Mathematical Operations- Deriving Conclusion
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)
A + 2B + C > C + 2D + A
2B > 2D
B > D
Hence, the correct option is D.
Illustration: In the following questions, the symbols @, ©, %, 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 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 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 P
Q (ii) P © Q
P
Q
(ii) P % Q P > Q (iv) P
Q
P < Q
(v) P $ Q P
Q and P
Q
P = Q.
Given statements : D = M, M > W, W R.
I. Relation between R and D : R W, W<M, M = D
R
W< M = D
R<D i.e., R
D.
II. Relation between W and D : W < M, M=D ; W<M=D
W<D ; i.e., W
D.
So, only I is true while II is not. Hence, the correct option is A
The symbols @, ©, %, '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 '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 : B @ H, H Conclusions : I. B @ N II. N % H | |||
| Right Option : B | |||
| View Explanation | |||
The symbols @, ©, %, '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 '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 Conclusions : I. M % T II. N © B | |||
| Right Option : D | |||
| View Explanation | |||
The symbols @, ©, %, '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 '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 : M @ R, R % T, T $ K Conclusions : I. K | |||
| Right Option : D | |||
| View Explanation | |||
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