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If x = 0.rstu, where r, s, t and u each represent a nonzero

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If x = 0.rstu, where r, s, t and u each represent a nonzero digit of x, what is the value of x?

(1) r= 3s = 2t = 6u
(2) The product of r and u is equal to the product of s and t

Please help for the first option. I did not understand the official explanation. OG says u= 1 r could not be 12 ro more because r is nonzero what does nonzero mean?
[Reveal] Spoiler: OA

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x = 0.rstu

What do we know about rstu;
None of these is 0.
r,s,t,u are all different digits selected from(1,2,3,4,5,6,7,8,9)


(1) r= 3s = 2t = 6u

Here; r=6u
If Minimum value for u=1; u=1; r=6*1=6
If u=2; or any digits greater than 1; what happens; u=2; r=6*2=12. r is a single digit variable ranging from 1 to 9 and can't be 12.
Thus we know the only value for u=1; for r=6*1=6
r=2t;6=2t; t=3
r=3s;6=3s;s=2
We know value for each of r,s,t,u.
Sufficient.

(2) r*u=s*t
Possible values; r=1,u=6,s=2,t=3
but it can also be; r=2,u=3,s=1,t=6.
Not sufficient.

Ans: "A"
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Re: QR: 30 Decimal Properties [#permalink]

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Baten80 wrote:
QR: 30 Decimal Properties
If x = 0.rstu, where r, s, t and u each represent a nonzero digit of x, what is the value of x?
(1) r= 3s = 2t = 6u
(2) The product of r and u is equal to the product of s and t

Please help for the first option. I did not understand the official explanation. OG says u= 1 r could not be 12 ro more because r is nonzero what does nonzero mean?


If x = 0.rstu, where r, s, t and u each represent a nonzero digit of x, what is the value of x?

(1) r = 3s = 2t = 6u --> as r, s, t and u each represent a nonzero digit then r, which equals to 6u, to be nonzero digit u must be 1 (if u is 2 or more then r is no more a digit, and u also can not be zero as given that all unknowns are nonzero) --> r=6, s=2, t=3, and u=1 --> x=0.6231. Sufficient.

(2) The product of r and u is equal to the product of s and t --> multiple values of x are possible: x=0.1111, x=2222, x=2211, ... Not sufficient.

Answer: A.
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Re: QR: 30 Decimal Properties [#permalink]

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New post 20 Feb 2011, 10:50
fluke wrote:
x = 0.rstu

What do we know about rstu;
None of these is 0.
r,s,t,u are all different digits selected from(1,2,3,4,5,6,7,8,9)


(1) r= 3s = 2t = 6u

Here; r=6u
If Minimum value for u=1; u=1; r=6*1=6
If u=2; or any digits greater than 1; what happens; u=2; r=6*2=12. r is a single digit variable ranging from 1 to 9 and can't be 12.
Thus we know the only value for u=1; for r=6*1=6
r=2t;6=2t; t=3
r=3s;6=3s;s=2
We know value for each of r,s,t,u.
Sufficient.

(2) r*u=s*t
Possible values; r=1,u=6,s=2,t=3
but it can also be; r=2,u=3,s=1,t=6.
Not sufficient.

Ans: "A"


So that r is single digit number! [My problem was in here.]
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x = 0.rstu

1. Sufficient

r s t u

r r/3 r/2 r/6

0 0

6 1

these are only possible values of r that satisfy the conditions here except the 0 as r,s,t,u are all positive

=> r can only be 6
=> r s t u

r r/3 r/2 r/6
6 2 3 1

2. Not sufficient

as different values satisfy the given condition

ru =st
1(4) = 4(1)
1(2) = 2(1)

Answer is A.
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New post 01 May 2012, 02:14
2 very good approaches to solve.
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Re: QR: 30 Decimal Properties [#permalink]

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New post 12 Dec 2012, 20:51
Bunuel wrote:
Baten80 wrote:
QR: 30 Decimal Properties
If x = 0.rstu, where r, s, t and u each represent a nonzero digit of x, what is the value of x?
(1) r= 3s = 2t = 6u
(2) The product of r and u is equal to the product of s and t

Please help for the first option. I did not understand the official explanation. OG says u= 1 r could not be 12 ro more because r is nonzero what does nonzero mean?


If x = 0.rstu, where r, s, t and u each represent a nonzero digit of x, what is the value of x?

(1) r = 3s = 2t = 6u --> as r, s, t and u each represent a nonzero digit then r, which equals to 6u, to be nonzero digit u must be 1 (if u is 2 or more then r is no more a digit, and u also can not be zero as given that all unknowns are nonzero) --> r=6, s=2, t=3, and u=1 --> x=0.6231. Sufficient.

(2) The product of r and u is equal to the product of s and t --> multiple values of x are possible: x=0.1111, x=2222, x=1221, ... Not sufficient.

Answer: A.


if u is 2 or more then r is no more a digit,

Bunuel , I did not understand the above.. Please explain
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Re: QR: 30 Decimal Properties [#permalink]

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Sachin9 wrote:
Bunuel wrote:
Baten80 wrote:
QR: 30 Decimal Properties
If x = 0.rstu, where r, s, t and u each represent a nonzero digit of x, what is the value of x?
(1) r= 3s = 2t = 6u
(2) The product of r and u is equal to the product of s and t

Please help for the first option. I did not understand the official explanation. OG says u= 1 r could not be 12 ro more because r is nonzero what does nonzero mean?


If x = 0.rstu, where r, s, t and u each represent a nonzero digit of x, what is the value of x?

(1) r = 3s = 2t = 6u --> as r, s, t and u each represent a nonzero digit then r, which equals to 6u, to be nonzero digit u must be 1 (if u is 2 or more then r is no more a digit, and u also can not be zero as given that all unknowns are nonzero) --> r=6, s=2, t=3, and u=1 --> x=0.6231. Sufficient.

(2) The product of r and u is equal to the product of s and t --> multiple values of x are possible: x=0.1111, x=2222, x=1221, ... Not sufficient.

Answer: A.


if u is 2 or more then r is no more a digit,

Bunuel , I did not understand the above.. Please explain


For example if u=2, then r=6u=12, but since r is single digit then it cannot be 12, thus u cannot be 2 (or more than 2).

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Re: If x = 0.rstu, where r, s, t and u each represent a nonzero [#permalink]

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New post 26 Feb 2013, 03:59
just plug numbers, nut it is not easy

want to follow this posting
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Re: If x = 0.rstu, where r, s, t and u each represent a nonzero [#permalink]

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New post 27 Feb 2013, 14:29
Hello thangvietnam,

An easy way to understand this is to ask yourself questions on what you could do with the information given.

What we know is that x = 0.rstu, where r, s, t and u each represent a single nonzero digit of x.

Statement 1) tells us that r= 3s = 2t = 6u.

1st question
how do we use this data to establish the value of the complete number? The information at hand gives us a chance to substitute the whole number in terms of r.
From 1) we find that s=r/3, t=r/2, u=r/6
We can substitute these values in x=0.rstu to get the value of x as x=0.(r)(r/3)(r/2)(r/6).

2nd question
What else do we know about these values?
We do know that these are single digit numbers. i.e r,r/3,r/6,r/2 are all single digit number.

3rd question
What is the possible single digit value that r could have so that r,r/3,r/2 and r/6 are all single digit positive numbers.
Since, r/6 has the greatest denominator, let us find a single digit number(r) than can be divided by 6 to give a single digit number. Only possible value is 6. So, we know r=6

Solve for the value of x

x=0.(r)(r/3)(r/2)(r/6)
implies x=0.6231
SUFFICIENT as we found the value of x

Let us consider statement 2)

The product of r and u is equal to the product of s and t
implies r*u=s*t

1st question
Can we find two sets of values for r,u and s,t such that it satisfies the above stated condition

Test with numbers
r=2,u=3,s=6,t=1
r*u=s*t=6
Rearrange the numbers such that
r=3,u=2,s=1,t=6
r*u=s*t=6

We get different numbers. INSUFFICIENT

ANSWER-A

Hope this helps! Let me know in case of any further queries or doubts.

thangvietnam wrote:
just plug numbers, nut it is not easy

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Re: QR: 30 Decimal Properties [#permalink]

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Bunuel wrote:
Baten80 wrote:
QR: 30 Decimal Properties
If x = 0.rstu, where r, s, t and u each represent a nonzero digit of x, what is the value of x?
(1) r= 3s = 2t = 6u
(2) The product of r and u is equal to the product of s and t

Please help for the first option. I did not understand the official explanation. OG says u= 1 r could not be 12 ro more because r is nonzero what does nonzero mean?


If x = 0.rstu, where r, s, t and u each represent a nonzero digit of x, what is the value of x?

(1) r = 3s = 2t = 6u --> as r, s, t and u each represent a nonzero digit then r, which equals to 6u, to be nonzero digit u must be 1 (if u is 2 or more then r is no more a digit, and u also can not be zero as given that all unknowns are nonzero) --> r=6, s=2, t=3, and u=1 --> x=0.6231. Sufficient.

(2) The product of r and u is equal to the product of s and t --> multiple values of x are possible: x=0.1111, x=2222, x=1221, ... Not sufficient.

Answer: A.


Sorry Bunuel, I just wanted to point out a typo in the post above. I think it should be x=1122 or 2211 rather than x=1221.
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Re: QR: 30 Decimal Properties [#permalink]

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New post 16 Sep 2013, 06:26
panda007 wrote:
Bunuel wrote:
Baten80 wrote:
QR: 30 Decimal Properties
If x = 0.rstu, where r, s, t and u each represent a nonzero digit of x, what is the value of x?
(1) r= 3s = 2t = 6u
(2) The product of r and u is equal to the product of s and t

Please help for the first option. I did not understand the official explanation. OG says u= 1 r could not be 12 ro more because r is nonzero what does nonzero mean?


If x = 0.rstu, where r, s, t and u each represent a nonzero digit of x, what is the value of x?

(1) r = 3s = 2t = 6u --> as r, s, t and u each represent a nonzero digit then r, which equals to 6u, to be nonzero digit u must be 1 (if u is 2 or more then r is no more a digit, and u also can not be zero as given that all unknowns are nonzero) --> r=6, s=2, t=3, and u=1 --> x=0.6231. Sufficient.

(2) The product of r and u is equal to the product of s and t --> multiple values of x are possible: x=0.1111, x=2222, x=1221, ... Not sufficient.

Answer: A.


Sorry Bunuel, I just wanted to point out a typo in the post above. I think it should be x=1122 or 2211 rather than x=1221.


Thank you. Please do point out typos if you notice. +1.
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Re: If x = 0.rstu, where r, s, t and u each represent a nonzero [#permalink]

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New post 09 Nov 2014, 21:42
The examples for the S2 included 0.2211, 0.1111...above. That would mean that the digits assigned for r,s,t and u repeat. Is that allowed? The question says 'each represent a nonzero digit of x', so that does leave open the possibility for repetition, i guess. But when various variables are assigned, does that not mean that they are all different?
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Re: If x = 0.rstu, where r, s, t and u each represent a nonzero [#permalink]

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New post 10 Nov 2014, 01:14
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deeuk wrote:
The examples for the S2 included 0.2211, 0.1111...above. That would mean that the digits assigned for r,s,t and u repeat. Is that allowed? The question says 'each represent a nonzero digit of x', so that does leave open the possibility for repetition, i guess. But when various variables are assigned, does that not mean that they are all different?


r, s, t and u each represent a nonzero digit means that neither is 0, it does not mean that they are distinct.

Generally, unless it is explicitly stated otherwise, different variables CAN represent the same number.
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Re: If x = 0.rstu, where r, s, t and u each represent a nonzero [#permalink]

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New post 18 Nov 2016, 21:25
Great Question
Here x=0.rstu
As r,s,t,u are non zero digits of a number => they can take any value of the following set => {1,2,3,...9}
In order to get x we need r,s,t,u

Lets look at statement 1 =>
here r=3s=2t=6u
Examine it closely as they are all non zero digits => r must be divisible by 6 as r=6u hence r=6
so x=0.6231
Hence Sufficient
NOTE=> If the question had not mentioned that the digits are non zero then we could say x ay be 0.0000 too.

Statement 2
Here x can be 0.3333 or 0.2222 or 0.2121 etc
Hence clearly this statement is insufficient to arrive at a unique answer.

Hence A
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Re: If x = 0.rstu, where r, s, t and u each represent a nonzero   [#permalink] 18 Nov 2016, 21:25
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If x = 0.rstu, where r, s, t and u each represent a nonzero

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