 = 38x(1000-1) = 38000-38 = 37962.

2. Multiplying by 11

To multiply a number by 11 you add pairs of numbers next to each other, except for the numbers on the edges.

Let me illustrate:

To multiply 436 by 11 go from right to left.

First write down the 6 then add 6 to its neighbor on the left, 3, to get 9.

Write down 9 to the left of 6.

Then add 4 to 3 to get 7. Write down 7.

Then, write down the leftmost digit, 4.

So, 436×11 = is 4796.

Let’s do another example: 3254×11.

The answer comes from these sums and edge numbers: (3)(3+2)(2+5)(5+4)(4) = 35794.

One more example, this one involving carrying: 4657×11.

Write down the sums and edge numbers: (4)(4+6)(6+5)(5+7)(7).

Going from right to left we write down 7.

Then we notice that 5+7=12.

So we write down 2 and carry the 1.

6+5 = 11, plus the 1 we carried = 12.

So, we write down the 2 and carry the 1.

4+6 = 10, plus the 1 we carried = 11.

So, we write down the 1 and carry the 1.

To the leftmost digit, 4, we add the 1 we carried.

So, 4657×11 = 51227 .

3. Multiplying by 5, 25, or 125

Multiplying by 5 is just multiplying by 10 and then dividing by 2. Note: To multiply by 10 just add a 0 to the end of the number.

12×5 = (12×10)/2 = 120/2 = 60.

Another example: 64×5 = 640/2 = 320.

And, 4286×5 = 42860/2 = 21430.

To multiply by 25 you multiply by 100 (just add two 0’s to the end of the number) then divide by 4, since 100 = 25×4. Note: to divide by 4 your can just divide by 2 twice, since 2×2 = 4.

64×25 = 6400/4 = 3200/2 = 1600.

58×25 = 5800/4 = 2900/2 = 1450.

To multiply by 125, you multipy by 1000 then divide by 8 since 8×125 = 1000. Notice that 8 = 2×2x2. So, to divide by 1000 add three 0’s to the number and divide by 2 three times.

32×125 = 32000/8 = 16000/4 = 8000/2 = 4000.

48×125 = 48000/8 = 24000/4 = 12000/2 = 6000.

4. Multiplying together two numbers that differ by a small even number

This trick only works if you’ve memorized or can quickly calculate the squares of numbers. If you’re able to memorize some squares and use the tricks described later for some kinds of numbers you’ll be able to quickly multiply together many pairs of numbers that differ by 2, or 4, or 6.

Let’s say you want to calculate 12×14.

When two numbers differ by two their product is always the square of the number in between them minus 1.

12×14 = (13×13)-1 = 168.

16×18 = (17×17)-1 = 288.

99×101 = (100×100)-1 = 10000-1 = 9999

If two numbers differ by 4 then their product is the square of the number in the middle (the average of the two numbers) minus 4.

11×15 = (13×13)-4 = 169-4 = 165.

13×17 = (15×15)-4 = 225-4 = 221.

If the two numbers differ by 6 then their product is the square of their average minus 9.

12×18 = (15×15)-9 = 216.

17×23 = (20×20)-9 = 391.

5. Squaring 2-digit numbers that end in 5

If a number ends in 5 then its square always ends in 25. To get the rest of the product take the left digit and multiply it by one more than itself.

35×35 ends in 25. We get the rest of the product by multiplying 3 by one more than 3. So, 3×4 = 12 and that’s the rest of the product. Thus, 35×35 = 1225.

To calculate 65×65, notice that 6×7 = 42 and write down 4225 as the answer.

85×85: Calculate 8×9 = 72 and write down 7225.

6. Multiplying together 2-digit numbers where the first digits are the same and the last digits sum to 10

Let’s say you want to multiply 42 by 48. You notice that the first digit is 4 in both cases. You also notice that the other digits, 2 and 8, sum to 10. You can then use this trick:

multiply the first digit by one more than itself to get the first part of the answer and multiply the last digits together to get the second (right) part of the answer.

An illustration is in order:

To calculate 42×48: Multiply 4 by 4+1. So, 4×5 = 20. Write down 20.

Multiply together the last digits: 2×8 = 16. Write down 16.

The product of 42 and 48 is thus 2016.

Notice that for this particular example you could also have noticed that 42 and 48 differ by 6 and have applied technique number 4.

Another example: 64×66. 6×7 = 42. 4×6 = 24. The product is 4224.

A final example: 86×84. 8×9 = 72. 6×4 = 24. The product is 7224

7. Squaring other 2-digit numbers

Let’s say you want to square 58. Square each digit and write a partial answer. 5×5 = 25. 8×8 = 64. Write down 2564 to start. Then, multiply the two digits of the number you’re squaring together, 5×8=40.

Double this product: 40×2=80, then add a 0 to it, getting 800.

Add 800 to 2564 to get 3364.

This is pretty complicated so let’s do more examples.

32×32. The first part of the answer comes from squaring 3 and 2.

3×3=9. 2×2 = 4. Write down 0904. Notice the extra zeros. It’s important that every square in the partial product have two digits.

Multiply the digits, 2 and 3, together and double the whole thing. 2×3x2 = 12.

Add a zero to get 120. Add 120 to the partial product, 0904, and we get 1024.

56×56. The partial product comes from 5×5 and 6×6. Write down 2536.

5×6x2 = 60. Add a zero to get 600.

56×56 = 2536+600 = 3136.

One more example: 67×67. Write down 3649 as the partial product.

6×7x2 = 42×2 = 84. Add a zero to get 840.

67×67=3649+840 = 4489.

8. Multiplying by doubling and halving

There are cases when you’re multiplying two numbers together and one of the numbers is even. In this case you can divide that number by two and multiply the other number by 2. You can do this over and over until you get to multiplication this is easy for you to do.

Let’s say you want to multiply 14 by 16. You can do this:

14×16 = 28×8 = 56×4 = 112×2 = 224.

Another example: 12×15 = 6×30 = 6×3 with a 0 at the end so it’s 180.

48×17 = 24×34 = 12×68 = 6×136 = 3×272 = 816. (Being able to calculate that 3×27 = 81 in your head is very helpful for this problem.)

9. Multiplying by a power of 2

To multiply a number by 2, 4, 8, 16, 32, or some other power of 2 just keep doubling the product as many times as necessary. If you want to multiply by 16 then double the number 4 times since 16 = 2×2x2×2.

15×16: 15×2 = 30. 30×2 = 60. 60×2 = 120. 120×2 = 240.23×8: 23×2 = 46. 46×2 = 92. 92×2 = 184.54×8: 54×2 = 108. 108×2 = 216. 216×2 = 432.

Quick multiplication by 12:

The basic recipe for multiplying by 12 is to double the digit and add its neighbor.

Let’s multiply 34 by 12.

We start with the right-most digit, 4. We double it and would add the neighbor to the right if there were one, so we just double 4 and get 8. Write down the 8 as the right-most digit of the answer.

We move over to the next digit, 3. Double the 3 to get 6 then add the neighbor, 4, to get 10. Write down the 0 from 10 and carry the 1.

We’re done with the digits but we have to move to the left one final time. We double the non-existent digit, which we’ll call 0, add the neighbor, 3, and add the carry, 1. So, we write down 4 as the final digit.

We’re done. We wrote down, from right to left: 8-0-4. Our answer is 408.

Let’s try another example: 346×12

Start with the right-most digit, 6. Double the 6 and add the neighbor (none in this case). We get 12. Write down 2 from 12, and carry the 1.

Move left to the next digit, 4. Double the 4 to get 8, add the neighbor, 6, to get 14, and add the carry, to get 15. Write down the 5, and carry the 1.

Move left to the next digit, 3. Double the 3 to get 6. Add the neighbor, 4, and we get 10. Add the carry, to get 11. Write down the 1, and carry the 1.

Move left to the non-existent digit. Double it to get 0, and add the neighbor, 3, which gives us 3. Finally, add the carry to get 4. Write down 4.

Our answer is 4152.

One final example. Let’s calculate 123456×12.

First digit is 6. Double 6 plus no neighbor = 12. Write down 2 and carry 1.

Next digit is 5. Double 5 plus neighbor 6 plus carry 1 = 17. Write down 7 and carry 1.

Next digit is 4. Double 4 plus neighbor 5 plus carry 1 = 14. Write down 4 and carry 1.

Next digit is 3. Double 3 plus neighbor 4 plus carry 1 = 11. Write down 1 and carry 1.

Next digit is 2. Double 2 plus neighbor 3 plus carry 1 = 8. Write down 8 and no carry.

Next digit is 1. Double 1 plus neighbor 2 plus no carry = 4. Write down 4 and no carry.

Next digit doesn’t exist. We double 0 plus neighbor 1 plus no carry = 1. Write down 1.

Our answer is 1481472.

Multiply Up to 20X20 In Your Head

In just FIVE minutes you should learn to quickly multiply up to 20x20 in your head. With this trick, you will be able to multiply any two numbers from 11 to 19 in your head quickly, without the use of a calculator.

I will assume that you know your multiplication table reasonably well up to 10x10.

Try this:

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 (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.

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 = 627Practice it on paper first!

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 34x40 The way I do it is 34x10=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. 3x3=9 which is the SECOND interim answer. Add the two interim answers to get the final answer. Answer: 1360 + 9 = 1369

The 11 Rule Expanded

You can directly write down the answer to any number multiplied by 11. Take for example the number 51236 X 11. First, write down the number with a zero in front of it.

051236

The zero is necessary so that the rules are simpler.

Draw a line under the number. Bear with me on this one. It is simple if you work through it slowly. To do

this, all you have to do this is "Add the neighbor". Look at the 6 in the "units" position of the number. Since there is no number to the right of it, you can't add to its "neighbor" so just write down 6 below the 6 in the units col.

For the "tens" place, add the 3 to the its "neighbor" (the 6). Write the answer: 9 below the 3.

For the "hundreds" place, add the 2 to the its "neighbor" (the 3). Write the answer: 5 below the 2.

For the "thousands" place, add the 1 to the its "neighbor" (the 2). Write the answer: 3 below the 1.

For the "ten-thousands" place, add the 5 to the its "neighbor" (the 1). Write the answer: 6 below the 5.

For the "hundred-thousands" place, add the 0 to the its "neighbor" (the 5). Write the answer: 5 below the 0.That's it ... 11 X 051236 = 563596

85*85 = (80+5)*(90-5) = 80*90 + (90-80)*5 - 25 = 80*90 + 25.

65*65 = 70*60+25, etc...

I can’t remember where or how I learned this but I can do cube roots in my head that

are derived from two digit numbers i.e. 185193 is 57. It is an easy math trick where

the last digit of the cube of one digit numbers corresponds to the last digit in the

problem and the first three digits are in the range of numbers not to exceed the next

single digit cube. See easy. Here is a cheat sheet

2=8

3=27

4=64

5=125

6=216

7=343

8=512

9=729

Once you learn this it is easy; in our example the cubed number 185193 ends in 3

which corresponds to the last digit of the cube of 7 being 3; therefore the second

digit is 7. The first three digits 185 are greater than the cube of 5 at 125 but less than

the cube of 6 at 216 therefore the first digit is 5. By learning this simple table you can

do cube roots of two digit numbers in your head. Other than mental masturbation

and to confirm to your friends that you are an idiot savant, or as a chick repellant I

am not sure what good it does.

What ever you do don't try this in a street fight. "Back off man I can do cube roots,"

unless you are wearing a bow tie, it scares the hell out of them.posted by MapGuy at 7:43 PM on May 29, 2007

Two significant digits is plenty. If you need more, then you probably have a pen

handy.

85*85 => 80*90 = 7200.

Dividing by 3

Add up the digits: if the sum is divisible by three, then the number is as well. Examples:

1. 111111: the digits add to 6 so the whole number is divisible by three.

2. 87687687. The digits add up to 57, and 5 plus seven is 12, so the original number is divisible by three.

Dividing by 4

Look at the last two digits. If the number formed by its last two digits is divisible by 4, the original number is as well. Examples:

1. 100 is divisible by 4. 2. 1732782989264864826421834612 is divisible by four also,

because 12 is divisible by four.

Dividing by 5

If the last digit is a five or a zero, then the number is divisible by 5.

Dividing by 6

Check 3 and 2. If the number is divisible by both 3 and 2, it is divisible by 6 as well.

Dividing by 7

To find out if a number is divisible by seven, take the last digit, double it, and subtract it from the rest of the number. Example: If you had 203, you would double the last digit to get six, and subtract that from 20 to get 14. If you get an answer divisible by 7 (including zero), then the original number is divisible by seven. If you don't know the new number's divisibility, you can apply the rule again.

Dividing by 8 Check the last three digits. Since 1000 is divisible by 8, if the last three digits of a number are divisible by 8, then so is the whole number.Example: 33333888 is divisible by 8; 33333886 isn't.

How can you tell whether the last three digits are divisible by 8? Phillip McReynolds answers:

If the first digit is even, the number is divisible by 8 if the last two digits are. If the first digit is odd, subtract 4 from the last two digits; the number will be divisible by 8 if the resulting last two digits are. So, to continue the last example, 33333888 is divisible by 8 because the digit in the hundreds place is an even number, and the last two digits are 88, which is divisible by 8. 33333886 is not divisible by 8 because the digit in the hundreds place is an even number, but the last two digits are 86, which is not divisible by 8.

Sara Heikali explains this test of divisibility by eight for numbers with three or more digits: 1. Write down the units digit of the original number.2. Take the other numbers to the left of the last digit,and multiply them by two.3. Add the answer from step two to the number from step one.4. If the sum from step three is divisible by eight, then the original number is divisible by eight, as well. If the sum is not divisible by eight, then the original number is not divisible by eight.

For example, if the number we are testing is 104, then1. Write down just the digits in ones place: 4.2. Take the other numbers to the left of that last digit,and multiply them by two: 10 × 2 = 20.3. Add the answer from step two to the number from step one:4 + 20 = 24.4. Twenty-four is divisible be eight. Therefore, our originalnumber, one hundred and four, is also divisible by eight.

Dividing by 9

Add the digits. If that sum is divisible by nine, then the original number is as well.

Dividing by 10

If the number ends in 0, it is divisible by 10.

Dividing by 11

Let's look at 352, which is divisible by 11; the answer is 32. 3+2 is 5; another way to say this is that 35 -2 is 33.

Now look at 3531, which is also divisible by 11. It is not a coincidence that 353-1 is 352 and 11 × 321 is 3531.

Here is a generalization of this system. Let's look at the number 94186565.

First we want to find whether it is divisible by 11, but on the way we are going to save the numbers that we use: in every step we will subtract the last digit from the other digits, then save the subtracted amount in order. Start with

9418656 - 5 = 9418651 SAVE 5 Then 941865 - 1 = 941864 SAVE 1 Then 94186 - 4 = 94182 SAVE 4 Then 9418 - 2 = 9416 SAVE 2 Then 941 - 6 = 935 SAVE 6 Then 93 - 5 = 88 SAVE 5 Then 8 - 8 = 0 SAVE 8

Now write the numbers we saved in reverse order, and we have 8562415, which multiplied by 11 is 94186565.

Here's an even easier method, contributed by Chis Foren:

Take any number, such as 365167484.

Add the first, third, fifth, seventh,.., digits.....3 + 5 + 6 + 4 + 4 = 22

Add the second, fourth, sixth, eighth,.., digits.....6 + 1 + 7 + 8 = 22

If the difference, including 0, is divisible by 11, then so is the number.

22 - 22 = 0 so 365167484 is evenly divisible by 11.

See also Divisibility by 11 in the Dr. Math archives.

Dividing by 12

Check for divisibility by 3 and 4.

Dividing by 13

Here's a straightforward method supplied by Scott Fellows:

Delete the last digit from the given number. Then subtract nine times the deleted digit from the remaining number. If what is left is divisible by 13, then so is the original number.

Rafael Ando contributes:

Instead of deleting the last digit and subtracting it ninefold from the remaining number (which works), you could also add the deleted digit fourfold. Both methods work because 91 and 39 are each multiples of 13.

For any prime p (except 2 and 5), a rule of divisibility could be "created" using this method:

1. Find m, such that m is the (preferably) smallest multiple of p that ends in either 1 or 9.

2. Delete the last digit and add (if multiple ends in 9) or subtract (if it ends in 1) the deleted digit times the integer nearest to m/10. For example, if m = 91, the integer closest to 91/10 = 9.1 is 9; and for 3.9, it's 4.

3. Verify if the result is a multiple of p. Use this process until it's obvious.

Example 1: Let's see if 14281581 is a multiple of 17. In this case, m = 51 (which is 17×3), so we'll be deleting the last number and subtracting it fivefold.

1428158 - 5×1 = 1428153 142815 - 5×3 = 142800 14280 - 5×0 = 14280 1428 - 5×0 = 1428 142 - 5×8 = 102 10 - 5×2 = 0, which is a multiple of 17, so 14281581 is multiple of 17.

Example 2: Let's see if 7183186 is a multiple of 46. First, note that 46 is not a prime number, and its factorization is 2×23. So, 7183186 needs to be divisible by both 2 and 23. Since it's an even number, it's obviously divisible by 2. So let's verify that it is a multiple of 23:

m = 3×23 = 69, which means we'll be adding the deleted digit sevenfold. 718318 + 7×6 = 718360 71836 + 7×0 = 71836 7183 + 7×6 = 7225 722 + 7×5 = 757 75 + 7×7 = 124 12 + 7×4 = 40 4 + 7×0 = 4 (not divisible by 23), so 7183186 is not divisible by 46.

Note that you could've stopped calculating whenever you find the result to be obvious (i.e., you don't need to do it until the end). For example, in example 1 if you recognize 102 as divisible by 17, you don't need to continue (likewise, if you recognized 40 as not divisible by 23). The idea behind this method it that you're either subtracting m×(last digit) and then dividing by 10, or adding m×(last digit) and then dividing by 10.

Jeremy Lane adds:

It may be noted that while applying these rules, it is possible to loop among numbers as results.

Example: Is 1313 divisible by 13? Using the procedure given we take 13×3 and obtain 39. This multiple ends in 9 so we add four-fold the last digit.

131 + 4×3 = 143 14 + 4×3 = 26 2 + 4×6 = 26 ...

Example: Is 1326 divisible by 13? Using the procedure given we take 13×7 = 91. This is not the smallest multiple, but it does show looping. The smaller multiple does loop at 39 as well. There are some examples where we would still need to recognize certain multiples. So we subtract nine-fold the last digit.

132 - 9×6 = 78 7 - 9×8 = -65 (factor out -1) 6 - 9×5 = -39 (again factor out -1) 3 - 9×9 = -78 (factor out -1)

This only occurs though if the number does happen to be divisible by the prime divisor. Otherwise, eventually you will have a number that is less than the prime divisor.

And here's a more complex method that can be extended to other formulas: 1 = 1 (mod 13)10 = -3 (mod 13) (i.e., 10 - -3 is divisible by 13)100 = -4 (mod 13) (i.e., 100 - -4 is divisible by 13)1000 = -1 (mod 13) (i.e., 1000 - -1 is divisible by 13)10000 = 3 (mod 13)100000 = 4 (mod 13)1000000 = 1 (mod 13)

Call the ones digit a, the tens digit b, the hundreds digit c, ..... and you get: a - 3×b - 4×c - d + 3×e + 4×f + g - .....

If this number is divisible by 13, then so is the original number.

You can keep using this technique to get other formulas for divisibility for prime numbers. For composite numbers just check for divisibility by divisors.

Dividing by 14

Sara Heikali builds on her divisibility test for seven: How can you know if a number with three or more digits is divisible by the number fourteen?

Check if the last digit of the original number is odd or even. If the number is odd, then the number is not divisible by fourteen. If the number is even, then apply the divisibility rule for seven.

(Keep in mind, the odd and even test is to see if the number is divisible by two.) If the original even number is divisible by seven, then it is also divisible by fourteen. If the original even number is not divisible by seven, it is not divisible by fourteen.

 _____________________________________________________________________

if yu wanna decide the greatest number between two fractionsthen cross multiply with each other

eg:A=5/6 and B=7/8to find which number is greatest from above thncross multiply with eachie 5*8 & 7*6here 7*8 is greater so..

so answer is B

Probalities we ve Group Formulas

its for 2 Groups

G1+G2+None-Both=Total

for 3 groups

G1+G2+G3+None-Any2+All3=Total

1. Which of the following fractions is least?A: 5/6B: 5/4C: 4/5D: 6/5

2. Which of the following fractions is the greatest?A: 5/6B: 7/8C: 9/8D: 7/6

two things always remember on goingas 1/2..2/3..3/4..the value increases from this can esily solve 1for 2nd remember3/2..4/3...5/4....the value decreases...

problem of : MEN DURATION WORKm= men d=durationw=work

then

[m1 x d1] / [m2 x d2] = [w1 / w2]

you can directly put the value and find the answer...

square of adjacent number

trick is....for eg we have to find square of 61...

we know....60^2=3600

61^2=60^2+(60+61)=3600+121=3721..

26^2=25^2+(25+26)=625+25+26=676....

TIP1/any decimal... is greater thn that decimal

eg:1/0.25 > 0.25

THUMB RULE>>>>

when the numerator and denominator of the fractions increases by constant value,the last fraction is the biggest..a=1/8b=4/9c=7/10

from this rule ans=7/10..as numerator increase by 3 (a constant value)...and denominator increase by 1 ( a constant value).....

" we have 10 bulbs and 2 are not working , if we choose 3 out of the lot what is the prob of getting one not working bulb?"

TOTAL 10 BULBS8 OF THEM R GUD2 R NOT WORKINU NEED TO SELECT 3 BULBS OUT OF 10.... SO 10C3ONE AMONG THEM SHLD NOT WORK...... SO 2C1AND THE OTHER TWO MUST BE FROM 8 ......... SO 8C2SO THE ANSWER IS 8C2*2C1/10C3 == 7/15

Use formula nCr = n!/ r! * (n-r)!

8C2*2C1/10C3 = ( (8!/2!(8-2)!)* (2!/1!(2-1)!))/ 10!/3!(10-3)!

=((8*7*6!/2*1*6!)*(2*1/1*1))/(10*9*8*7!/3*2*1*7!)

=(8*7)/(10*9*8/3*2)

=7/15

#magical method of multiplication

why this u can find product of number like....abxacbxc=write at lastax(a+1)=initial

eg46x44

6x4=24..write 24 at last..

4+1=5..&4x5=20...ans=2024

69x619x1=96+1=7....&7x6=42..ans=4209(why 0 xtra..note right side of answer should always have two digit)

i just miss the one thing that..on adding the right hand digit u must get10

76x79 cant as9+6=15

sry for not describing that

56x54..73x77..etc in this...6+4=10...and7+3=10..

John has 8 friends. In how many ways can he invite one or more of them to dinner?

this q tell how much u know abt permutation and question????2(power,8) -1

i think most of u now the 2,3,4,5,6,8,9,11

now iam discussing of DIVISIBILITY RULE FOR 13 find whether 1001..is divisible by 13???? divisibilty rule for 13

1001=100+1(last digit)*4(0perator)=104=10+4(last digit)*4(operator)=26

as 26 divisible by 13 therefore 1001also algebra is nothing but expression of a pattern using variable

...the best thing abt algebra is that its q can easily be solved by the tricks ....now i am discussing that tricks consider q...q let x be the arithmetic mean and y,z be two geometric mean b/w any two positive numbers the value of (y^3+z^3)/xyz is...

a.2b.3c.1/2d.3/2

pleaze try that..then iwill tell u trick by which u can do it in 3 sec try another one

K^2 and 2K^2 are root of equation x^2-px+q..find q+4q^2+6p.q

a.q^2b.P^3c.0d.2P^3

try this one also..ANS:2.assume eq with root 1&2...k=1....sum of roots=3..product=2..substitute in q+4q^2+6p.q got=54..

2.p^3=54 ans=2 p^3

ans: 1.assume a gp..1,2,4,8.....y=2,z=4 are terms..am=(8+1)/2=4.5

let x be the arithmetic mean and y,z be two geometric mean b/w any two positive numbers the value of (y^3+z^3)/xyz is...

a.2b.3c.1/2d.3/2

here a gp is assume..y=2,z=4...am=4.5..just put all these values

y^3=8...z=64..y^3+z^3=64+8=72..x.y.z=4.5x2x4=36..

ans=72/36=2

perfect number.

if sum of divisor of n excluding n itself is equal to n..then n is called a perfect number

eg..28=1+2+4+7+14

6=1+2+3

DEVISIBILITY OF 7

133=13-3*2=13-6=7.ITS DEVISIBLE BY 7

where does d 2 in (3*2) come from?

DEVISIBILITY OF 13

2336=233+6*4=260;ITS DIVISIBLE BY 13

ang plz tell d same for the 4 in (6*4)

In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?

A)5 B)10 C)15 D)20 E)25

n a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?

p(aUbUc)=p(a)+p(b)+p(c)-p(anb)-p(bnc)-p(cna)+p(anbnc)

let x=p(anb)+p(bnc)+p(cna) ie intrested in two products

.85=.5+.3+.2-x+5

x=5.15

wat v need is intrested in more than one that is intrested in 2 products + intrested in 3 products

x is intrested in 2 products

so 5.15+5=10.15

Hope this may help u while finding sq & cubes..to find sq of a num..Ex: 38^2use simple formula.. (a+b)^2= a^2+2ab+b^2value for a=8 & b=3.. jus substitute dese values in d equ

b^2=8^2=64(write down 4 n carry 6)2ab+6= 2*3*8+6= 54(write down 4 n carry 5)a^2=3^2+5= 14

38^2= 1444.

to find cube of a num.. use (a+b)^3=a^3+3a^2b+3ab^2+b^387^3 = 343 (b^3)1176 (3ab^2)1344 (3a^2b)512 (a^3)------------658503

a number when divided by a divisor leaves a reminder of 24,when twice the original number is divided by the same divisor ,the reminder is 11.what is the value of divisor??

a.13b.59c.35d.37ans=37

=original numberdivisor=dquotient=xa=dx+24given

2a=2dx+48

2dx+48/d.....leaves reminder 11....

actually i close this thread due to no..further responses

2dx....perfectly divisivle byd

48/d.....gives remnder eleven only...when d=37

2.how many keystrokes are needed to type number from 1 to 1000???a.3001b.2893c.2704d.28901------9 .......9keys

10-----99.....2.90=180 keys

100----9000.....900.3=2700keys..

1000-----4 keys

anss=9+180+2700+4=2893...quicker way 2 solve squaresfirstly 2 cal. square of a 2 digit no.let 67....we just cal. D of tht no. individually..means....D of 6/ D of 67/ D of 7

D of a single digit no. wud be square of tht no.D of a 2 digit no. wud be twice of the multiplication of the no. i.e. 2abD of a 3 digit no. wud b twice of multiplication of the extreme digits + square of the middle 1.

here...for 67D of 6 wud be 6^2 = 36

D of 67 wud b 2*6*7 = 84D of 7 wud b 7*7 = 49i.e. 36/84/49no 2 rearrange these nos.just carry on the last digit as it is..here it is 9 n carry over is 4..now 4+84 is 88 now 8 is caaried down...and the other 8 is caary over...now 36+8 =44thts it the answer...is 4489...quite interesting method...

square of 3 digit no

suppose v hav 2 cal d square of 719..simply as goin by d above method....v break d no. as...D of 7/ D of 71/ D of 719/ D of 19/ D of 9

D of 7 = 7^2 = 49D of 71 = 2*7*1 = 14D of 719 = 2*7*9+1^2 = 127D of 19 = 2*1*9 = 18D of 9 = 9^2 = 81

recollectin these results...49/14/127/18/81...

goin frm right to left...1 is taken down...8 as carry over...18+8 = 26...6 goes down...2 carry over...now 127+2 = 129....similarly...9 is down...n 12 is carry over..12+14 = 26....6 is down...nd 2 carries over..lastly...49+2 = 51...thts it...d answer is...516961just chk d answer i hope it wud b right...enjoy guys...d rly cooler method...hav a gr8 time...

SHORTCUT METHOD TO FIND RANK OF A GIVEN WORD

This shortcut method is used when the lettors of the given word are not repeated.Given word is MASTERThe letters of the are M,A,S,T,E,R.Write the alphabetical order of the letters of the given word ' MASTER ' as A,E,M,R,S,TNow strike off the first letter M.

A,E,M,R,S,T.Then count the no.of letters before M, and it is equal to 2,which is the coefficient of 5!.Again strike off the first letter A.A,E,M,R,S,TThen count the no.of letters before A and it is equal to 0 which is coefficient of 4!Again strike off the first letter S.A,E,M,R,S,TThen count the no.of letters before S and it is equal to 2 which is coeffcient of 3!Again strike off the first letter T.A,E,M,R, S, TThen count the no.of letters before T and it is equal to 2 which is coeffcient of 2!Again strike off the first letter E.A,E, M,R, S,TThen count the no.of letters before E and it is equal to 0 which is coeffcient of 1!Finally add 1 to the above values to get the rank of the word MASTER as follows:2(5!) + 0(4!) +2(3!)+2(2!)+0(1!)+1=257