Bunuel wrote:

If m is an integer, is \(7^m > 1000\)?

(1) \(7^{(m-2)} = 7^m - 1000\)

(2) \(7^{(m + 1)} > 1000\)

question: is (7^m-1000)>0

(1) tells us 7^m/7^2 = 7^m - 1000

for any integer value LHS will remain + i.e. greater than 0..hence sufficient

(2) 7^m - 1000/7 >0

7^m - ~142 > 0

for m = 3, 7^m-1000 is negative

for m = 4, 7^m-1000 is positive

Hence not sufficient

A

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