Directions: In these questions symbols ©, #, %, $ and @ are used with…
2022
Directions: In these questions symbols ©, #, %, $ and @ are used with different meanings as follows.
‘M © N’ means ‘M is smaller than N’
‘M # N’ means ‘M is either smaller than or equal to N’
‘M % N’ means ‘M is greater than N’
‘M $ N’ means ‘M is either greater than or equal to N’
‘M @ N’ means ‘M is neither smaller than nor greater than N’
In each of the following questions assuming the given statements to be true, find out which of the conclusions I, II and III given below them is/are definitely true.
Statements:
B $ D % G @ Q; L # M © N # Q; M $ P % U
Conclusions:
I. D % U
II. N % G
III. M © B
- A.
Both I and II
- B.
Only III
- C.
Both I and III
- D.
All I, II and III
- E.
Only I
Attempted by 2 students.
Show answer & explanation
Correct answer: C
Concept
Coded-inequality problems replace each symbol with a strict relation, then ask whether a conclusion is forced by the statements. First translate every symbol into <, ≤, >, ≥ or =. A conclusion is 'definitely true' only if a single unbroken chain of relations of the SAME direction links its two terms; a direction reversal anywhere in the chain breaks the deduction.
Translate the symbols
© → 'less than' (<)
# → 'less than or equal to' (≤)
% → 'greater than' (>)
$ → 'greater than or equal to' (≥)
@ → 'equal to' (=)
Decode the statements
B $ D % G @ Q gives B ≥ D, D > G, G = Q.
L # M © N # Q gives L ≤ M, M < N, N ≤ Q.
M $ P % U gives M ≥ P, P > U.
Build the master chain
Since G = Q, replace Q by G. From N ≤ Q we get N ≤ G, and from M < N we get M < N ≤ G, so M < G. Combining with D > G and B ≥ D gives the ordered chain:
B ≥ D > G = Q ≥ N > M ≥ P > U, with L ≤ M as a side branch.
Test each conclusion
D > U: D > G and G ≥ N > M ≥ P > U, so D > … > U is one unbroken 'greater' chain. True.
N > G: the chain gives G = Q ≥ N, i.e. N ≤ G, the opposite direction. So N > G cannot be forced. False.
M < B: M < G, G < D (from D > G) and D ≤ B (from B ≥ D), so M < G < D ≤ B gives M < B. True.
Cross-check
Take a concrete set obeying every relation, e.g. B=10, D=9, G=Q=8, N=7, M=6, P=5, U=4, L=2. Then D>U (9>4) holds, N>G (7>8) fails, and M<B (6<10) holds — matching I and III true, II false.
Result
Conclusions I and III are definitely true while II is false, so the answer is 'Both I and III'.