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0 < x < 1. Is the tenth digit of x nonzero? (1) 16 * x

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0 < x < 1. Is the tenth digit of x nonzero? (1) 16 * x [#permalink] New post 26 Nov 2005, 07:28
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15. 0 < x < 1. Is the tenth digit of x nonzero?

(1) 16 * x is integer.
(2) 8 * x is integer.
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Auge um Auge, Zahn um Zahn :twisted: !


Last edited by gamjatang on 01 Dec 2005, 00:46, edited 1 time in total.
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Re: DS - (AG) Tenth digit of X [#permalink] New post 26 Nov 2005, 20:31
gamjatang wrote:
15. 0 < x < 1. Is the tenth digit of x nonzero?

(1) 16 * x is integer.
(2) 8 * x is integer.


let x= 0.abc.....
Consider (2) first: since 0<x<1 and 8*x is integer -----> 8*x>=1 ( 8*x can be 0 coz x>0 )
then, we have 1=< 8*x <10*x = a.bc.... ---->a can't be 0 ---->suff

(1) consider 16*x=1 ( the smallest one) ...x=0.0625
0.5*16 = 8 ---> a can be nonzero and zero -->insuff.

B it is.
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Re: DS - (AG) Tenth digit of X [#permalink] New post 27 Nov 2005, 07:13
laxieqv wrote:
gamjatang wrote:
15. 0 < x < 1. Is the tenth digit of x nonzero?

(1) 16 * x is integer.
(2) 8 * x is integer.


let x= 0.abc.....
Consider (2) first: since 0<x<1 and 8*x is integer -----> 8*x>=1 ( 8*x can be 0 coz x>0 )
then, we have 1=< 8*x <10*x = a.bc.... ---->a can't be 0 ---->suff

(1) consider 16*x=1 ( the smallest one) ...x=0.0625
0.5*16 = 8 ---> a can be nonzero and zero -->insuff.

B it is.


I am also speechless here!

Nice job, laxie!

The OA is (B).
_________________

Auge um Auge, Zahn um Zahn :twisted: !

Re: DS - (AG) Tenth digit of X   [#permalink] 27 Nov 2005, 07:13
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0 < x < 1. Is the tenth digit of x nonzero? (1) 16 * x

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