bajjuri6 wrote:In the decimal representation of x, where 0 < x < 1, is the tenths digit of x nonzero?
(1) 16x is an integer.
(2) 8x is an integer.
1/10 = .1.
Any positive fraction 1/10 or greater will have a nonzero tenths digit.
Question rephrased: Is x ≥ 1/10?
Statement 1: 16x is an integer.
It's possible that x = 1/16, since 16(1/16) = 1.
It's possible that x = 1/8, since 16(1/8) = 2.
Since in the first case x < 1/10 and in the second case x > 1/10, INSUFFICIENT.
Statement 2: 8x is an integer.
Since x is positive, 8x is positive.
The smallest positive integer is 1. Thus:
8x ≥ 1
x ≥ 1/8.
Since x ≥ 1/8, we know that x > 1/10.
SUFFICIENT.
The correct answer is
B.
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