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if x=0.rstu, where r,s,t,u each represent a non-zero digit

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if x=0.rstu, where r,s,t,u each represent a non-zero digit [#permalink] New post 15 Jun 2008, 23:07
if x=0.rstu, where r,s,t,u each represent a non-zero digit of x, What is the value of x?

(1) r=3s=2t=6u
(2) The product of r and u is equal to product of s and t
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Re: if x=0.rstu [#permalink] New post 15 Jun 2008, 23:12
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statement 1 : r=3s=2t=6u

We know that each of them is a single digit number. The only possible value for u is 1, if we take 2,3.... onwards, r will be 12, 18.....
so u = 1, r=6, s=2, t=3

Suff.

Statement 2:
ru = st
1*8 = 2*4
1*6 = 2*3

Not Suff.

Answer A.
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Re: if x=0.rstu [#permalink] New post 17 Jun 2008, 15:12
excellent..i totally forgot that they were digits..

A it is..

r=6u..and since r and u represent non-ZERO DIGITs..u can only be 1..r=6..

durgesh79 wrote:
statement 1 : r=3s=2t=6u

We know that each of them is a single digit number. The only possible value for u is 1, if we take 2,3.... onwards, r will be 12, 18.....
so u = 1, r=6, s=2, t=3

Suff.

Statement 2:
ru = st
1*8 = 2*4
1*6 = 2*3

Not Suff.

Answer A.
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Re: if x=0.rstu [#permalink] New post 24 Jul 2011, 08:43
1) rstu each is single digit so u can not be greater than 1. If u is greater than 1 then the value will become double digit number (12, 18, 24 etc.) which is not possible.
so, r = 3s = 2t = 6 x 1
r = 6, s = 2, t = 3 and u = 1
statement 1 is sufficient.
2) ru = st give no information about the value. insufficient.

Ans. A
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Re: if x=0.rstu   [#permalink] 24 Jul 2011, 08:43
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if x=0.rstu, where r,s,t,u each represent a non-zero digit

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