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Mathematical Operations- Deriving Conclusion

Mathematical Operations - Concepts

Mathematical Operations - Letter Substitution

Mathematical Operations - Interchanging of Symbols

Mathematical Operations - Symbol Substitution

Mathematical Operations - Letter Substitution With Digits

Mathematical Operations - Balancing Inequalities

Mathematical Operations- Deriving Conclusion

Class - LIC ADO Prelims Subjects

Concept Explanation

Mathematical Operations- Deriving Conclusion

Mathematical Operations - Deriving Conclusions: In this type of questions, certain relations between different sets of elements is given (in terms of 'less than', 'greater than' or 'equal to'), using either the real symbols or substituted symbols. The candidate is required to analyse the given statements and then decide which of the relations given as alternatives follows from those given in the statements.

Illustration: If A + B > C + D and B + C > A + D, then it is definite that

A. D > B B. C > D C. A > D D. B > D

Answer: D

Solution: Given : A + B > C + D ........... (i) and B + C > A + D ........ (ii)

Adding (i) and (ii), we get :

(A + B) + (B + C) > (C + D) + (A + D)

$Rightarrow$ A + 2B + C > C + 2D + A $Rightarrow$ 2B > 2D $Rightarrow$ B > D

Hence, the correct option is D.

Illustration: In the following questions, the symbols @, ©, %, $bigstar$ and $ are used with the following meanings as illustrated below :

'P @ Q' means 'P is either greater than or equal to Q';

'P © Q' means 'P is either smaller than or equal to Q';

'P % Q' means 'P is greater than Q';

'P $bigstar$ Q' means 'P is smaller than Q';

'P $ Q' means 'P is neither greater than nor smaller than Q';

Assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true ?

Statements : D $ M, M % W, W @ R

Conclusions : I. R $bigstar$ D II. W © D

A. Only conclusion I is true B.; Only conclusion II is true C. Either conclusion I or II is true; D. Neither I nor II is true

E. Both conclusions I and II are true.

Solution: Clearly, we have :

(i) P @ Q $Rightarrow$ P $geq$ Q (ii) P © Q $Rightarrow$ P $leq$ Q

(ii) P % Q $Rightarrow$ P > Q (iv) P $bigstar$ Q $Rightarrow$ P < Q

(v) P $ Q $Rightarrow$ P $ngtr$ Q and P $nless$ Q $Rightarrow$ P = Q.

Given statements : D = M, M > W, W $geq$ R.

I. Relation between R and D : R $leq$ W, W<M, M = D $Rightarrow$ R $leq$ W< M = D $Rightarrow$ R<D i.e., R $bigstar$ D.

II. Relation between W and D : W < M, M=D $Rightarrow$ ; W<M=D $Rightarrow$ W<D ; i.e., W $bigstar$ D.

So, only I is true while II is not. Hence, the correct option is A

Sample Questions

(More Questions for each concept available in Login)

Question : 1

The symbols @, ©, %, $bigstar$ and $ are used with the following meanings as illustrated below : 'P @ Q' means 'P is either greater than or equal to Q'; 'P © Q' means 'P is either smaller than or equal to Q'; 'P % Q' means 'P is greater than Q'; 'P $bigstar$ Q' means 'P is smaller than Q'; 'P $ Q' means 'P is neither greater than nor smaller than Q'; Assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true ? Statements : H % J, B © J, B @ F Conclusions : I. F $ J II. J % F
A. Only conclusion I is true		B. Only conclusion II is true
C. Either conclusion I or II is true		D. Both conclusions I and II are true
Right Option : C
View Explanation

Question : 2

The symbols @, ©, %, $bigstar$ and $ are used with the following meanings as illustrated below : 'P @ Q' means 'P is either greater than or equal to Q'; 'P © Q' means 'P is either smaller than or equal to Q'; 'P % Q' means 'P is greater than Q'; 'P $bigstar$ Q' means 'P is smaller than Q'; 'P $ Q' means 'P is neither greater than nor smaller than Q'; Assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true ? Statements : A © N, N $bigstar$ V, V $ J Conclusions : I. J @ N II. A © V
A. Only conclusion I is true		B. Only conclusion II is true
C. Either conclusion I or II is true		D. Neither I nor II is true
Right Option : D
View Explanation

Question : 3

The symbols @, ©, %, $bigstar$ and $ are used with the following meanings as illustrated below : 'P @ Q' means 'P is either greater than or equal to Q'; 'P © Q' means 'P is either smaller than or equal to Q'; 'P % Q' means 'P is greater than Q'; 'P $bigstar$ Q' means 'P is smaller than Q'; 'P $ Q' means 'P is neither greater than nor smaller than Q'; Assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true ? Statements : K $bigstar$ T, T @ B, B © M Conclusions : I. M % T II. N © B
A. Only conclusion I is true		B. Only conclusion II is true
C. Either conclusion I or II is true		D. Neither I nor II is true
Right Option : D
View Explanation