Amazing Set of Fractions!

What if I tell you to form two fractions with sums equal to their products?

This is like think of two numbers: Add the two numbers and then multiply the two numbers.

The result should be the same!

Is there a way for you to find out how can this be?

Fortunately, there is a formula for this!

Let x be any whole number.

Then the two numbers (x) and (x/x-1) are the two numbers we are looking for!

Sample: Let x be 5.

Then the two numbers should be 5 and 5/4.

Both have a sum and product of 6.25!

Agree with me?

Multiplication Techniques: Part 2

Multiplying a two-digit number by itself starting with 5.

Sample: 54 x 54 = ?

First, multiply the last digit: 4 x 4 = 16. This will be the last two digits of the answer.

Second, multiply the other digit by itself: 5x5 = 25

Now add the last digit to the product in Step 2. This will give you ->

25 + 4 = 29. This will be the first two-digits of the answer!

Presto! The answer is 2916. Got it?

Another example: 59 x 59? Did you see how did you arrive at 3,481?

Tickle IQ Test

I visited one of the IQ tests over the internet last January 18, 2008.

I was surprised that I got an IQ of 120 with Intellectual Type of the mathematician Pythagoras.

Attached is the report of my answers vs. the correct answers to the questions. IQ Report.

Before you view the report, take a shot and know your IQ too.

Exercise your mind.

Hardest Logical IQ Problem

They say that logic problems is the best way to measure one's IQ because these kinds of problems do not take into consideration your background. Although, it certainly helps having a degree in analysis subjects such as mathematics, engineering, finance, accounting, etc.

This is so far the hardest logic IQ problem that I encountered. They say that when you solved this IQ Problem, you'll belong to the top 2% of the world's most intelligent people. It was called Einstein Quiz!

Modesty aside, I was able to solve this problem in around 1 hour of hard thinking.

Luckily, with just one try I got the answer correctly!

Try it for yourself too!

Here's the file!

Multiplication Techniques

Let me share to you multiplication techniques.

This involves a two-digit number!

1. How to multiply any two-digit number by 11?


Example: What is 23 x 11? 41 x 11? What about 97 x 11?

You want to know the technique?

Very Simple!

Just add the digits and insert the sum in the middle!

Very simple right?

Here's how it works...

23 x 11 => 2 + 3 = 5

Insert 5 in the middle of 2 and 3 so it will become -> 253!

What about 41 x 11?

41 x 11 => 4 + 1 = 5

Insert 5 in the middle of 4 and 5 so it will become -> 451!

Got it?

There's one problem....

How about if the sum exceeds 10? Just in the case of 97 x 11?

Simple... 9 + 7 = 16

So how can you insert 16 in the middle of 9 and 7?

Simple...

Insert 6 and 1 should be carried over to 9 just like addition...

So the last two digits of the answer is 67...

What happened to the 1 from the sum 16?

Add it to 9.

So then, 9+1 = 10

So there 10 is the first two digit of the answer!

And the last two digit is 67 as stated above...

So the answer is 1067!!!!

Isn't it amazing?


2. How to multiply any two-digit number ending in 5 by itself?

Sample: What is 25 x 25?

What about 95 x 95?

Simple...

Take the first digit of the number....

In the first example, that would be 2.

Add 1 to it. 2 + 1 = 3

And the multiply it to the original digit.

That would be 3 x 2 = 6

Lastly, affixed 25 as the last two-digits

Presto!

Answer is 625!!!


So can you now decipher how 95 x 95 became 9,025?

Isn't it amazing?

Simple Logic Problem

OOPPPSSS.... Don't scroll down too much!!!


What is:

(a-x) (b-x) (c-x) (d-x) ... (z-x) = ????

Please note that parentheses indicates multiplication.

Come on use your intuition!

Guess it first and before you view the answer below...



















KEPT THINKING????















ANSWER IS ZERO!!!!

WHY?





Beacause there will come a time for (x-x) which is of course ZERO.
And any number multiplied by zero is ZERO!!!


Isn't it amazing?

Magic Squares

One of the things that fascinated me was the so-called Magic Squares.

I did a self-study on this. Magic Squares are a set of numbers 1 to n squared, without repetition, that were placed in an n by n grid of square such that the sum of all the columns, rows, and diagonals were all the same and equivalent to a single number.

Please refer to this post to my other blog:

Fascinating Magic Squares