9th Class Mental Ability Mathematical Operations Mathematical Operations

Type-I

Solving by Substitution

In this type of problems, you are required to simplify the given statement by substituting various signs and numerals as per given terms. To simplify a statement, the BODMAS rule is very useful.

Type-II

Interchanging of Signs and Numbers

In this type of problems, you would require to interchange the pair(s) of symbols/numbers. Simplify if asked the given statement(s) using BODMAS rule.

Type-III

Analysing the Conclusions

In this type of problems, relations between different statements are given in terms of mathematical operations (less than, more than etc.) A student is required to analyse amongst them to get correct conclusions.

EXAMPLE

Consider the following statements.

'A @ B' means 'A is not greater than B'.

'A © B' means 'A is not smaller than B'.

'A # B' means "A is neither greater than nor equal to B'.

'A $ B' means "A is neither smaller than nor equal to B'.

Assuming the given below statements to be true, analyse which of the two conclusions I and II is/are definitely true and choose your option accordingly.

Statements: P @ Q, Q © R, R # S.

Conclusions: 1. P $ R        II. R $ P

(a) Only I is true             (b) Only II is true            (c) None is true               (d) Both are true

Explanation (c):

We have

A@B AB  A < B

A©B A  B  A > B

A # B  A  B and A  B  A < B

A $ B A  B and A  B  A > B

Given statements: P < Q, Q >. R, R < S.

Relationship between P and R: P < Q, Q >. R

No definite relationship between P and R.

Hence none of I and II is true.