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25 Jul 2017, 11:19
Kudos
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
67% (02:04) correct
33%
(03:39)
wrong
based on 3
sessions
History
Date
Time
Result
Not Attempted Yet
For an integer n = 2^16 * 3^13 * 5^5 * 7^5 * 11^3, what is the value of the first non-zero digit from the right?
A) 1
B) 2
C) 4
D) 6
E) 8
A) 1
B) 2
C) 4
D) 6
E) 8
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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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25 Jul 2017, 11:37
Kudos
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Take out the 10s (the 2*5 pairs) and we have:
n = 2^5 * 5^5 * 2^11 * 3^13 * 7^5 * 11^3
n = 10^5 * ( 2^11 * 3^13 * 7^5 * 11^3 )
All the zeros at the end of the number come from the 10^5. The first nonzero digit (from the right) will be the units digit of the number in brackets. So this is now a units digits problem. The units digit of 11^3 is '1', the units digit of 7^5 is 7, the units digit of 3^13 is '3', and the units digit of 2^11 is '8' (anyone unsure how I found those should review units digits and exponents). Multiplying just these units digits, we get
1*7*3*8
which ends in 8.
n = 2^5 * 5^5 * 2^11 * 3^13 * 7^5 * 11^3
n = 10^5 * ( 2^11 * 3^13 * 7^5 * 11^3 )
All the zeros at the end of the number come from the 10^5. The first nonzero digit (from the right) will be the units digit of the number in brackets. So this is now a units digits problem. The units digit of 11^3 is '1', the units digit of 7^5 is 7, the units digit of 3^13 is '3', and the units digit of 2^11 is '8' (anyone unsure how I found those should review units digits and exponents). Multiplying just these units digits, we get
1*7*3*8
which ends in 8.
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 Problem Solving (PS) 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!
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