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

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20 Feb 2011, 10:26

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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?

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.

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.

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.]
_________________

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
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

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).

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

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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.

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.

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.
_________________

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

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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?

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.
_________________

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

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15 Nov 2015, 03:11

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

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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.

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