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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, 11:26

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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, 15:29

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, 22:42

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?

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

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10 Nov 2014, 02:14

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Expert's post

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. _________________

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

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15 Nov 2015, 04:11

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