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A bar over

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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
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Source: — Problem Solving |

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.
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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.
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