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Infinite decimal loops

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by Patrick_GMATFix » Thu Feb 20, 2014 9:03 am
In general when a DS question gives you an expression you can factor, you should factor it. Conversely when a DS question gives you an expression you can expand (as is the case here), you should expand it. This should make sense; the GMAT will not give you expressions in the form that would make the answer obvious.

The full solution below is taken from the GMATFix App.

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by Abhishek009 » Thu Feb 20, 2014 9:15 am
(10^4 - 10^2 )(0.0012....)

Can be re written as -

(10^2)^2 - (10)^2 { 0.0012.... }

( 10^2 + 10 )( 10^2 - 10 ) { 0.0012.... }

( 110 )( 90 ){ 0.0012.... }

( 110 )( 90 )( 12 / 9900)

Hence answer is 12
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by Brent@GMATPrepNow » Thu Feb 20, 2014 9:23 am
EricKryk wrote:Image
(10� - 10²)(0.00121212...) = 10�(0.00121212...) - 10²(0.00121212...)
= 12.121212... - 0.121212...
= 12 (since the decimal parts, in blue, are identical

Answer: E

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Last edited by Brent@GMATPrepNow on Thu Feb 20, 2014 3:01 pm, edited 1 time in total.
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by Matt@VeritasPrep » Thu Feb 20, 2014 2:37 pm
How about this? Since multiplying by 10� is like moving the number four places to the left, and multiplying by 10² is like moving the number by two places to the left, we really have

(10� - 10²)(.00121212...)

= 12.1212... - .121212...

= 12
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by Brent@GMATPrepNow » Thu Feb 20, 2014 3:01 pm
Image

We can also apply some number sense here.

(10� - 10²)(0.00121212...) = (10,000 - 100)(0.00121212...)
= 9900(0.00121212...)
= (a bit less than 10,000)(0.00121212...)

Well, (10,000)(0.00121212...) = 12.121212
So, (a bit less than 10,000)(0.00121212...) = a bit less than 12.121212...

Check the answer choices:
A) 0
B) 0.121212...
C) 1.2
D) 10
E) 12

E is the best match

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by GMATGuruNY » Thu Feb 20, 2014 5:03 pm
EricKryk wrote:Image
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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