Source: Official Guide for the GMAT 13th Ed. Problem Solving; #150 Official Guide for the GMAT 2015 14th Ed. Problem Solving; #150

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# A bar over a sequence of digits

A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of (10-10)(0.0012)?

### 3 Explanations

2 Cydney Seigerman, Magoosh Tutor

Thank you all for letting us know about the issue with the video explanation. I've sent a note to our content editors so that this can be fixed. However, since we have a very small team with lots to work, it may take a while for a new video explanation to be uploaded. In the meantime, here's a text explanation to accompany Mike's explanation in the video :)

We are asked to find the product of (10^4-10^2)(0.0012), where 0.0012 represents a repeating decimal. First, let's distribute the term (0.0012) across the first term:

(10^4-10^2)(0.0012) = (10^4)(0.0012) - (10^2)(0.0012)

Now, we can evaluate the two exponential terms separately:

1. (10^4)(0.0012)

To find the product, we will move the decimal point of the second term four places to the right: (10^4)(0.0012) = 12.1212...

2. (10^2)(0.0012)

Likewise find the product, we will move the decimal point of the second term to the right but only by 2 places: (10^2)(0.0012) = 0.1212...

From here, let's recombine the terms and subtract 0.1212... from 12.1212...

(10^4)(0.0012) - (10^2)(0.0012) = 12.1212... - 0.1212...

Since the two terms have the same decimal value (0.1212...), when we carry out the subtraction, the decimal cancels out, leaving us with the difference, 12 (answer E).

I hope this helps :)

Nov 29, 2015 • Comment

1 Sam Kinsman, Magoosh Tutor

Hi Jonathan! To watch the video, you'll need to remove the "https://" from the address bar in your browser, and replace it with "http://" (without the "s"). Then refresh the page, and the video should work! :)

Nov 20, 2015 • Comment

Michael Romrell

no, the video is actually broken. Or rather, it zooms off to a corner of the screen where you can't see mike writing.

4 Mike McGarry, Magoosh Tutor

Dec 28, 2013 • Comment

Jonathan Woodward

This video is broken.