A bar over

This topic has expert replies
Senior | Next Rank: 100 Posts
Posts: 42
Joined: Fri Oct 30, 2015 9:01 am

A bar over

by shahfahad » Thu Nov 26, 2015 2:12 am
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)?

Note: There is a bar over "12" in 0.0012. Couldn't figure out how to insert it.

(A) 0
(B) 0.12 (with the bar on 12)
(C) 1.2
(D) 10
(E) 12

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Thu Nov 26, 2015 3:07 am
shahfahad 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)?

Note: There is a bar over "12" in 0.0012. Couldn't figure out how to insert it.

(A) 0
(B) 0.12 (with the bar on 12)
(C) 1.2
(D) 10
(E) 12
The repeating digits beyond the bar represent values that are EXTREMELY SMALL relative to the other values.
Thus, we can safely ignore the repeating digits beyond the bar.

(10� - 10²)(.0012)

= (10²)(10² - 1)(12/(10�)

≈ (10²)(10²)(12/10�)

= 12.

The correct answer is E.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Fri Nov 27, 2015 12:29 am
Another approach:

If xy is a two digit number (i.e. x = tens digit, y = units digit), then xy/99 = .xyxyxy...

We want this to be moved two places to the right, so we have xy/9900 = .00xyxyxy...

Hence .00121212... is 12/9900.

From there, we have (10� - 10²) * 12/9900, or 9900 * 12/9900, or 12.