Given below is a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. You should use the given data and your knowledge of Mathematics to choose between the possible answers.
James looked at the clock on wall. The hour and minute hands of the clock are perpendicular to each other. What is the time now?
I. After 6 hours, the hour and minute hands of the clock will be perpendicular again.
II. After 3 hours, the hands of the clock will be along a straight line.
Solution
Correct Answer: Option D
From statement I:
After 6 hours, the hour and minute hands of the clock will be perpendicular again.
⇒ Present time can be 3 o’clock or 9 o’clock. But it cannot be uniquely determined.
∴ Statement I alone is not sufficient to answer the question.
From statement II:
After 3 hours, the hands of the clock will be along a straight line.
⇒ Present time can be 3 o’clock or 9 o’clock. But it cannot be uniquely determined.
Note: Minute and Hour hands are in straight line at both 12 o’clock (in same directions) and 6 o’clock (in opposite direction).
∴ Statement II alone is not sufficient to answer the question.
From statements I and II together:
After 6 hours, the hour and minute hands of the clock will be perpendicular again. After 3 hours, the hands of the clock will be along a straight line.
⇒ Here again, present time can be 3 o’clock or 9 o’clock, even if both informations are used.
Essentially, both statement I and II provide equivalent information.
∴ Even using both the statements together, we cannot answer the given question.
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