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 two conclusions I and II given below them is/are definitely true. Give answer
Statements:
22 $ 26 $ 35 @ 41 # 29; 53 $ 29 @ 32 # 38
Conclusions:
I. 35 © 32
II. 53 $ 41
III. 41 $ 29
- A.
Both I and II
- B.
Only II and either I or III is true
- C.
Both I and III
- D.
Both II and III
- E.
Only II
Attempted by 1 students.
Show answer & explanation
Correct answer: B
Concept:
Coded-inequality questions replace real comparisons with symbols, so first decode every symbol into a relation, then chain relations along a common term. Two relations combine only when their directions agree: ≥ chains with ≥ (and with =), ≤ chains with ≤ (and with =). A strict result (<, >) appears only if at least one strict link is in the chain; otherwise the most you can claim is ≤ or ≥. An “either–or” holds when two conclusions cover the same pair with complementary operators (e.g. < and ≥) so that one of them is forced to be true even though neither is individually certain.
Decode the symbols:
© = “less than” (<), # = “less than or equal” (≤)
% = “greater than” (>), $ = “greater than or equal” (≥)
@ = “equal to” (=)
Translate the statements:
22 $ 26 $ 35 @ 41 # 29 → 22 ≥ 26 ≥ 35 = 41 ≤ 29
53 $ 29 @ 32 # 38 → 53 ≥ 29 = 32 ≤ 38
Apply — test each conclusion:
Conclusion II (53 ≥ 41): From 41 ≤ 29 and 53 ≥ 29 we get 41 ≤ 29 ≤ 53, hence 53 ≥ 41. This is definitely true.
Conclusion I (35 < 32) and Conclusion III (41 ≥ 29) both concern the same pair, because 35 = 41 and 29 = 32. Chaining 35 = 41 ≤ 29 = 32 gives only 35 ≤ 32 — a non-strict link, so neither 35 < 32 nor 35 ≥ 32 is certain on its own.
But I claims 35 < 32 and III claims 35 ≥ 32: these are exact complements (< versus ≥) on the pair 35–32. Since 35 ≤ 32 is established, exactly one of them must hold, so “either I or III” is true even though neither is individually definite.
Cross-check:
II is definitely true; among I and III neither is certain but one of the pair is forced, so the correct statement is “Only II is true, and either I or III is true.”