Question

Directions: The symbols %, @ and \# are used with the following meanings: A % B \(\rightarrow\) A is greater than B, A @ B \(\rightarrow\) A is either greater than or equal to B, A \# B \(\rightarrow\) A is smaller than B.
Statement: T\#B, Q%S, T%M, Q@R, U\#S, S@T
Conclusions: I) Q%T,
II) U\#T

• A. Only conclusion I is true
• B. Only conclusion II is true
• C. Both conclusion I and II are true
• D. Neither conclusion I nor II is true

Hint:

For coded inequalities, first translate all symbols into standard mathematical notation (\textgreater, \textless, \(\geq\), \(\leq\), =). Then, try to combine the individual statements into a single chain to easily compare the variables mentioned in the conclusions.

Answer 1

The Correct Option is A

Step 1: Convert the statements into standard inequality symbols.T < B, Q > S, T > M, Q \(\geq\) R, U < S, S \(\geq\) T.
Step 2: Combine the relationships to establish connections between variables.From Q > S and S \(\geq\) T, we derive: Q > S \(\geq\) T.From U < S and the above chain, we obtain: U < S \(\geq\) T.
Step 3: Assess the conclusions.- Conclusion I: Q % T \(\rightarrow\) Q > T. Our chain Q > S \(\geq\) T confirms Q is greater than T. Conclusion I is correct.- Conclusion II: U # T \(\rightarrow\) U < T. Our chain U < S \(\geq\) T doesn't provide a definitive relationship between U and T. For example, if S=10, T=8, U could be 9 (U > T) or 7 (U < T). Conclusion II is incorrect.