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If x = 0.rstu, where r, s, t and u each represent a nonzero
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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?
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Re: QR: 30 Decimal Properties
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20 Feb 2011, 11:36
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
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20 Feb 2011, 11:35
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
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20 Feb 2011, 11:50
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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Re: QR: 30 Decimal Properties
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20 Feb 2011, 11:55
Baten80 wrote: So that r is single digit number! [My problem was in here.] It's given in the stem: "x = 0.rstu, where r, s, t and u each represent a nonzero digit of x..."
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Re: QR: 30 Decimal Properties
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20 Feb 2011, 12:10
thx bunnel understand.
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Re: QR: 30 Decimal Properties
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03 Jun 2011, 18:33
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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Re: If x = 0.rstu, where r, s, t and u each represent a nonzero
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01 May 2012, 03:14
2 very good approaches to solve.
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Re: QR: 30 Decimal Properties
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12 Dec 2012, 21:51
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
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13 Dec 2012, 03:47
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). Similar questions to practice: ifthethreedigitintegerxabcwhereabandc131904.htmlify0jkmnwherejkmandneachrepresentanonzero130018.htmlifx0abcdwhereabcanddeachrepresentanonzero127399.htmlwhatisthetwodigitpositiveintegerwhosetensdigitisa128766.html
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Re: If x = 0.rstu, where r, s, t and u each represent a nonzero
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26 Feb 2013, 04:59
just plug numbers, nut it is not easy
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Re: If x = 0.rstu, where r, s, t and u each represent a nonzero
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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 ANSWERA 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
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16 Sep 2013, 07:24
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
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16 Sep 2013, 07:26
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
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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?



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Re: If x = 0.rstu, where r, s, t and u each represent a nonzero
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10 Nov 2014, 02:14
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
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18 Nov 2016, 22:25
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
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Re: If x = 0.rstu, where r, s, t and u each represent a nonzero
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