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25 Feb 2020, 02:04
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
47% (02:01) correct
53%
(01:55)
wrong
based on 263
sessions
History
Date
Time
Result
Not Attempted Yet
What is the rightmost non-zero digit in 15!?
A. 2
B. 4
C. 6
D. 8
E. 9
Are You Up For the Challenge: 700 Level Questions
A. 2
B. 4
C. 6
D. 8
E. 9
Are You Up For the Challenge: 700 Level Questions
25 Feb 2020, 02:52
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What is the rightmost non-zero digit in 15!?
—>[ \(\frac{15}{5}\) ] ...= 3 (there are three zeroes at the end of 15!; \(5^3\))
—> \([\frac{15}{2}]+ [\frac{15}{4}]+ [\frac{15}{8}]+...= 7+3+1= 11\) (—> \(2^{11}\) )
—> \([\frac{15}{3}]+ [\frac{15}{9}]+...= 5+1 = 6\)( —> \(3^6\))
—> \([\frac{15}{7}]+...= 2\) (—> \(7^{2}\))
So, \(15! = 2^{11}* 3^{6} *5^{3} *7^{2}*11*13\)
And eliminate the zeroes:
—> \(\frac{15!}{1000}= 2^8*3^6*7^2*11*13 \)
Now, just find the units digits and multiply one another to get the last digit —> ...6*...9...*9...*1...*3 = ...18...* 81 = ...8
The rightmost nonzero digit of 15! is 8
The answer is D.
Posted from my mobile device
—>[ \(\frac{15}{5}\) ] ...= 3 (there are three zeroes at the end of 15!; \(5^3\))
—> \([\frac{15}{2}]+ [\frac{15}{4}]+ [\frac{15}{8}]+...= 7+3+1= 11\) (—> \(2^{11}\) )
—> \([\frac{15}{3}]+ [\frac{15}{9}]+...= 5+1 = 6\)( —> \(3^6\))
—> \([\frac{15}{7}]+...= 2\) (—> \(7^{2}\))
So, \(15! = 2^{11}* 3^{6} *5^{3} *7^{2}*11*13\)
And eliminate the zeroes:
—> \(\frac{15!}{1000}= 2^8*3^6*7^2*11*13 \)
Now, just find the units digits and multiply one another to get the last digit —> ...6*...9...*9...*1...*3 = ...18...* 81 = ...8
The rightmost nonzero digit of 15! is 8
The answer is D.
Posted from my mobile device
General Discussion
25 Feb 2020, 07:44
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Bunuel
15/5 = 3 => A
Remainder is 0 =>B
So, Last Non zero digit will be \(2^A*A!*B!\)
= \(2^3*3!*0!\)
= 8* 6* 1
=>8 , Hence Answer must be (D) 8
