idontknowwhy94 wrote:
If x , p and q are positive integers , then \(x^{p} / x ^ {q}\) = ?
1. p = q + 5
2. \(x^{q}\) = 32
NOTE: I have edited my response to reflect the new wording of the question
Target question: What is the value of \(x^{p} / x ^ {q}\)?This is a good candidate for
rephrasing the target question.
Since the base is x in both the numerator and denominator, we can apply the Quotient Law to get: x^(p-q).
So, we can REPHRASE the target question....
REPHRASED target question: What is the value of x^(p-q)?Aside: Here’s a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100 Given: x , p and q are positive integers Statement 1: p = q + 5 Rearrange to get: p - q = 5
Great! So, the exponent in x^(p-q) must equal 5.
However, we don't know the value of x, so there's no way to determine the value of
x^(p-q)Since we cannot answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x^q = 32Since there's no information about q, there's no way to determine the value of
x^(p-q)Since we cannot answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that p = q + 5
Statement 2 tells us that x^q = 32. Since we're told that x and p are positive integers, there are only 2 possible cases to consider: x = 2, q = 5 AND x = 32 and q = 1
Case a: If x = 2, q = 5, then (from statement 1), we know that p = 10. In this case,
x^(p-q) = 2^(10-5) = 32Case b: If x = 32, q = 1, then (from statement 1), we know that p = 6. In this case,
x^(p-q) = 32^(6-1) = some BIG numberSince we cannot answer the
REPHRASED target question with certainty, the combined statements are NOT SUFFICIENT
Answer: