A question is followed by two statements numbered (I) and (II). You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and decide the appropriate answer. Question: Among 5 poles, W, O, K, G and Y each having a different height, which pole is the shortest? Statements: I. Y is taller than K. II. G is taller than Y. W is only shorter than one pole.
Both statements I and II together are NOT sufficient to answer the question
Statement I alone gives only Y > K; nothing is known about W, O and G, so the shortest pole cannot be found from I alone.
Statement II alone gives G > Y and W as the second tallest pole. The positions of O and K are unknown, so II alone is not sufficient.
Combining I and II: G > Y > K, and W is shorter than exactly one pole. That pole cannot be Y or K, because G (and Y) would then also be taller than W. So the one pole taller than W is either G or O, and W is second in every case. If O is the tallest, the order is O, W, G, Y, K; if G is the tallest, O can take any of the three places below W.
| Case | Order (tallest to shortest) | Shortest |
| O tallest | O, W, G, Y, K | K |
| O third | G, W, O, Y, K | K |
| O fourth | G, W, Y, O, K | K |
| O fifth | G, W, Y, K, O | O |
Since the shortest pole can be K or O, even both statements together do not give a unique answer.
Check: every listed order keeps Y taller than K, G taller than Y and exactly one pole (G or O) taller than W, yet the last place changes between K and O – so the data are insufficient.
Hence, Both statements I and II together are NOT sufficient to answer the question.
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