GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Jul 2018, 14:33

### 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

# If X is a repeating decimal = 0.TBCDBCD, where T, B, C, and

Author Message
Founder
Joined: 04 Dec 2002
Posts: 17060
Location: United States (WA)
GMAT 1: 750 Q49 V42
If X is a repeating decimal = 0.TBCDBCD, where T, B, C, and [#permalink]

### Show Tags

Updated on: 09 Nov 2011, 16:38
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 1 sessions

### HideShow timer Statistics

One of the GMAT Club's best came up with this question for fun. Originally it was at about 800 level but I think this version is close to 750 - would be curious to hear what you think. (I personally had not idea how to tackle it)

If X is a repeating decimal = 0.TBCDBCD, where T, B, C, and D are different integers, what is the value of T?

(1) X = 9115/N where N is a whole number
(2) T has 3 distinct factors: W, Y and T and the sum of W, Y and T is 10W+Y.

Solution:

(1) X = 0.TBCDBCD
10x = T. BCDBCD ………………………….1
1000(10x) = TBCD. BCDBCD………………2
Deduct 1 from 2:
9990x = TBCD – T
x = (TBCD – T)/9990
x = 9115/9990
x = 1823/1998
x = 0.9124124124
Sufficient

(2) T should be 9, only odd with 3 distinct factors: 1, 3 and 9. Sum = 1+3+9 = 13 = 10(1)+3.
Sufficient

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

Founder of GMAT Club

Just starting out with GMAT? Start here... or use our Daily Study Plan

Co-author of the GMAT Club tests

Originally posted by bb on 02 Jun 2009, 23:11.
Last edited by wizardsasha on 09 Nov 2011, 16:38, edited 2 times in total.
Senior Manager
Joined: 15 Jan 2008
Posts: 263
Re: Challenge: Can you crack THIS? [#permalink]

### Show Tags

03 Jun 2009, 00:01
1
Is it b,

1, insufficient.. I have no clue how to proceed with this..
2, sufficient..

the only single digit numbers with 3 distinct factors are 4 ( 4,2,1) and 9 ( 9,3,1)..

and 4 doesnt satisfy the other condition but 9 satisfies..

9+1+3 = 10*1 + 3
13 = 13.

Hence T = 9.

The answer must be B or D..
but still dont have how to proceed withe the option 1.
Founder
Joined: 04 Dec 2002
Posts: 17060
Location: United States (WA)
GMAT 1: 750 Q49 V42
Re: Challenge: Can you crack THIS? [#permalink]

### Show Tags

03 Jun 2009, 10:17
You are on the right Track. The OA is D.
_________________

Founder of GMAT Club

Just starting out with GMAT? Start here... or use our Daily Study Plan

Co-author of the GMAT Club tests

Senior Manager
Joined: 16 Jan 2009
Posts: 339
Concentration: Technology, Marketing
GMAT 1: 700 Q50 V34
GPA: 3
WE: Sales (Telecommunications)
Re: Challenge: Can you crack THIS? [#permalink]

### Show Tags

03 Jun 2009, 16:02
Statement 2 :

T has 3 distinct factors.
T can be 4 ( 4,2,1) OR 9 ( 9,3,1).
W+Y+T=10W+Y for 9

SUFFICIENT.

For N=5 , T=0 and B,C,D are not different.
9115/N=0.4
Statement 1 NOT SUFFICIENT.

IMO B.

I also tried to use the value of T we got from (1) ; however it becomes complex.
We have to use 2 values of X (0.913 and 0.931) in order to check the value of N.

Could you please explain how this one is D?
_________________

Lahoosaher

Manager
Joined: 14 May 2009
Posts: 188
Re: Challenge: Can you crack THIS? [#permalink]

### Show Tags

03 Jun 2009, 17:27
I got B/D right away, and I would have gone with D.

(1) is too difficult to do with a calculator and far too time consuming, but I'd like to see the solution.
_________________

Intern
Joined: 17 May 2009
Posts: 10
Location: USA
Schools: Kellogs, Wharton, Chicago
Re: Challenge: Can you crack THIS? [#permalink]

### Show Tags

03 Jun 2009, 19:36
for 1.

X = 9115/N

when we divide any integer with the same digit number with all 9s we are sure to get a recurring decimal
ex 1/9 = 0.11111111
10/99 = 0.101010101010....
100/999 = 0.100100100..
1000/9999 = 0.100010001000....

therefore for 9115/N to be recurring and also < 1, N =9999 and in that case X = 0.911591159115...... and in that case T =9, only problem this is of the form 0.TBCDTBCDTBCD and not 0.TBCDBCD and also B and C are not different since both = 1.....I give up here....somebody show the light please......
Founder
Joined: 04 Dec 2002
Posts: 17060
Location: United States (WA)
GMAT 1: 750 Q49 V42
Re: Challenge: Can you crack THIS? [#permalink]

### Show Tags

03 Jun 2009, 21:19
Solution:

(1) X = 0.TBCDBCD
10x = T. BCDBCD ………………………….1
1000(10x) = TBCD. BCDBCD………………2
Deduct 1 from 2:
9990x = TBCD – T
x = (TBCD – T)/9990
x = 9115/9990
x = 1823/1998
x = 0.9124124124
Sufficient

(2) T should be 9, only odd with 3 distinct factors: 1, 3 and 9. Sum = 1+3+9 = 13 = 10(1)+3.
Sufficient
_________________

Founder of GMAT Club

Just starting out with GMAT? Start here... or use our Daily Study Plan

Co-author of the GMAT Club tests

Senior Manager
Joined: 15 Jan 2008
Posts: 263
Re: Challenge: Can you crack THIS? [#permalink]

### Show Tags

03 Jun 2009, 22:43
1. x = (TBCD – T)/9990

2. x = 9115/9990

How can we deduce the second statement from 1st statement..
whats is the approach..
Founder
Joined: 04 Dec 2002
Posts: 17060
Location: United States (WA)
GMAT 1: 750 Q49 V42
Re: Challenge: Can you crack THIS? [#permalink]

### Show Tags

03 Jun 2009, 23:04
Neochronic wrote:
1. x = (TBCD – T)/9990

2. x = 9115/9990

How can we deduce the second statement from 1st statement..
whats is the approach..

I think the idea is that in Statement (1) that X = 9115/N where N is a whole number, but I am not sure that it works that way now that you are asking. Let me check.
_________________

Founder of GMAT Club

Just starting out with GMAT? Start here... or use our Daily Study Plan

Co-author of the GMAT Club tests

SVP
Joined: 29 Aug 2007
Posts: 2425
Re: Challenge: Can you crack THIS? [#permalink]

### Show Tags

04 Jun 2009, 07:36
bb wrote:
One of the GMAT Club's best came up with this question for fun. Originally it was at about 800 level but I think this version is close to 750 - would be curious to hear what you think. (I personally had not idea how to tackle it)

If X is a repeating decimal = 0.TBCDBCD, where T, B, C, and D are different integers, what is the value of T?

(1) X = 9115/N where N is a whole number
(2) T has 3 distinct factors: W, Y and T and the sum of W, Y and T is 10W+Y.

Solution:

(1) X = 0.TBCDBCD
10x = T. BCDBCD ………………………….1
1000(10x) = TBCD. BCDBCD………………2
Deduct 1 from 2:
9990x = TBCD – T
x = (TBCD – T)/9990
x = 9115/9990
x = 1823/1998
x = 0.9124124124
Sufficient

(2) T should be 9, only odd with 3 distinct factors: 1, 3 and 9. Sum = 1+3+9 = 13 = 10(1)+3.
Sufficient

bb wrote:
Neochronic wrote:
1. x = (TBCD – T)/9990

2. x = 9115/9990

How can we deduce the second statement from 1st statement..
whats is the approach..

I think the idea is that in Statement (1) that X = 9115/N where N is a whole number, but I am not sure that it works that way now that you are asking. Let me check.

IMO, 2 cannot be deduced from 1 above if x = 9115/N is not given.

Since X = 9115/N is given, x should be = 9115/9990.
"9115 is/should be (TBCD -T) as given in statement 1 and N has to be 9990 if "TBCD -T = 9115".

Can you elaborate your problem that why 2 cannot be deduced from 1 if x = 9115/N is given in detail?
_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Manager
Joined: 14 May 2009
Posts: 188
Re: Challenge: Can you crack THIS? [#permalink]

### Show Tags

04 Jun 2009, 21:30
TBCD - T............. I agree with neochronic, that doesn't make any sense
_________________

Intern
Joined: 28 Mar 2009
Posts: 23
Re: Challenge: Can you crack THIS? [#permalink]

### Show Tags

06 Jun 2009, 16:52
Good question, I got D quite quickly.

For statement 1 use the standard method to convert a recurring decimal to a fraction:

x = 0.TBCDBCD

Using x form two different numbers whose difference will eliminate the recurring digits:
10000x = TBCD.TBCD...
10x = T.BCD...

Take the second equation from the first:

9990x = TBCD - T

x = (TBCD - T)/9990

So TBCD - T = 9115 - The only possibility is T=9.

Statement 2 points to answer very quickly - only 2 single digit numbers have 3 distinct factors, 4 and 9. Easy to eliminate 4.
Intern
Joined: 28 Mar 2009
Posts: 23
Re: Challenge: Can you crack THIS? [#permalink]

### Show Tags

06 Jun 2009, 17:01
Neochronic wrote:
1. x = (TBCD – T)/9990

2. x = 9115/9990

How can we deduce the second statement from 1st statement..
whats is the approach..

10000x - 10x = 9990x. With a recurring decimal in the form of 0.TBCDBCD... only the numerator with 9990 as the denominator will consist of the recurring digits (that's not totally correct, there are other possible denominators, but they are irrelevant to a four digit numerator). Statement 1 gives x = 9115/N
Therefore, TBCD - T = 9115 is the only possibility.
Manager
Joined: 14 May 2009
Posts: 188
Re: Challenge: Can you crack THIS? [#permalink]

### Show Tags

06 Jun 2009, 17:12
Quote:
10000x = TBCD.TBCD...
10x = T.BCD...

Take the second equation from the first:

9990x = TBCD - T

Still doesn't make any sense. You're making a pretty big jump in logic. If you were to literally subtract T.BCD from TBCD.TBCD...
we'd get

TBC(D-T).(T-B)(B-C)(C-D).........ignoring any carrying etc........................ how that converts to TBCD - T is beyond me
_________________

Intern
Joined: 28 Mar 2009
Posts: 23
Re: Challenge: Can you crack THIS? [#permalink]

### Show Tags

06 Jun 2009, 17:16
Quote:
10000x = TBCD.TBCD...
10x = T.BCD...

Take the second equation from the first:

9990x = TBCD - T

Still doesn't make any sense. You're making a pretty big jump in logic. If you were to literally subtract T.BCD from TBCD.TBCD...
we'd get

TBC(D-T).(T-B)(B-C)(C-D).........ignoring any carrying etc........................ how that converts to TBCD - T is beyond me

It's TBCD.BCD not TBCD.TBCD. So using your method that'll give us:

TBCD - T. (T-T)(B-B)(C-C) giving us TBCD - T
Manager
Joined: 14 May 2009
Posts: 188
Re: Challenge: Can you crack THIS? [#permalink]

### Show Tags

06 Jun 2009, 17:24
I disagree with the logic there... I guess it works

TBCD - T isn't proper mathematics
_________________

SVP
Joined: 29 Aug 2007
Posts: 2425
Re: Challenge: Can you crack THIS? [#permalink]

### Show Tags

06 Jun 2009, 23:53
bb wrote:
If X is a repeating decimal = 0.TBCDBCD, where T, B, C, and D are different integers, what is the value of T?

(1) X = 9115/N where N is a whole number
(2) T has 3 distinct factors: W, Y and T and the sum of W, Y and T is 10W+Y

From 1: X = 0.TBCDBCD
multiply both side by 10 (because ine digit from the decimal is not repeating.
10x = T. BCDBCD ………………………….1
Multiply 10 by 1000 (because 3 digits right to the decimal are repeating)
1000(10x) = TBCD. BCDBCD………………2
Deduct 1 from 2:
9990x = TBCD – T
x = (TBCD – T)/9990
Since the neumarator of x is given, (TBCD-T) should be = 9115. With the given information (i.e 0.TBCD in which T is not a repeating but B, C, and D are), the neuramator of x can not be > 9115. So..

x = 9115/9990
x = 1823/1998
x = 0.9124124124
Sufficient

(2) No dispute.

Sufficient:- D.
_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

SVP
Joined: 29 Aug 2007
Posts: 2425
Re: Challenge: Can you crack THIS? [#permalink]

### Show Tags

06 Jun 2009, 23:57
mujimania wrote:
Good question, I got D quite quickly.

For statement 1 use the standard method to convert a recurring decimal to a fraction:

x = 0.TBCDBCD

Using x form two different numbers whose difference will eliminate the recurring digits:
10000x = TBCD.BCD...
10x = T.BCD...

Take the second equation from the first:

9990x = TBCD - T

x = (TBCD - T)/9990

So TBCD - T = 9115 - The only possibility is T=9.

Statement 2 points to answer very quickly - only 2 single digit numbers have 3 distinct factors, 4 and 9. Easy to eliminate 4.

Thats much clearer.
Good job.
_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Manager
Joined: 14 May 2009
Posts: 188
Re: Challenge: Can you crack THIS? [#permalink]

### Show Tags

07 Jun 2009, 01:24
Can anyone show a proper Mathematical proof as to why (1) is sufficient?

TBCD - T is not based in any solid Mathematical framework... You can interpret TCBD as literally T*C*B*D or 10^3*T+10^2*C+10^1*B+10^0*D - 10^0*D...

But I still have no idea in hell how it magically morphs to 9115/X....... Sorry but nobody has provided any concrete Mathematics behind it.
_________________

Manager
Joined: 14 May 2009
Posts: 188
Re: Challenge: Can you crack THIS? [#permalink]

### Show Tags

07 Jun 2009, 01:26
And also, what if there is another value s.t. X=9115/N is equal to .TBCDBCD..... such that T != 9?

You haven't shown that either, you're assuming there is only one answer.

[deleted an attitude comment]
_________________

Re: Challenge: Can you crack THIS?   [#permalink] 07 Jun 2009, 01:26

Go to page    1   2    Next  [ 22 posts ]

Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.