December 13, 2018 December 13, 2018 08:00 AM PST 09:00 AM PST What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL. December 14, 2018 December 14, 2018 09:00 AM PST 10:00 AM PST 10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.
Author 
Message 
TAGS:

Hide Tags

Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 521

If x = 0.rstu, where r, s, t and u each represent a nonzero
[#permalink]
Show Tags
20 Feb 2011, 10:26
Question Stats:
73% (01:31) correct 27% (02:04) wrong based on 712 sessions
HideShow timer Statistics
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?
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Collections: PSof OG solved by GC members: http://gmatclub.com/forum/collectionpswithsolutionfromgmatclub110005.html DS of OG solved by GC members: http://gmatclub.com/forum/collectiondswithsolutionfromgmatclub110004.html 100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmatprepproblemcollections114358.html Collections of work/rate problems with solutions http://gmatclub.com/forum/collectionsofworkrateproblemwithsolutions118919.html Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixtureproblemswithbestandeasysolutionsalltogether124644.html




Math Expert
Joined: 02 Sep 2009
Posts: 51121

Re: QR: 30 Decimal Properties
[#permalink]
Show Tags
20 Feb 2011, 10:36
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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Retired Moderator
Joined: 20 Dec 2010
Posts: 1820

Re: QR: 30 Decimal Properties
[#permalink]
Show Tags
20 Feb 2011, 10:35
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"
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings




Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 521

Re: QR: 30 Decimal Properties
[#permalink]
Show Tags
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.]
_________________
Collections: PSof OG solved by GC members: http://gmatclub.com/forum/collectionpswithsolutionfromgmatclub110005.html DS of OG solved by GC members: http://gmatclub.com/forum/collectiondswithsolutionfromgmatclub110004.html 100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmatprepproblemcollections114358.html Collections of work/rate problems with solutions http://gmatclub.com/forum/collectionsofworkrateproblemwithsolutions118919.html Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixtureproblemswithbestandeasysolutionsalltogether124644.html



Math Expert
Joined: 02 Sep 2009
Posts: 51121

Re: QR: 30 Decimal Properties
[#permalink]
Show Tags
20 Feb 2011, 10:55



Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 521

Re: QR: 30 Decimal Properties
[#permalink]
Show Tags
20 Feb 2011, 11:10



Director
Joined: 01 Feb 2011
Posts: 659

Re: QR: 30 Decimal Properties
[#permalink]
Show Tags
03 Jun 2011, 17:33
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.



Manager
Joined: 17 Sep 2011
Posts: 147

Re: If x = 0.rstu, where r, s, t and u each represent a nonzero
[#permalink]
Show Tags
01 May 2012, 02:14
2 very good approaches to solve.
_________________
_________________ Giving +1 kudos is a better way of saying 'Thank You'.



Senior Manager
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 449
Location: India
GMAT 1: 640 Q43 V34 GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)

Re: QR: 30 Decimal Properties
[#permalink]
Show Tags
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
_________________
hope is a good thing, maybe the best of things. And no good thing ever dies.
Who says you need a 700 ?Check this out : http://gmatclub.com/forum/whosaysyouneeda149706.html#p1201595
My GMAT Journey : http://gmatclub.com/forum/endofmygmatjourney149328.html#p1197992



Math Expert
Joined: 02 Sep 2009
Posts: 51121

Re: QR: 30 Decimal Properties
[#permalink]
Show Tags
13 Dec 2012, 02:47
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
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Director
Joined: 08 Jun 2010
Posts: 866

Re: If x = 0.rstu, where r, s, t and u each represent a nonzero
[#permalink]
Show Tags
26 Feb 2013, 03:59
just plug numbers, nut it is not easy
want to follow this posting



Manager
Joined: 24 Sep 2012
Posts: 83
Location: United States
Concentration: Entrepreneurship, International Business
GPA: 3.2
WE: Education (Education)

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



Intern
Joined: 09 Oct 2012
Posts: 11

Re: QR: 30 Decimal Properties
[#permalink]
Show Tags
16 Sep 2013, 06:24
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.



Math Expert
Joined: 02 Sep 2009
Posts: 51121

Re: QR: 30 Decimal Properties
[#permalink]
Show Tags
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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 23 Aug 2014
Posts: 34
GMAT Date: 11292014

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



Math Expert
Joined: 02 Sep 2009
Posts: 51121

Re: If x = 0.rstu, where r, s, t and u each represent a nonzero
[#permalink]
Show Tags
10 Nov 2014, 01:14
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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Current Student
Joined: 12 Aug 2015
Posts: 2627

Re: If x = 0.rstu, where r, s, t and u each represent a nonzero
[#permalink]
Show Tags
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
_________________
MBA Financing: INDIAN PUBLIC BANKS vs PRODIGY FINANCE! Getting into HOLLYWOOD with an MBA! The MOST AFFORDABLE MBA programs!STONECOLD's BRUTAL Mock Tests for GMATQuant(700+)AVERAGE GRE Scores At The Top Business Schools!



NonHuman User
Joined: 09 Sep 2013
Posts: 9129

Re: If x = 0.rstu, where r, s, t and u each represent a nonzero
[#permalink]
Show Tags
09 Jul 2018, 02:09
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If x = 0.rstu, where r, s, t and u each represent a nonzero &nbs
[#permalink]
09 Jul 2018, 02:09






