Direction: Study the information given carefully and answer the question given below. ‘A # B’ means ‘A is either smaller than or equal to B.’
‘A $ B’ means ‘A is neither smaller than nor equal to B.’
‘A + B’ means ‘A is either greater than or equal to B.’
‘A @ B’ means ‘A is neither greater than nor equal to B.’
‘A * B’ means ‘A is neither greater than nor smaller than B.’
Statement: U @ V + W # Y * X; V + P $ Q Conclusion: I) P # X II) Q @ U III) W # X
Solving Coding Decoding Inequalities
This question involves decoding a set of symbols representing inequality relations and then evaluating given conclusions based on a statement provided in the same symbolic language.
Decoding the Symbols
Let's first understand what each symbol represents in terms of standard mathematical inequalities:
| Symbol | Meaning | Standard Inequality |
|---|---|---|
| # | either smaller than or equal to | ≤ |
| $ | neither smaller than nor equal to (i.e., greater than) | > |
| + | either greater than or equal to | ≥ |
| @ | neither greater than nor equal to (i.e., smaller than) | < |
| * | neither greater than nor smaller than (i.e., equal to) | = |
Decoding the Statement
The given statement is: U @ V + W # Y * X; V + P $ Q
Let's decode each part using the standard inequality symbols:
U @ Vmeans U < VV + Wmeans V ≥ WW # Ymeans W ≤ YY * Xmeans Y = XV + Pmeans V ≥ PP $ Qmeans P > Q
Combining the Statement
Now, let's combine the decoded relations into a single chain or set of relations:
From the first part: U < V ≥ W ≤ Y = X
From the second part: V ≥ P > Q
We can link these through V:
U < V ≥ W ≤ Y = X
Q < P ≤ V > U (rewriting the second part starting from Q for clarity when evaluating Conclusion II)
Evaluating the Conclusions
We will now check each conclusion based on the combined statement.
Conclusion I: P # X
Decoding this, we get P ≤ X.
From the combined statement, we have the path connecting P and X: P ≤ V ≥ W ≤ Y = X.
Tracing from P to X: P ≤ V and V ≥ W ≤ Y = X.
The relation between P and X depends on the relationship between P and W (or Y or X) via V. Since we have opposing signs (`≤` and `≥`) between P and W via V (i.e., `P ≤ V ≥ W`), a definite relation between P and W cannot be established. Therefore, a definite relation between P and X cannot be established from the given statement.
Conclusion I (P ≤ X) does not definitively follow.
Conclusion II: Q @ U
Decoding this, we get Q < U.
From the combined statement, we have the path connecting Q and U: Q < P ≤ V > U.
Tracing from Q to U: Q < P and P ≤ V and V > U.
Combining these, we get Q < P ≤ V > U. Similar to Conclusion I, there are opposing signs (`≤` and `>`) between Q and U via P and V (i.e., `P ≤ V > U`). This indicates that a definite relation between Q and U cannot be established.
For example, if Q=1, P=2, V=3, U=2.5, then Q < P ≤ V > U holds, and Q < U (1 < 2.5) holds. However, if Q=1, P=2, V=3, U=0.5, then Q < P ≤ V > U holds, but Q > U (1 > 0.5).
Conclusion II (Q < U) does not definitively follow.
Conclusion III: W # X
Decoding this, we get W ≤ X.
From the first part of the statement, we have the chain: U < V ≥ W ≤ Y = X.
Focusing on the part involving W and X: W ≤ Y = X.
Since W ≤ Y and Y = X, it directly follows that W ≤ X.
Conclusion III (W ≤ X) definitively follows from the statement.
Summary of Conclusions
- Conclusion I (P ≤ X): Does not follow.
- Conclusion II (Q < U): Does not follow.
- Conclusion III (W ≤ X): Follows.
Therefore, only Conclusion III follows.
Important Questions from Coded Inequalities
In a certain code language, ‘TERRAIN’ is written as ‘VETTAIP’ and ‘TRAFFIC’ is written as ‘VTHAHIE’. How will ‘MOTOR’ be written in that language?
Select the option that is related to the third word in the same way as the second word is related to the first word. (The words must be considered as meaningful English words and must not be related to each other based on the number of letters/number of consonants/vowels in the word) Pig : Piglets :: Deer : ?
In the question two statements are given, followed by two conclusions, I and II. You have to consider the statements to be true even if it seems to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements.
Statements:
P = U < M < K ≤ I > N
Conclusions:
I. N ≥ K
II. I > PStatements:
P # B $ T; R & B $ S; L % R # Q
Conclusions:
I. P # Q
II. L & Q
III. T % S
IV. P # S
Statement:
R $ W % P; N & W # S; J % T @ N; K & T
Conclusions:
I. N # J
II. P # S
III. R @ P
IV. W $ K
