It is currently 23 Sep 2017, 15:03

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A bar over a sequence of digits in a decimal indicates that

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1414

Kudos [?]: 762 [0], given: 5

Re: A bar over a sequence of digits in a decimal indicates that [#permalink]

Show Tags

New post 04 May 2016, 09:21
fatihaysu wrote:
A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of (10^4 -10^2)(0.0012)?

(A) 0
(B) 0.12
(C) 1.2
(D) 10
(E) 12



Remember that the notation [12] means there is a bar over the 12, indicating that the decimal is nonterminating.

Now, let’s start the problem by factoring out 10^2 from (10^4 – 10^2). This gives us:

(10^4 – 10^2) (0.00[12])

10^2 (10^2 – 1)(0.00[12])

We can distribute 0.00[12] with the two quantities in the parentheses. This gives us:

10^2(0.[12] - 0.00[12])

100(0.[12] - 0.00[12])

12.[12] – 0.[12] = 12

Alternate solution:

The number .00[12] is the number .00121212… if we write it without the bar notation. By the distributive property, we have

(10^4 – 10^2) (.00[12]) = 10^4(.00[12]) – 10^2(.00[12]

Without the bar notation, we write this as 10^4(.00121212…) – 10^2(.00121212…)

Multiplying a number by 10^4 indicates that we move the decimal point four places to the right, giving us:

10^4(.00121212…) = 12.1212…

Similarly, multiplying a number by 10^2 indicates that we move the decimal point two places to the right, giving us:

10^2(.00121212…) = 0.1212…

Now, if we subtract the two quantities, we have

10^4(.00121212…) – 10^2(.00121212…) = 12.1212… - 0.1212… = 12 (because the .1212… gets canceled out by the subtraction).

Answer is E.
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 762 [0], given: 5

Intern
Intern
avatar
Joined: 22 Sep 2015
Posts: 6

Kudos [?]: 1 [0], given: 49

Re: A bar over a sequence of digits in a decimal indicates that [#permalink]

Show Tags

New post 10 Nov 2016, 08:08
10^4 = 10*10*10*10 = 10,000
10^2 = 10*10 = 100

Therefore 10^4−10^2 = 10,000 − 100 = 9900

Now, I just multiplied 9900*12 = 118,800
Finally add back the 4 decimal places of the 0.0012 = 11.8800 which is more or less 12, Hence E.

Kudos [?]: 1 [0], given: 49

Director
Director
avatar
G
Joined: 02 Sep 2016
Posts: 767

Kudos [?]: 33 [0], given: 259

Premium Member CAT Tests
Re: A bar over a sequence of digits in a decimal indicates that [#permalink]

Show Tags

New post 01 Apr 2017, 06:22
(10^4-10^2)(0.00(12)) [ (12) is the repeating number]
=10^2(10^2-1)(0.00(12))
=10^2(99)(0.00(12))

Let's just handle 0.00(12)
Converting it to a fraction
Let x= 0.00(12)
100x=0.(12) .........eq.1 (100 because we have to move the non-repeating part i.e.00 to the left of the decimal point. So two non- repeating digits, 100. If one digit, then 10 and so on.)

10000x= 12.(12) ..........eq.2 (Same logic as above. We already had 100 as we moved 00 to the left of the decimal point. Now we have to move 12 also to the left of the decimal point.)


Now eq.2 -eq. 1

9900x=12
x=12/9900 (Don't solve)

Now putting it back in the original equation given in the question

We get: 10^2*99*12/9900
=12
_________________

Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.

Kudos [?]: 33 [0], given: 259

1 KUDOS received
Director
Director
User avatar
P
Joined: 04 Dec 2015
Posts: 696

Kudos [?]: 274 [1], given: 261

Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
GMAT ToolKit User
A bar over a sequence of digits in a decimal indicates that [#permalink]

Show Tags

New post 14 Jun 2017, 00:26
1
This post received
KUDOS
1
This post was
BOOKMARKED
fatihaysu wrote:
A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of (10^4 -10^2)(0.0012)?

(A) 0
(B) 0.12
(C) 1.2
(D) 10
(E) 12


Note : Rule to convert mixed recurring decimal to fraction : In the numerator write the entire given number formed by the (recurring and non - recurring parts) and subtract from it the part of the decimal that is not recurring. In the denominator, write as many nines as the number of digits recurring and then place next to it as many zeros as there are digits without recurring in the given decimal.

Converting the mixed recurring decimal (0.0012) to fraction we get;
\(\frac{(12 - 00)}{9900} = \frac{12}{9900} = \frac{4}{3300}\)

(\(10^4\) -\(10^2\))(0.0012) can be written as = \((10^4 -10^2)* \frac{4}{3300}\)
\(10^2(10^2 - 1)* \frac{4}{3300}\)= \(100 * (100 - 1)* \frac{4}{3300}\)
\(99 * \frac{4}{33}\) \(= 3 * 4 = 12\). Answer E...

_________________
PS: Consider giving Kudos if my post helped you in some way :)

Kudos [?]: 274 [1], given: 261

Manager
Manager
User avatar
B
Joined: 06 Sep 2016
Posts: 63

Kudos [?]: 14 [0], given: 56

Location: Italy
GPA: 3.2
WE: General Management (Human Resources)
Premium Member
Re: A bar over a sequence of digits in a decimal indicates that [#permalink]

Show Tags

New post 20 Jun 2017, 07:13
I did this in an unconventional way:

10^4 - 10^2 = 9900 ---> 99 x 100

99 x 100 x 0,0012 ---> 99 x 0,12 = 11,88 thus the answer is E

Kudos [?]: 14 [0], given: 56

Top Contributor
SVP
SVP
User avatar
G
Joined: 12 Sep 2015
Posts: 1753

Kudos [?]: 2296 [0], given: 355

Location: Canada
Re: A bar over a sequence of digits in a decimal indicates that [#permalink]

Show Tags

New post 28 Aug 2017, 15:44
Top Contributor
fatihaysu wrote:
A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of (10^4 -10^2)(0.0012)?

(A) 0
(B) 0.12
(C) 1.2
(D) 10
(E) 12



(10⁴ - 10²)(0.00121212...) = 10⁴(0.00121212...) - 10²(0.00121212...)
= 10,000(0.00121212...) - 100(0.00121212...)
= 12.121212... - 0.121212...
= 12 (since the decimal parts, in blue, are identical, they cancel out]

Answer:
[Reveal] Spoiler:
E


RELATED VIDEO FROM OUR COURSE

_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2296 [0], given: 355

Re: A bar over a sequence of digits in a decimal indicates that   [#permalink] 28 Aug 2017, 15:44

Go to page   Previous    1   2   [ 26 posts ] 

    Similar topics Author Replies Last post
Similar
Topics:
38 EXPERTS_POSTS_IN_THIS_TOPIC What is the tenth digit to the right of the decimal point gmatpapa 16 31 Aug 2017, 21:39
13 EXPERTS_POSTS_IN_THIS_TOPIC If the digits 37 in the decimal 0.00037 repeat indefinitely, aimingformba 12 18 Jul 2017, 08:20
M is the length of the sequence of digits that are duplicated in an in dimri10 1 06 Jul 2011, 14:11
7 How many digits will be there to the right of the decimal vinnik 9 16 Aug 2016, 07:58
7 In a decimal, a bar over a digit indicates that the digit repeats inde hazelnut 4 14 Jun 2017, 02:30
Display posts from previous: Sort by

A bar over a sequence of digits in a decimal indicates that

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.