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First, let's rewrite the target question as "Is p+q > 2(3^m + 4^m) ?"
Originally Posted by Sumon1
Statement 1: If we replace p and q with their respective values, we can reword the target question as:
Is 3^(m+1)+2^(2m+1) > 2(3^m + 4^m) ? (do we have sufficient information to answer this question? let's find out)
To simplify the right-hand-side, first recognize that 4^m = (2^2)^m = 2^2m
So, we can reword the target question as: Is 3^(m+1)+2^(2m+1) > 2(3^m + 2^2m) ?
If we expand the right-hand-side, we get: Is 3^(m+1)+2^(2m+1) > (2)3^m + 2^(2m+1)?
At this point, we can subtract 2^(2m+1) from both sides to get: Is 3^(m+1) > (2)3^m?
Now, if we divide both sides by 3^m, we get: Is 3 > 2?
Yes, 3 is greater than 2.
Since we can answer the reworded target question with certainty, statement 1 is sufficient.
Statement 2: Since we have no information about p and q, we cannot answer the target questions. So, statement 2 is not sufficient and the answer is