In the following questions assuming the given statement to be true, find which…
2022
In the following questions assuming the given statement to be true, find which of the conclusion(s) among given conclusions is/are definitely true and then give your answers accordingly.
Statements: Q ≥ W > X > Z; E > Z; E > C
Conclusions:
I. C < Q
II. E ≤ W
- A.
Only I is true.
- B.
Only II is true.
- C.
Either I or II is true.
- D.
Neither I nor II is true.
- E.
Both I and II are true.
Attempted by 2 students.
Show answer & explanation
Correct answer: D
Concept
In coded-inequality problems, a conclusion is definitely true only when an unbroken chain of inequalities links the two variables with consistent directions. If no chain connects them, or two variables merely share a common term that each exceeds (or that exceeds each), the relation between those two variables stays undetermined.
Applying it to the statements
List the chains: from Q ≥ W > X > Z we get Q ≥ W, W > X, X > Z, and by transitivity Q > Z and W > Z. Separately, E > Z and E > C.
Test C < Q: C appears only in E > C, while Q appears only in Q > Z. The only common variable in reach is Z, but C is not tied to Z by any inequality, so no chain joins C and Q — their order is undetermined, hence C < Q is not definitely true.
Test E ≤ W: E is linked through E > Z and E > C; W is linked through W > X > Z, giving W > Z. Both E and W exceed the common term Z, but two values that each exceed the same term have no forced order between themselves — so E ≤ W is undetermined and not definitely true.
Cross-check on the Either-Or rule
The either-or verdict arises only when the two conclusions form a complementary pair on the SAME two variables (for example A > B and A ≤ B). Here the conclusions involve different variable pairs — C,Q and E,W — so an either-or relationship cannot exist.
Result
Both conclusions are undetermined, so neither is definitely true.