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The decimal representation of x

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The decimal representation of x

by alex.gellatly » Sat Jul 28, 2012 11:31 pm
In the decimal representation of x, where 0,x,1, what is the tenths digit if x is nonzero?

1. 16x is an integer
2. 8x is an integer

OA is B, but I got E... could someone please explain? Thanks
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by tutorphd » Sat Jul 28, 2012 11:53 pm
The way the problem is stated, I get E also. There must be a typo, either in the problem or in the answer.
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by Anurag@Gurome » Sun Jul 29, 2012 8:26 pm
alex.gellatly wrote:In the decimal representation of x, where 0,x,1, what is the tenths digit if x is nonzero?

1. 16x is an integer
2. 8x is an integer

OA is B, but I got E... could someone please explain? Thanks
(1) If x = 1/2 = 0.5, then tenths digit of x = 5
If x = 1/16 = 0.0625, then tenths digit of x = 0
So, the tenths digit of x may or may not be zero. No unique answer.
So, (1) is NOT SUFFICIENT.

(2) If x = 1/2 = 0.5, then tenths digit of x = 5, which is non-zero.
If x = 1/8 = 0.125, then tenths digit of x = 1, which is non-zero. This implies that all numbers in the tenth place between 0 < x < 1 will always have a non-zero integer.
So, (2) is SUFFICIENT.

The correct answer is B.
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by alex.gellatly » Mon Aug 06, 2012 10:22 pm
Anurag@Gurome wrote:
alex.gellatly wrote:In the decimal representation of x, where 0,x,1, what is the tenths digit if x is nonzero?

1. 16x is an integer
2. 8x is an integer

OA is B, but I got E... could someone please explain? Thanks
(1) If x = 1/2 = 0.5, then tenths digit of x = 5
If x = 1/16 = 0.0625, then tenths digit of x = 0
So, the tenths digit of x may or may not be zero. No unique answer.
So, (1) is NOT SUFFICIENT.

(2) If x = 1/2 = 0.5, then tenths digit of x = 5, which is non-zero.
If x = 1/8 = 0.125, then tenths digit of x = 1, which is non-zero. This implies that all numbers in the tenth place between 0 < x < 1 will always have a non-zero integer.
So, (2) is SUFFICIENT.

The correct answer is B.
I don't understand. How can you get B if you clearly have two different numbers for the tenth digit of x. You say x=1/2 (.5) or x=1/8 (.125). So in your two examples the tenths digit could be either 5 or 1. Shouldn't this be insufficient?
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by Anurag@Gurome » Mon Aug 06, 2012 10:27 pm
alex.gellatly wrote: I don't understand. How can you get B if you clearly have two different numbers for the tenth digit of x. You say x=1/2 (.5) or x=1/8 (.125). So in your two examples the tenths digit could be either 5 or 1. Shouldn't this be insufficient?
There is a typo in the question, correct question is: In the decimal representation of x, where 0 < x < 1, is the tenths digit of x nonzero?
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