Abhijit K wrote:
If n is a positive integer, what is the hundreds digit of 30^n?
(1) 30^n > 1000
(2) n is the multiple of 3.
If n=1, then 30^n = 30¹ = 30.
If n=2, then 30^n = 30² = 900.
If n=3, then 30^n = 30³ = 27000.
If n=4, then 30^n = 30� = 810000.
If n=5, then 30^n = 30� = 24300000.
The cases in red indicate the following:
If n≥3, the hundreds digit of 30^n is 0.
Statement 1: 30^n > 1000
Only the cases in red satisfy the constraint that 30^n > 1000, implying that n≥3.
Since n≥3, the hundreds digit of 30^n is 0.
SUFFICIENT.
Statement 2: n is a multiple of 3
Since n≥3, the hundreds digit of 30^n is 0.
SUFFICIENT.
The correct answer is
D.
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