SOLUTION

We are given:

• Two numbers, \(3x\) and \(4y\).

We need to find:

• Arithmetic mean of \(3x\) and \(4y\).

o Thus, we need to find the value of \(\frac{(3x + 4y)}{2}\).

Let us analyze both the statements one by one.

Statement-1: \(\frac{y}{6}\)-\(\frac{x}{8}\)=\(\frac{2}{3}\)Simplifying the above equation, we can write:

• \(\frac{(8y-6x)}{48}\)=\(\frac{2}{3}\)

• \(\frac{(4y-3x)}{16}\)=\(1\)

• \(4y-3x\)=\(16\)

Since we cannot find the value of \((3x+4y)\) from the above expression, hence statement 1 is not sufficient to answer the question.

Statement-2: \(\frac{y}{6}\) + \(\frac{x}{8}\) = \(\frac{5}{3}\)Simplifying the above equation, we can write:

• \(\frac{(8y+6x)}{48}\)=\(\frac{2}{3}\)

• \(\frac{(4y+3x)}{16}\)=\(1\)

• \(4y+3x\)=\(16\)

Since we are getting a unique value of \(4y+3x\). Hence, we can easily find the value of \(\frac{(4y+3x)}{2}\) from this information.

Therefore, Statement 2 ALONE is sufficient to answer the question.Answer: B
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