Read the following question and decide which of the given statements is/are sufficient.

Question:

Is Y > 0?

Statements:

1. X + Y > 0

2. X - Y > 0

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RRB ALP CBT I 30 Aug 2018 Shift 3 Official Paper
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  1. Both 1 and 2 together are sufficient to answer the question.
  2. 1 alone is sufficient while 2 alone is not sufficient to answer the question.
  3. Neither 1 nor 2 is sufficient to answer the question.
  4. 2 alone is sufficient while 1 alone is not sufficient to answer the question.

Answer (Detailed Solution Below)

Option 3 : Neither 1 nor 2 is sufficient to answer the question.
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Detailed Solution

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The correct answer is indeed option 3) Neither 1 nor 2 is sufficient to answer the question. Here's the explanation:

Statement 1: X + Y > 0

This statement only tells us that the sum of X and Y is greater than 0. However, it doesn't give us any information about the value of Y alone, so we can't determine whether Y is greater than 0. For example, if X = -5 and Y = 6, then X + Y = 1, which is greater than 0, but Y alone is greater than 0.

Statement 2: X - Y > 0

This statement tells us that the difference between X and Y is greater than 0. However, it still doesn't give us any information about the value of Y alone. For example, if X = 10 and Y = 5, then X - Y = 5, which is greater than 0, but Y alone is greater than 0.

Combining both statements, we have:

X + Y > 0 and X - Y > 0

Adding these inequalities, we get:

2X > 0

Therefore, X > 0.

However, we still cannot determine whether Y is greater than 0 or not, since we don't have enough information about the value of Y.

Hence, neither statement alone nor both together are sufficient to answer the question "Is Y > 0?".

The correct answer is option 3) Neither 1 nor 2 is sufficient to answer the question.

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