Each of the following questions is followed by two statements 1 If either of the statements I or II ...........

Math and Mental Ability Data Sufficiency

Each of the following questions is followed by two statements.

1.If either of the statements I or II alone but not the other is sufficient to answer the question.

2.If both the statements I or II alone are sufficient to answer the question.

3.If questions can be answered with the help of both statements together, but not with the help of either statement alone.

4.If question cannot be answered unless more information is provided.

Find x and y such that 7 is the greatest integer that divides both x and y exactly.

I. 294 is the smallest number that is divisible by both x and y.

II.x + y is divisible by 7

- First, let's break down the problem: We need to determine \( x \) and \( y \), with 7 being the greatest integer that divides both exactly.

- Statement I: 294 is the smallest number divisible by both \( x \) and \( y \).

- This tells us the least common multiple (LCM) of \( x \) and \( y \) is 294, but not their greatest common divisor (GCD).

- Statement II: \( x + y \) is divisible by 7.

- This doesn't help determine the values of \( x \) and \( y \), but just confirms their sum is a multiple of 7.

- Assessing sufficiency:

- Neither statement I nor statement II alone provides enough information.

- Even together, they don’t specify \( x \) and \( y \) due to multiple possibilities that satisfy both conditions.

- Option Analysis:

- 1: Incorrect — Neither statement alone is sufficient.

- 2: Incorrect — Both statements together still lack information.

- 3: Incorrect — Both statements together do not specify \( x \) and \( y \).

- 4: Correct — More information is needed to solve fully.

- Answer: Option 4: The question cannot be answered unless more information is provided.

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