Question

In the following question, the symbols $@,\copyright ,\%,\$$ and $\star$ are used with the following meaning as illustrated.
${}^{\prime }P\copyright Q^{\prime }$ means 'P is not greater than Q'.
${}^{\prime }P\star Q^{\prime }$ means 'P is not smaller than Q'.
${}^{\prime }P\%Q^{\prime }$ means 'P is neither greater than nor equal to Q'.
${}^{\prime }P\$Q^{\prime }$ means 'P is neither smaller than nor greater than Q'.
${}^{\prime }P@Q^{\prime }$ means 'P is neither greater than nor smaller to Q'.
In each of the following questions assuming the given statements to be true, find out which of the three conclusions I, II and III given is/are definitely true.
© $\Rightarrow \le$, @ $\Rightarrow$ = $\star \Rightarrow \ge$, % $\Rightarrow$ < $\$$ $\Rightarrow$ >
Statements
$M\star K$
$K@R$
$R\%N$
Conclusions
I. $R\%M$
II. $R@M$
III. $N\$K$

• A. Only I is true
• B. Only II is true
• C. Only III is true
• D. Only either I or II is true
• E. Only either I or II and III are true

Answer 1

The correct option is E Only either I or II and III are true

Given statements are
M $\star$ K $\Rightarrow M\ge K$ ...(i)
K @ R $\Rightarrow K=R$ ...(ii)
R % N $\Rightarrow R<N$ ...(iii)
After combining these statements, we get M $\ge$ K = R < N
I. R % M $\Rightarrow$ R < M
or
II. R @ M $\Rightarrow$ R = M
As, M $\ge$ K = R
So, M $\ge$ R
Either R < M or R = M
III. N $\$$ K = True
As, N > R = K
So, N > K