Inequalities

In Reasoning Part, another important Topic is Inequality Problems. It is a common topic for all competitive exams. We can expect 5 or 6 questions from Inequality. It is one of the topic, where you can get full marks very easily. I am going to explain a very simple method and i assure you that it’s possible to solve 5 questions in just two minutes.

In Inequality, at first they give some directions for the Problems. And in each problem, there will be statements followed by 4 conclusions. Our job is to find the conclusions which are true.

There are two types of models in Inequality.

1) Coded Inequality.

2) Direct Inequality.

In Coded Inequality, symbols like $, #, %, &, @ are used. In Direct Inequality, we use symbols like <, >, =, ≤, and ≥ . Before learning shortcuts, lets understand what these symbols mean. Most of us learn these symbols in lower classes and they all are familiar ones.

< – Less than

≤ – Less than or Equal to

> – Greater than 

≥ – Greater than or Equal to

= – Equal to

I hope everybody know this. Let’s go to Coded Inequality.

Directions 

P $ Q means P is not smaller than Q

P @ Q means P is neither smaller than nor equal to Q

P # Q means P is neither greater than nor equal to Q

P ∂ Q means P is neither greater than nor smaller than Q

P © Q means P is not greater than Q

Now our first work is to find what does the symbol means indirectly?

Lets solve it one by one.

P is not smaller than Q. So P can be either equal to Q or Greater than Q. Symbol is ≥.

P is neither smaller than nor equal to Q. So P is Greater than Q. Symbol is >.

P is neither greater than nor equal to Q. So P is lesser than Q. Symbol is <.

P is neither greater than nor smaller than Q. So P is equal to Q. Symbol is =.

P is not greater than Q. So P can be either equal to or lesser than Q. Symbol is ≤.

Now form a small table before solving this kind of problems.

Now we decoded the symbols and we clearly know what is the meaning of each symbol. Make sure that you form a table as above. The symbols >, ≥, and = should be in one row and the symbols <, ≤, and = should be in another row. Don’t memorize the table. Usually Symbols change. You have to decode it correctly and form a table.

Note:

———-> Forward Direction. 

<———- Reverse Direction.

 In Row 1, First Priority should go to >. Next ≥. Last =. Similarly,

In Row 2, First Priority should go to <. Next ≤. Last =. 

Just remember these lines. You will understand it while solving problems.

Never make a mistake in forming this table. If you make a mistake then you loose all the 5 or 6 marks.