Logic - Number Series

Logic comes in various shapes and sizes. And it is often tested in the weirdest of manners. However, entrance exams have a set repertoire of questions. So let's just plunge into one of those typical type of questions.

Number series is a typical type of question that tests the candidate's mathematical ability.

A series of numbers is given and one has to identify the pattern that connects all the numbers. Typical series are arithmetic of geometric progressions. However, questions asked in entrance tests are not typical. One needs to think in terms of

- arithmetic progressions
- geometric progressions
- primes odds evens multiples squares cubes....
- multiple series (combination of 2 or 3 different series done alternatively)

Repeated practice with number series questions is the only key to crack these type of questions

Percentages

One of the math topics which is actually the easiest, but a pet peeve of many students, is percentages.

Let's see if we can simplify it.

The word percentage literally means out of one hundred. (per century) So, all we do in this is try and see how many parts of 100 are involved in the game.

Assume we have an apple. We cut it into two equal halves. One part would be half of the whole. This is equal to 50 portions out of 100. (as 50 is half of 100). So one part out of two works out to be 50 per century or 50 %

We may do our calculations like this

out of 2 - 1
out of 100 - ?

? = (100 x 1)/2 = 50

Similarly, if we had 40 students in the class and 10 of them were boys, then 10 out of 40 is 1/4th. We know that 25 is 1/4th of 100. So 10 out of 40 is the equivalent of 25 %

Remembering reciprocals is a good way to do percentages. Reciprocals are nothing but 1/x where x is any natural number. For instance the reciprocal of 2, i.e. 1/2 = 50%

Reciprocal of 4 (double of 2) = 1/4 = 25% (half the reciprocal of 2)
Reciprocal of 8 (double of 4) = 1/8 = 12.5% (half the reciprocal of 4)

Calculating percentages of numbers is a very simple process, as long as we are good at doubling or halving numbers.

For instance, to calculate 37% of 500, we can split it as 10 + 10 + 10 + 5 + 2
10 % of any number is easy. 10% of 500 is 50
5% is half of 10% = 25
and 2% = twice 1% Now, 1% = 5 so 2% = 10

So we get 37% = 50+50+50+25+10=185

Of course, calculating it by formula 500x37/100 is also ok. Use whichever method is faster and more convenient.

Vocabulary

Hello people,

A common crib among students who wish to do well in various entrance tests is that they are not able to do well in the English section of the paper.

I believe, the first step towards this, is to build your vocabulary. Just as Rome wasn't built in a day, building a good vocabulary takes up a lot of time and practice.

However, if you are willing to spare 15-20 minutes everyday, you can definitely have a better vocabulary. The trick is not in memorizing OED or Websters (come on, we are not aiming to set records here). Just as quick mathematics involves learning the basics like multiplication tables, a good command over words requires one to understand word roots and how words in English are formed.

A simple Google search will give you lists of word roots. Go through these roots to understand how words are formed. For example http://www.virtualsalt.com/roots.htm provides one such list.

Sites such as http://wordsmith.org/awad/ will help you learn new words everyday.

Remember, memorizing a word is not going to be of much use. You need to learn the usage of the word and then practice using it in sentences of your own.

Hope this helps you start in your preparation towards a better vocabulary.

Ciao!