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.
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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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(1) 16x is an integer.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.
If 16x = 1, then x = 1/16 = 0.06; here tenths place = 0
If 16x = 8, then x = 8/16 = 1/2 = 0.5; here tenths place = 5
No definite answer; NOT sufficient.
(2) 8x is an integer.
If 8x = 1 (this is the minimum value), x = 1/8 = 0.12; here tenths place = 1.
We took the minimum possible value of 8x in the above example and we get the tenths place as 1, which implies that tenths place will never be zero; SUFFICIENT.
The correct answer is B.
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