GATE ECE 2014 Set 3 | GA | Question: 5

Question

In which of the following options will the expression $P < M$ be definitely true?

• A. $M < R > P > S$
• B. $M > S < P < F$
• C. $Q < M < F = P$
• D. $P = A < R < M$

Answer 1

Answer $D.$
As $P=A$
and $A<R$ and $R<M \implies A<M \implies P<M$

Comments

Why are other options false?

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put M=1,P=0 and check all the options

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Because it occur's maybe or maybe not condition !

Answer 2

I guess everyone knows why option d is right so will not answer on that I'll rather focus on why other options are wrong, M<P is shown in option c. in option b, M is greater than S, and P is also greater than S, so no relation between M and S can be found similarly in option A, M and P both are less than R, but no direct connection between them. The only sure option we can see is option D where P is less than M(Just interchange M and A if you're finding difficulty in Option D.)

Answer 3

These patterns are important:

• (A < B < C   → A < C)

• (A > B > C       →  A > C)

• (A < B > C) → no relation between (A,C)

• (A > B < C) → no relation between (A,C)

option A,B no relation  and option C  M<P

Correct : option D  

P=A<R<M 

P<M