In the following questions, the symbols @, #, $, © and % are used with the following meaning as illustrated below: P @ Q ⇒ P ≥ Q P # Q ⇒ P ≤ Q P $ Q ⇒ P < Q P © Q ⇒ P > Q P % Q ⇒ P = Q Statements: M © N N # O Conclusions: I. M © O II. M @ O
- (a)If only conclusion I is true.
- (b)If only conclusion II is true.
- (c)If only conclusion III is true.
- (d)Neither I nor II is true
Answer
Why
Correct — D. Decode the symbols, join the statements, then test each conclusion.
Rule: when the signs between two letters face opposite ways, no definite relation follows.
M © N means M > N
N # O means N ≤ O
Together: M > N ≤ O
The signs between M and O face opposite ways. With M = 5, N = 1, O = 10 both statements hold and M is below O.
So I (M > O) and II (M ≥ O) are both uncertain: neither is true, option (d).
Why the others are wrong
- (a)If only conclusion I is true. — Only I needs M > O for certain. M = 5, N = 1, O = 10 satisfies both statements with M below O, so I is not definite.
- (b)If only conclusion II is true. — Only II, M ≥ O, fails on the same numbers: M = 5 is below O = 10. The ≤ in N # O lets O rise above M.
- (c)If only conclusion III is true. — Conclusion III does not exist: the question prints conclusions I and II and nothing more. This option describes nothing in the item.
Concept
A coded inequality item first asks you to translate: here @ is ≥, # is ≤, $ is <, © is > and % is =. After that it is an ordinary chain.
Join the statements at the shared letter, N: M > N ≤ O. N is below M and no higher than O, but nothing compares M with O. When the signs between two letters face opposite ways, no relation between them is certain: M can sit above O, below it or level with it.
Option (c) refers to a 'conclusion III' that the question never states; the paper prints it that way. It changes nothing: I and II both fail, and (d) is the option that says so.
Key facts
- In this item @ is ≥, # is ≤, $ is <, © is > and % is =.
- M > N and N ≤ O give no definite relation between M and O.
- M = 5, N = 1, O = 10 fits both statements and puts M below O.
Study next
Common traps
- Mixing up # and @: N @ O would mean N ≥ O, and M > N ≥ O would then make both conclusions true.
- Testing one set of numbers where M happens to be above O, instead of looking for a case where it is not.
Neither also answers 17 Sep 2025, 16:00, Reasoning Q.7, for a different reason: there O = S > T fixes O above T, so T = O and T > O are both definitely false.
At 19 Sep 2025, 09:00, Reasoning Q.7, the chain Q < S ≤ T = R never changes direction, so Q < R follows.
Related PYQs
No directly related past PYQ was found.