Friday, 25 December 2009

Math Challenge 21

Some math questions are simple and can be answered easily.

See this math challenge 20 and its answer in the comment.

But a twist of the questioning will and can make it more challenging without changing the math expression.

Below is one:

Base on math challenge 20, if all unknowns CANNOT be repeated, what are they?
Again they are integers and below 10.

Enjoy the math thrill answering this.

Merry Christmas!

Saturday, 19 December 2009

Math Challenge 20

Can anyone come out the answers for A, B, C and D in the below math expression?

A2 + B2 + 2C2 = D2

The rule is that the unknowns are all integers and below 10.

Happy trying, and
don't forget that maths is interesting!


Monday, 7 December 2009

Percentage | Common Mistake

Percentage problems can be tricky at times when you are careless.

Let's us look at one maths word problem related to it.

There are 3 persons, John, Mary and Jane.
John is richer than Mary by 10%, and Mary is richer than Jane by 20%.
Is John richer than Jane by (10 + 20)% = 30% ?

Most students, upon quick thinking, will acknowledge that 30% is the correct answer.

Is it so?

To verify the answer, let us assume that Jane has $1000.
As such, Mary will have (100+20)% of $1000 = 1.2 x $1000 = $1200.
John is then 1.1 x $1200 = $1320 richer than Jane ==> By 32%.

If 30% is correct, we should get 1.3 X $1000 = $1300.

The latter number (dollar) is not the same as the first worked out solution.

Mistake in understanding what is percentage:
To assume that John is 10% + 20% richer than Jane is incorrect.
This is due to the fact that percentage has to take a common reference for this to be correct.

In the word problem, the percentages of comparison are not to a common reference.
The first one is to Mary, while the next is to Jane.

These made the denominator of the ratio different.
Thus adding the percentage up is a mistake, and an easy one too!