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If you are not badly hurt, you don't learn. If you don't learn, you don't grow. If you don't grow, you don't live. If you don't live, you don't know your worth. If you don't know your worth, then what's the point?

Target question:What is the value of (2^p)/(2^q) ? This is a good candidate for rephrasing the target question. Aside: The video below has tips on rephrasing the target question

Take: (2^p)/(2^q) Apply the Quotient law to get: 2^(p - q) This means (2^p)/(2^q) = 2^(p - q) So, in order to evaluate (2^p)/(2^q), all we need to do is determine the value of p - q So,...... REPHRASED target question:What is the value of p-q ?

Statement 1: p = q + 2 Subtract q from both sides to get: p - q = 2 So, the answer to the target question is p - q = 2 Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: pq = 8 There are several values of x and y that satisfy statement 2. Here are two: Case a: p = 8 and q = 1. In this case, the answer to the REPHRASED target question is p - q = 7 Case b: p = 4 and q = 2. In this case, the answer to the REPHRASED target question is p - q = 2 Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Modifying the question: What is the value of \(\frac{2^p}{2^q}= 2^{p-q}\)? So, we need to be able to find the value of \(p-q.\)

Thus, condition 1), which is equivalent to \(p – q = 2\), is sufficient.

Condition 2): If \(p =4\) and \(q = 2\), then \(\frac{2^p}{2^q}= 2^{p-q} = 2^2 = 4.\) If \(p =8\) and \(q = 1\), then \(2^p/2^q= 2^{p-q} = 2^7 = 128.\) Since we don’t have a unique solution, condition 2) is not sufficient.

Therefore, A is the answer. Answer: A
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