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14 Jan 2016, 17:00
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The problem:
If k is an integer and \((0.0025)( 0.025)( 0.00025) × 10k\) is an integer, what is the least possible value of k?
The solution (from the Official 2016 Guide to GMAT):
Let \(N = (0.0025)( 0.025)( 0.00025) × 10^k\) ...etc etc
Why \(10*k\) has become \(10^k\) in the solution???
Right to knowledge, this is the full explanation:
Let \(N = (0.0025)( 0.025)( 0.00025) ×10^k\). Rewriting each of the decimals as an integer times a power of 10 gives \(N = (25 × 10 ^{− 4})( 25 × 10^{ − 3})( 25 × 10^{ − 5}) × 10^k = (25^3) × 10^{k − 12}\). Since the units digit of \((25^3)\) is 5, it follows that if k = 11, then the tenths digit of N would be 5, and thus N would not be an integer; and if k = 12, then N would be \((25^ 3) × 10^0 = (25^ 3)\), which is an integer. Therefore, the least value of k such that N is an integer is 12.
If k is an integer and \((0.0025)( 0.025)( 0.00025) × 10k\) is an integer, what is the least possible value of k?
The solution (from the Official 2016 Guide to GMAT):
Let \(N = (0.0025)( 0.025)( 0.00025) × 10^k\) ...etc etc
Why \(10*k\) has become \(10^k\) in the solution???
Right to knowledge, this is the full explanation:
Let \(N = (0.0025)( 0.025)( 0.00025) ×10^k\). Rewriting each of the decimals as an integer times a power of 10 gives \(N = (25 × 10 ^{− 4})( 25 × 10^{ − 3})( 25 × 10^{ − 5}) × 10^k = (25^3) × 10^{k − 12}\). Since the units digit of \((25^3)\) is 5, it follows that if k = 11, then the tenths digit of N would be 5, and thus N would not be an integer; and if k = 12, then N would be \((25^ 3) × 10^0 = (25^ 3)\), which is an integer. Therefore, the least value of k such that N is an integer is 12.
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14 Jan 2016, 20:49
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vignuol
Hi,
shifting your Query to general maths..
if the Q is "If k is an integer and \((0.0025)( 0.025)( 0.00025) × 10^k\) is an integer, what is the least possible value of k?" and that seems is the case from other discussions done on this site, then the answer is ofcourse what is explained as it is..
but say it is 10*k.., then the answer will change..
you will have to recheck it..
14 Jan 2016, 23:05
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vignuol
This question is discussed here: if-k-is-an-integer-and-0-0025-0-025-0-00025-10k-is-an-integer-w-207309.html
Locking the topic.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
