If x = 0.rstu, where r, s, t and u each represent a nonzero : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 28 Feb 2017, 00:10

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 651
Followers: 43

Kudos [?]: 893 [3] , given: 39

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

### Show Tags

20 Feb 2011, 10:26
3
KUDOS
13
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

73% (02:12) correct 27% (01:28) wrong based on 545 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?
[Reveal] Spoiler: OA

_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2021
Followers: 162

Kudos [?]: 1743 [6] , given: 376

Re: QR: 30 Decimal Properties [#permalink]

### Show Tags

20 Feb 2011, 10:35
6
KUDOS
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"
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 37151
Followers: 7275

Kudos [?]: 96822 [3] , given: 10800

Re: QR: 30 Decimal Properties [#permalink]

### Show Tags

20 Feb 2011, 10:36
3
KUDOS
Expert's post
3
This post was
BOOKMARKED
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.

_________________
Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 651
Followers: 43

Kudos [?]: 893 [0], given: 39

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/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Math Expert
Joined: 02 Sep 2009
Posts: 37151
Followers: 7275

Kudos [?]: 96822 [0], given: 10800

Re: QR: 30 Decimal Properties [#permalink]

### Show Tags

20 Feb 2011, 10:55
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..."
_________________
Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 651
Followers: 43

Kudos [?]: 893 [0], given: 39

Re: QR: 30 Decimal Properties [#permalink]

### Show Tags

20 Feb 2011, 11:10
Director
Joined: 01 Feb 2011
Posts: 755
Followers: 14

Kudos [?]: 119 [2] , given: 42

Re: QR: 30 Decimal Properties [#permalink]

### Show Tags

03 Jun 2011, 17:33
2
KUDOS
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)

Manager
Joined: 17 Sep 2011
Posts: 209
Followers: 0

Kudos [?]: 111 [0], given: 8

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'.

Director
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 547
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Followers: 3

Kudos [?]: 61 [0], given: 562

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.

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/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : http://gmatclub.com/forum/end-of-my-gmat-journey-149328.html#p1197992

Math Expert
Joined: 02 Sep 2009
Posts: 37151
Followers: 7275

Kudos [?]: 96822 [1] , given: 10800

Re: QR: 30 Decimal Properties [#permalink]

### Show Tags

13 Dec 2012, 02:47
1
KUDOS
Expert's post
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.

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:
if-the-three-digit-integer-x-abc-where-a-b-and-c-131904.html
if-y-0-jkmn-where-j-k-m-and-n-each-represent-a-nonzero-130018.html
if-x-0-abcd-where-a-b-c-and-d-each-represent-a-nonzero-127399.html
what-is-the-two-digit-positive-integer-whose-tens-digit-is-a-128766.html
_________________
VP
Joined: 08 Jun 2010
Posts: 1427
Followers: 3

Kudos [?]: 120 [0], given: 826

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

_________________

visit my facebook to help me.

Manager
Joined: 24 Sep 2012
Posts: 90
Location: United States
GMAT 1: 730 Q50 V39
GPA: 3.2
WE: Education (Education)
Followers: 5

Kudos [?]: 135 [0], given: 3

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

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

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

Intern
Joined: 09 Oct 2012
Posts: 13
Followers: 0

Kudos [?]: 2 [1] , given: 14

Re: QR: 30 Decimal Properties [#permalink]

### Show Tags

16 Sep 2013, 06:24
1
KUDOS
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.

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: 37151
Followers: 7275

Kudos [?]: 96822 [0], given: 10800

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.

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.
_________________
Intern
Joined: 23 Aug 2014
Posts: 42
GMAT Date: 11-29-2014
Followers: 0

Kudos [?]: 9 [0], given: 28

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: 37151
Followers: 7275

Kudos [?]: 96822 [1] , given: 10800

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

### Show Tags

10 Nov 2014, 01:14
1
KUDOS
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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13994
Followers: 592

Kudos [?]: 168 [0], given: 0

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

### Show Tags

15 Nov 2015, 03:11
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.
_________________
BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 1928
Followers: 59

Kudos [?]: 429 [0], given: 478

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
_________________

Give me a hell yeah ...!!!!!

Re: If x = 0.rstu, where r, s, t and u each represent a nonzero   [#permalink] 18 Nov 2016, 21:25
Similar topics Replies Last post
Similar
Topics:
7 If x = 0.rstu, where r, s, t, and u each represent a nonzero 6 09 Jan 2014, 05:56
2 If y = O.abcd, where a, b, c, and d each represent a nonzero 3 01 May 2013, 11:06
17 If y = 0.jkmn, where j, k, m, and n each represent a nonzero 7 01 Apr 2012, 11:33
17 If x = 0.abcd, where a, b, c, and d each represent a nonzero 5 11 Feb 2012, 18:10
If x=0.rstu, where r,s,t and u each represent a nonzero 1 01 Jun 2011, 00:32
Display posts from previous: Sort by