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A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of

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by Gmat_mission » Wed Sep 29, 2021 8:34 am

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A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of \((10^4-10^2)(0.00\bar{12})?\)

(A) \(0\)
(B) \(0.\bar{12}\)
(C) \(1.2\)
(D) \(10\)
(E) \(12\)

Answer: E

Source: Official Guide
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Re: A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of

by Brent@GMATPrepNow » Thu Sep 30, 2021 6:33 am
Gmat_mission wrote: ↑
Wed Sep 29, 2021 8:34 am
 A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of \((10^4-10^2)(0.00\bar{12})?\)

(A) \(0\)
(B) \(0.\bar{12}\)
(C) \(1.2\)
(D) \(10\)
(E) \(12\)

Answer: E

Source: Official Guide
(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: E
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