Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 1507:00 PM EDT
-09:00 PM EST
Elite scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Tues/Thurs Sept. 15, 2026 - Nov. 15, 2027, 7:00pm-9:00pm EST
Sep 2107:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included! Class starts Mon, Tues, Wed, Thur, Fri Sept. 21, 2026 - Oct. 9, 2027, 7:00pm-10:00pm EST
14 Jan 2016, 17:00
Kudos
Bookmarks
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.
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 below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
14 Jan 2016, 20:49
Kudos
Bookmarks
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
Kudos
Bookmarks
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!
