Direction: Each of the following questions is followed by two Stateme...
From Statement I, b can be either negative or positive. Also, from Statement II, b can be either negative or positive, so Statements 3 and II cannot be combined.
Hence, we cannot find out the answer.
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Direction: Each of the following questions is followed by two Stateme...
Question:
Is b positive?
Statements:
i. a b is positive.
ii. a ~ b is positive.
Answer:
The answer is option E, if both statements I and II together are not sufficient to answer the question.
Explanation:
We need to determine whether b is positive or not. Let's analyze the given statements individually.
Statement I: a b is positive
This statement only tells us that the difference between a and b is positive, but we cannot determine the sign of b from this information alone. For example, if a = 5 and b = 2, then a b is positive, but b is negative. Hence, Statement I alone is not sufficient to answer the question.
Statement II: a ~ b is positive
The symbol ~ represents the absolute value of a number. Hence, this statement tells us that the absolute value of the difference between a and b is positive. But again, we cannot determine the sign of b from this information alone. For example, if a = 5 and b = -2, then a ~ b is positive, but b is negative. Hence, Statement II alone is not sufficient to answer the question.
Combined Statements:
From Statement I and II, we know that the difference between a and b is positive, and the absolute value of the difference between a and b is positive. But we still cannot determine the sign of b from this information alone. For example, if a = 5 and b = -2 or a = -5 and b = -8, both statements would still hold true. Hence, both statements together are not sufficient to answer the question.
Conclusion:
Therefore, the answer is option E, if both statements I and II together are not sufficient to answer the question.
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