Is 4^x less than 5000?
1) 4^(x+1) > 16,000
2) 4^(x+1) = 4^x + 12,288
The correct version of the question appears above.
Statement 1: 4^(x+1) > 16,000
4^x * 4 > 16,000
4^x > 4000.
Since 4^x = 4001 and 4^x = 5001 both satisfy statement 1, insufficient.
Statement 2: 4^(x+1) = 4^x + 12,288
Since statement 2 gives us an equation (as opposed to an inequality), we can solve for the value of 4^x (and for the value of x).
Sufficient.
The correct answer is
B.
Here's the math behind statement 2:
4^(x+1) = 4^x + 12,288
4^(x+1) - 4^x = 12,288
(4^x * 4) - 4^x = 12,288
4^x * (4-1) = 12,288
4^x = 4096
(since 4096 = 4^6, x=6).
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